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# Work: https://leibnizlegible.com/work/170380998X
# Title: The Description and Use Of Two Arithmetick Instruments. Together With a Short Treatise, explaining and Demonstrating the Ordinary Operations of Arithmetick. As likewise, A Perpetual Almanack, And serveral Useful Tables. ... (shelfmark Ob-A 236)
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1e11
il
l
atUr: O

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A Hd∞

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NLB HannOVOrIZB 35
03c150000

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lIlII
noscner
Tur: OD- A 23C

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AMIII

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ite
1
1t1tt1
O
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lll s

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pocen aa ae no
IBI STHEC
5
6.+1sP RRR
noromanam
a

## Folio  -  — 170380998X:0010
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e
mm a) ne
SAAVEL DR d
Auralus & Baronel
CAMIERFPEATE
dd
LADUS EqeS
sopus nec non
O GenerOtus
touina
OD- A 23

## Folio  -  — 170380998X:0011
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ne Delerirtion and
OF
TNVO ARITTIMETICR
INSTRLIMEMV
TOOF THF R
Witha Shore Treatise explainir
and Demonstracing the Ordinari
Operations ot ARTZTTMETTC
as litremise,
A PerpetuaLA L M AZ AC
And serecal Usetul T ABL. F S
Presenred to His Nost FxceMlenEMX
CAARLESI
Rins ot Oreac Bricain, France, and Treland
By S. MORL AXD
L.ONDON,
Prinred, and are ro be Soldby Moses
ae che White. Barr in Lirle- Britain, 1673.

## Folio  -  — 170380998X:0012
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a
e

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ANeWV, and mostusetul
LASTRUMEHTT
FOR
ADDITION
A N D
STIBSTRACTIOH
OF
Ponnds, Shillines, Pence
and Farthinesi
Nichoue chargins cheMemory, disturb.
insche Mind, or expolins theopera-
cor coany uncerrainer; Whichno Me.
chod hicherro. publisted, can justly pre-
tend 10.
Invenced and Presemed ro His most FX-
celenEMajeCy CH ARLES ILI. Ring
OEGreat Britain, France, and lreland, EC.
1666.
By S. NIORE AND.
And byche imporcuniey of his very g00d
Eriends, made publick 16721

## Folio  -  — 170380998X:0014
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t
e
H
O
M

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et

## Folio 1r — 170380998X:0016
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Sec or Dispote
THIF
N S Y R H M F N Y
FOR
DP E R A Y EON:
erbich Instrumene mast beheld in the Lefe
hand, and the Index or blen Pin in the
Richt band, es men usuaty hold a Pen, bUE
somethine more uprieht ot perpendicular.
XM  CB) N chole sire uxper Plares, Cin everv
ge
oF irhich chere are 10 (maII holes D
F any oF che Digits (suppose 3) ap-
pear in any ot che Wrindors, puc che
Poine ofchie Index inco che hole ovex
againa chac Fioure in che Margent,
ots itich is che Complemene 10 10
(namely 7.) And chen curn ic under che windon, where
(0) will appear. Thisdone, pur che poine oF the in-
dex inco che (0) ot che sinali Place abore ic; and
chen, it vou vould prepare che Instrument For Addirion,
turn about chat (naIs Plare, eill 0 Rand just under thac
Line or mark in che upper Plare whichis on che RighE-
trand, chus 3 25 in Fis. A. Buc iF For Substraction
chen curno on under the Let-hand line or mark, thus
63 25 in +18. D
oF Shillings, Pence, and Farthines cobe dispoled; Re-
membrino onely chac in che place ot Shillines, evhere
(20) Iochenander, ene omeencio(5315 (1))
And in Pence, the Complemenero (3) is (9) And
in Farrhines, che Complement 10 (3) is (7) And
chus
Alcerche very Tame manner are all che lorver plates
e

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se

## Folio 2r — 170380998X:0018
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chus are als che Plares sicred for Operarion 25 in
FiB
mene is lec: lt any ot che elares mich HlolesRiek, and
vill noc curn aboue Formards, ic is because noither (0)
nor any Fisure oEche (mall elare abore it is under che
Righc-hand. lino or marke. And it chey will nOE cvEN
backmards, ic is because neither (, nor any Figure ot
the Cmall elace abore ic is under the Letr-hand- line Ox
mark, andlastiy, it cheimall Place above vill noc
more, ic is because no Iole in che lorver elare is di-
rectlus under chewindom.
The Operation os cuc
Dec thesumsro be added rogether, be cheleo
This is likemile eo be observed betore the Instru-
FixsLTet OnY I. Chacis, I pue che poine ot che index
inco chehole oEche place os Vnites ot Pounds, wrhich
is overagainst (7) in cheMargene, and rurn ic under
thewindom. Atcer chac, Pcurn on (14) in theplace
aE Shillines; (3) incheplace ot Pences and. C1) in
che plaee ot Farthines.
Againu as eoche 2 Summe, I Pet on (48) chus,
namelr, (4) inche place otTens, and (8) in che
place ot vniies: Aslikerise er inche place of Shillines.
(10) incheplace oF Pences and (1) in che place
OE Farrbines. And having sec on aII che summes inche
nanner and mechod atoresaid, ther will appear on che
Instrumene as in Fic. B.
In Ane, copertect the Operation, I beoin wich che
place oE Faribines, and because ehe Fisure (L) oE che
DIaTES

## Folio 2v — 170380998X:0019
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## Folio 3r — 170380998X:0020
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Plates ovex head Rands DerWVCen ThC EIVO Lines Ox MaTKS,
cherCFOre Y turn On (X) in the place OF Fence. And
Decause (2) is betmeen checvo Lines in the place ot
Pence, T eurn On (2) in che place ot Sbillines: ANS
Decause (2) is becween checivo Lines in the place ot
Shillines, Peurnon (2) in che place ot vaites ob
Pounds. Thus, For (2) Becreen checuo L. ines in the
place oF Vnires oF Pounds, Peurn on 2 inche place ot
Pens. And For CY) in the place oF Tens, L EUEn On
(1) in che place oF Hundreds. Wrhich done, checrue
Summe or Agoregac oF allche summes, appears in elie
Sereral rindows, viz. 4646 l. - 225. - 3d..
35
as in Fig. C. Thelame ching may bepertormed by 2d-
ding cogecher, First che Barthines apare, chenche Pence,
nexe che Shillines, and lastly che Pounds.
TF peradrencure che summes arc (onumerous, asthat
by otten curning oF che Places vich holes, che (naII
Places abore chem arc like co be over-charged, Thac
IS, IE che Figure (7) (8) or (9) ot chole Cinall
Places come betveen the 2 Lines or Miarks, then I dis-
charse chem, bycurnius on che lame numbers in che
pexcplaces: For example, it che Figure (7) oF che
Imali Plate abore che place ot Farthines, De undex the
Cine, Peurn on (3) incheplace oF lence. IF thCFi
sure (7) oF che Imall Place aborerhe Pence Be Becween
hervo Lines I turn on (7) in cheplace ot sbil’ings,
and (o eo che. end. And lasIV, L eurn O oF cacti
Imall Place under ies proper Line, and hen procced
(Wichour Pertins che lorver PlateS 1O (O) or ac aII
alcerins chem ocherwise rhan aforesaid) eo sec on che
remaine sums lo a Million oF Pounds. (Or ific be
detreu, che lutcruene mas be made For a Farpreater
Summe.) Bec ene turest vay, isto divide a lono Parc
neolto or chreesatio, and so eo work chem distinct

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F.
d
(
C
osees)
8
s
FE

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Theoperation of Sublraction
Having prepared che Instrument For Substraction asis
betore directed, suppole LWould Erom 327 l. - 125, -07 do
dedua 39 l. - 145, - 3 d.
First, I (et on 327l. - 12 5.7 d. in cheir proper places
Then L begin wich 3 d. ot che summe eo be deducted,
and set ic backeward, Thacis, I puc che poine of etie
Index inco che hole under che wr indon ot Pence, and eurn
et tillsECand over azainst (3) inhe Margene, ertict
Wil leare (A) inchacwindom. ThusI sec 14 5. back-
ards in cheplace ot Shillings; Andchus (39) inche
2nites and Tens oE Pounds. And havine (0 done, Fob-
serre it any (0) oF che linall Places orer head be remon
ved From under ies Line (as in Fir. D. in the place ot
Sbillines, I And the (mali Place over head mored) I pue
che poine ofche index intochac hole of che next place,
chac is under thewindom, and curn ic backevards under
(1) in che maroene. Atcerthe lamemanner, because
the (nal Plate over the place ot Vnites of poundsisre-
mored one of ies place, I set back For ic (X) in che
Place ofTens; And (o likerise, Decau se che (malI Plare
overthe place of Tens is removed, I ser back (1) in
the place oF Hundreds. Which done, che remainina
Summe, viz. 2871. - 18 5. -04 d. is found in chere-
spectire rindoms. As in FIG. E

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lae

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Phe Delcriprion and TCe oF an
Addicionat rrheet. applicable t0
chis Nem INST RD MIF N Y
For aII chose niho Mal desire ic, whict
renders ic uletul, bepond exception, For the
longest Accompes, withour eicher diridins
chePage, or Terrins O oF anx of the (maiI
Places under cheir Lines a secondrime.
VI forasmuch as et may and will often happen, in ibc
addins ap lons Pases of Accompe- B0OKS, That thC
Tinalt Plares vill beover-charged C and that more than once
In a PaGC) Which maybe somethine troublesome 20 the Ope=
rACOE; Therefore Thave cnirived an Addirionat Wheel, a5
In FIB. P. S0 That NO OnC Or EVO PareS of any ACCOmPE
B00K whacsoener can overcharee it: all ihe difference is on
y ihis, That wbat Fisure soever of ibis Wheel is found op-
Posire rothe Line Cor marz) aboreit, it must be set on
Cnor in thenext place but) in the next place (ave one, In
ihe manner follovine: That i5 10 Say, The Fieure of thc
(mail Wheel above the Farchines, opposireto ihe Line above
AE, must be turned off in ibe place of Stillings. The Figure
of the smali Wheel above the Pence, opposire 20 ihe Linc
abore ic, must be turned off in the place of Unices
of Pounds. And is any Fieure of ihe Smait Whect
debalf a division berond ihe said Line, there must be 10
rurned off for it in ihe place of Strillinos, (which is the preat-
est intrigue in the whole Operation, Fir,) The Figure ofthe
Smali Wheel above the place of Thillinos opposire ro ihe Line.
must be rurned off in the place of Tens of Pounds. ThCFi-
Sure of the sinall WV heel opposire torhe Line, in the place of
Unices of Pounds, must be turned off in the place of Trun-
dreds. Tastly, the Fisure of ihe Pmait Wtiect opposite 10
ihe Line, above the place of Tens of Pounds, must becurn-
es off in cheplace of Thoulands. and (0 +o ihe end, a5 in
Fis. C. S0 ibat by she addirion of ehis (malt Wticet, a
PlacC

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C

## Folio 6r — 170380998X:0026
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6)
place more is gained, and ihe Instrumene, is need mere–
ould add upan Accom enonos eous, ds
acoareati Lie. il more evidenilus appear
1.
F X AMPL F.
5. d. 4
36534-73-03. 3
76534- 20. 11-2
85637. T4-05-2
93792- 57- 40-2
14379-09 -08. 3
85466-79-10.2
72954-10-04-2
6TIY7- 26-08-3
52252 -26-06. 3
65579-x5. 05. 3
42573-75-02.3
92876-19. 09-2
69955. 17 - 2X - 2
y2yy - 13-09-Y
85855-04-70-3
98888-74- 06-2
37744- 26. 07-2
45757-22- 04- 3
93879 -16. TT-3
64549 -29-08 -2
97872- 24-06-T
85678 -10 -20-2
96644-08-06. 3
ol3- 16-03. 2
I. 5o d. 9.
45772-15-05-3
56572-27-20-2
67699-24-T1- 2
77578-78-08-2
89979- 19- 10-3
97979-Oc-06. 3
95878-08-71-2
36788-10-09 - F
99678 -13-10. 2
89485. 77-06. 2
47632 -16-03 -F
57416-25. 09.3
62517-24. 07- 2
74528-13 -1T-2
43215 -12-05 -2
67742 -1T-08-3
35418-09-04 -1
9226F-O1-09-3
44415- 12-06. 3
43324-24. 03-F
7338-02 -12- 2
345T2- 79- 04 - 2
567552502
2283761-1F-06 -7

## Folio 6v — 170380998X:0027
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0
 _ n ∞
O
C
fia
sd
neo
c
1C
O
+
n edrc 2
90
+s)
1 E) ∞

## Folio  -  — 170380998X:0028
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Machina Nova
GYCLOLOGICA
Pro Mulriplicatione.
OR,
a nem Mulciplvino.
TISTRUMETTI:
nvented, and humblu present
ed +0 the Kinos motex
)
CCIEnEMAJESTY
ARLE STI.
S. MIOR L A N D, 1666.
v
le Labrick otchis In rumenebe-
ing cruly represenced in Perspect
ive, chere wii benoncedot any
laroe Delcriprion ofit.
The s upper Circles wherenn
are che Fixures 55732 re-
presene s moveable Plares wvticta
lie alivays ready co becaken oA
nes Semi-circular Dinions (O2
Cellst 632, b,t. a, alla lobe lec on any ot, or all
che Cencers (or Semicircular Pinions) a, e, m, n, 0, P,
incerchanseably. And underneach ench ot chole uxpex
etaces

## Folio  -  — 170380998X:0029
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B X m ∞
o
8
fi
+
L
O
D

## Folio 9r — 170380998X:0030
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The Multiplrinq Inctrument.
Plares aforelaid, are placed sorher Places oF che same
dimentions, and rich che Pame Figures orared on boch
Sides; (o chac oF chele upper Plates chere are 30, chac
is colar, six oF each kinc, belides sorher Plates un
dex theplace marked Ed Which serve For excractino che
Square, Cube, and Square-Square-RooEs, ot ihiek
in ies place.
F. F. 15 a Line dirided into o equal Parts, on whicte
tuns a (mail Black Pin or Index Forivards or backvarde
ac pleature, beino curned abour by G. H Wtichis like
coche Kerota Wacch.
Lastly, P_ is a Place openinu rich hinges, and MuE=
ting dornuxon che lover Circular Plates, and a licele
Bolc ac R, Jockinp ic comn, irtrich Dlace has 6 Equare
holes (orfrramina) chrouxh whichare discorered sucto
Fioures onelv, as are necessary For cheoperacion
K, L, M, is a long Rack on chebackde oF che Im
Rrumene, by wrhich aIlche elaces are curned aboue ou
the Pinions a, e, m, n, c, The meanino oF aII ivtich in
ehis The Instrument is eo be suppoledas itis reprelene
ed in Figure A Care onely chacchere are as vec no Cir-
cular Plares raken of che Semi-circular Pinions S, T, V
W, X, and chat che number siven eo be mulciplied is
(1734. Then onc oEche Places markcd = is Arst toBC
taten off che Pinion x and sec on the lover Semi-circu-
lar Pinion (x) erhich ische Furchest on cheriohe hand.
Atcermards one oF che Plares marked Z is co be rakeu oH
the Pinion W, and sec on che Pinion Co)nexe ro ehe orher.
Thirdly, onc ofche Places marked Z is eobe raken oA
he Dinion V and sec on che Pinion (n. )
Lastly, onc oFchePlaces marked  istobe caken oH
che Pinion T, and sec on che Pinion Cm) Wtick
done, the Place P 9. is cobe Buc donn; and chen wrilt
appear che number 1734 chrough cheholes, 25 in Fig. P
aud chis is ail checrouble oF che InRrumene in chis Or
ens operacion.
X

## Folio 9v — 170380998X:0031
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 10 lines, status machine
X m ∞
4 f
ins es
a
ee
c
10
O
O
e

## Folio 10r — 170380998X:0032
# Source image: https://digitale-sammlungen.gwlb.de/content/170380998X/jpgs/default/00000032.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 36 lines, status machine
The Multiplrine Instrument
The Figure B reprelenes che rery same potture ot
che inctrumene in che Foregoine Pioure A lave one-
Ly chac cheelare Y Q is non Buc donn and locke
lixon che four lover circular Places marked on che
former Figure A wichche large Figures  Z8 = wtich,
ras in effect, a preparacion For che Mulciplication
oE che Numbex (1284) wtich Namber no ap-
pears chroush che Lnall holes ox foramina ol chelaid
Place P O hiding al che ocher Fixures from che
tiye oE che Operator. In irhich particular chis In-
strument tar lurpasses che LOrd Napiers Lamine Os
Bones, irtuch expole a greac number ot Figures 10
ehc PrC ac che Came instane of cime (a5 well chole
thac arc noc utetul as chole chac are) Besides chac
al che Fisures in chole Bones are placed Diaponally,
erhich does very much Arain and force che Eve nt chie
Operator; Whereas in chis chey lic all in a Araishe
Linc, and 25 distinaly a5 can be desired.
The Instrumene beins dispoled as atoresaid, sup
pole che given Number 1934 be co be mulcipliec
by 24. L. ArA sec ic donn in Wricing chus 2734
2 A
ehen Ars Lcurn chen Fand or K ex O H eill che Index
poincro + inche Line EF (0 have I che CrA Produa
6936) siven me in che Windoms or Foramina ot
che Place P _ 25 in Fig C Wtich L Pet
dounchus
Thisdonc, lcurnthe Hand or Keyback-
vard, cill che Index poine coche Picure 6936
(2) inche Linc F. F and in che HIOleS Or 3 468
Foramina oFche Plate P Q (in Figure D.) A1618
50 hare 1.
siven me chC
734
aae

## Folio 10v — 170380998X:0033
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 7 lines, status machine
  M ∞
A
O
+
(8 tri
m
L

## Folio 11r — 170380998X:0034
# Source image: https://digitale-sammlungen.gwlb.de/content/170380998X/jpgs/default/00000034.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 29 lines, status machine
1
The Multiplyinqe Inctrumene.
The Sccond Produa, viz. 31468.
potrich L sec donn under che Ars
Produa, and add aH oF chem a5 In
the ordinary Mechod oE Multipli-
carion, or elle by che help oE Napiers
Bones.
and atrex ehis manner may any Number be Mulci-
plied bx che help. oF chis instrument, erhich is capa.
ble ot beine made tor any Number ot places
This instrument alone is alto oF excellene ule in Di-
vision; as likevise in exeracting che square, Cube, and
Square Square-RooEs, For irtrich che s Places ac che
end ot etic instrument on che riphehand are extreme
ready and serriceable, and are eo be uscd afcerthe
very Came mansier as are che Lord Napiers Bones, and
cheretore needno furcher explication.
Buc it any person have che Curiolicy, and is willine
eo eoc eoche Expence; che Addinq instrument beino
Torned coche Mulcipigine instrument, pertorms Additione
Subtraction. Mulriplicarion, and Division; a5 likemile
che excraction ot che square, and Cubc- RODtS, 8C.
vichoue ehie help ot Den and Ink, or exposing che
Operacor co any difticuley or uncerraines.
SOLY DEO OEORIA.
b
66E6
Lb

## Folio 12 — 170380998X:0035
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 19 lines, status machine
C12
1.1I. 1. tA
CRUI
VoalInho delireto make IIC
OEcither ot chele
TTISTRUMENTS.
F any per son desire to have either of
these Iuctruments exactly made–
and se as it may be serviceable for
many rears. Ile maybespeak it of AIr
umphry adamlon, livine at pres
sent at the Fonse of TOnaSMOOP, Fsq
in the lorver, who is theoncly Nonz-
manthat ever as pet contdbe fonndby
the Author to perform the said In-
Etrumene, ith that exactness that is
absolutely necessary for such Operati-
pns
FINIS

## Folio 13 — 170380998X:0036
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 39 lines, status machine
e
de
For
UI
p
A StorE
Concernins che
ANTIEAT, _ COMMON
W AY OF
NTUMBRITIO
=09L, 29=. UE For che berter understandins ofchete
9E i. F a) CaC) Rrichmetical Instruments, I IhaII en-
0+
d
2i
s
 er dearor (o co explain and demonstrace
6 B d cherealon ofche Operacions oF Addi-
+
+
F tion, Subtraction, Multiplicarion, Division,
5 and extraction oE che Square, and
Cont Certa lente Cubc-RoOIs, 25 co renderthem plain
and obrious en chemeanest capacicies.
The wayoE Numbrins in ule wich che Antients, vas by
the Leccers oF cheir respectire Alphabets; For example
wichche Romans C hionitied 100. B500. M 100O. DMC
10000. CC. l. 33 20000. C95 100000. 8C.
S0amons he Frecians, a or a. Bgnitied 1.
BOr B 2. T Or 13. L1. 20. P5. 100, a, 1000. 8.
4000, ( 7030. c.
Byt nore chacthe most common vay oF expressino the
value of Numbers, is byche Arabick Noces Or Charact
ers called Ziphers, by cho Hebrems, Sephers; and by US
Erphers; and chey are cen, VIZ. 2, 2, 3, 4, 5, 6, 7,8, 9,0.
The way ot placinq chose Characters, is from che
riohchand coche lefi, atcer the manner oEche Hlebrens
in cheir Wricinos, a5 Gemma Frisius and ochers obserre
ThC

## Folio 14 — 170380998X:0037
# Source image: https://digitale-sammlungen.gwlb.de/content/170380998X/jpgs/default/00000037.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 63 lines, status machine
a
d
ona
du
du a
SE
6s
e
c
eu e
 
e
s ci
D=
E
2 00
 
e
52
c
eot
2
es
a0
Ed
53
e
6
 eti
e
i
a
E
a
ud
3
B i L i
3
6
3
C
E0a
2.
E0
en
∞
C03
e
e
= E
a 
 dce
C
∞∞8 3
∞3
 et a C
= 
5
t C 0 ee
3
uta
 
+2

## Folio 15 — 170380998X:0038
# Source image: https://digitale-sammlungen.gwlb.de/content/170380998X/jpgs/default/00000038.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 32 lines, status machine
E
Arichmerick in plain Wlumbers. 18
CMRL.
TBE PreCEPt for ADDITIOHOf Intesers in
Plair Numbers.
prino placea e es vicne ceclare eto-
 L frections in Rantes and Biles; chen bexin and gdd
cogecher che Unices. sFche righe-hand-File, Cecring down
thesum underneact, if ic be under 13. buc it just cen-
ser donno and carry L. co chenent place; and itabore
20. Tec dounthe oxcels in che Ars Place, For erery 10.
o conoete
Examples.
Summ 30
10
add 4
y
06
384
enad
 Lp for SUIBTRACTTON of In.
avins placed chelels number under the glealer
LL according coche respectire places or Progressions,
besin ac che rigtic hand, Substractins the lover Figure
ouc oechac abore ic, and serrins che Remainder under-
neach. BuriF che Pigure chance co be che lels, (a5
OA ic FaIIS out) then chere must De an Unice borromed.
and broughe tromthe next Progrection, to supply che
defect, irhich must bc agnin repaid, by adding an Unite
eo chenext lorrer Fixure on chelete, which is chelame
chino
recers in Plain Numbers.

## Folio 16 — 170380998X:0039
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 46 lines, status machine
16
Ariehmetick in Plain Numbers.
rhing as ifthe Figure abore ic ivere diministied by an
Unire, And For 2 prooF aF che operacion, che number
Suberacted, and the remainde; mut erermore equalchat
oue ot whichr ic ras suberaaed.
FOr ouc of anumber A C lec a lelsnumber A B bC de
ductcd, Then byche Hyporheses, A B cogether wich che
remainder B C are equal cothe ertiole namber A C FOr.
amuch as The parrs united, are alvays cqual zo the rbole.
ALITELCET BETTETTMMLMLCLERO
Exampler.
From 34
Tubrraa 7
Remains 27.1
trom 40
Tuberac 26
Remains 379
From 32453+
Tuberact 95088
Remains 2245 43
From 28
tubcrale en
Remains 13
CHA P I
ThC PrECePt for MLTIPLICATION a
Incegers in Plain Numbers.
FArino placed che Numbers one under the other as in
ll Addition, Mulciply che las righe-hand Fioure oE
ehe Multiplicand, by che last riohe-hand Fioure oF che
Mulriplicator, and sec che Produa (iF le(S chen 1O) un.
derneath; buc it oreater, carryche excess (chacis For
erery 13, an Unice) cochenext place. Anditche My)-
tiplicator hare more places chenonc, Pec donnche Arst
Pigure oFcach respectire Product under chac Figure of
ehe Nulciplicaror by erhich ic was made, and (0 on co the
letr: obterrine Rants and Fyles.
F02
413
ehe
eat
the
31
rie
1
etI

## Folio 71 — 170380998X:0040
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 28 lines, status machine
a
d
Arichmetick in Plain Numbers. y2
For example, 3 cimes sis. 426 Mulciplicand.
42chac is Cerring doon 2 in
the place ot unires and
carryinq 4 in ihe mind e0
the next place. Ao2iny cimes
8 15 X4, and + THaC W2S CAr -
ried in mind makes 18, rHaC
is fecring domn 8, and carry-
ino s10 che nexr. Again7
329 Mulciplicacor.
2982 First Produa.
852 Sccond erodua
2278 Third Produa.
times 4i5 28, and 11529, 13930
And (o in che second Pro--
dua ririce 6 15 12, chac i5 2
carrgins  co chenexc, and
E0 on coche end.
Summe oF 2II
chrec Produas.
Thereaton of Which operacion is plain by che tollom-
ing Table.
et
e
_M

## Folio 81 — 170380998X:0041
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 55 lines, status machine
FOT
 20
Arichmela i LlainNumbers.
CimeE 4OC
Ea
anea
ana 
Or Fiol uand:
LHI
18
60
LI
2
e_ ZA e C X 115
4)2]6 seautcipticant
C
Musciplicaro
Fixst Produt
Sccond Prod
Third Prodi
=
Thousand eiohe hundred.
T2OC
6
IS A
30
15 8000
sbuca ei
a Laat LL
nata ada
es 20
40015
andred
O
O
oSenencaeto
8
and crvency chousand.
oEiotch Prol
0(0 Ninch Prod
H. 1
undchircy
11
2
umme et
Ot 2II i
Produas.
S
F
PrO
Dr
eitee
evo lonals.
C e
8

## Folio 19 — 170380998X:0042
# Source image: https://digitale-sammlungen.gwlb.de/content/170380998X/jpgs/default/00000042.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 50 lines, status machine
aIl
codut
e
Arithmerick in Plain Numbers.
2 22222
The PreCOPE for DIVISION in Plain
Numbers.
ATVISTON, is in effea noching else, buc che de.
duaine oF a leIs number 25 oEc 25 may bc ouc ot a
Grearer, and (0 Anditis ac laR che number, by Wvholeu-
nices chacless number being repcaced, mates a number
equalcoche GreaTeT.
Nom chepreacer ot chese xumbers is Vulgariy called
ehe Dividend, cheless che Divisor, and che lastche que
duS Ox Quorient.
The mechod oschis Operarion is chus;
2. Secche Figures oEche Divisor under un equal num
ber ot Figures oF che Dividend on che lete hand, il chole
Fioures oCche Dividend be ot greater, or ac lcast ot cqual
value michchole oF che Divisor: Ochermise vou must
placeche hrst Figure ofthe Divisor under chesecond Pi-
pure oE che Dividend. And harins set che Divisorriohe
our prickes over che Figures ot che Dividend, From che
Anice place oCche Divisor, inclusire. And chenumber oF
PricKs denore chenumher oEplaces in che Quorient.
2. Tou must evermore prepare Cuch a Tariffa (OcT2-
BIc oE Mulsiplicarion) For che Divisor, 25 is here Pet
donn on one side oFche operarion, and is of excellent ule,
makine ihe work cen cimes more catre and certain.
2. Tou must sind by che Farissa hou many cimes che.
Divisor is Found in chole Figures oF che Dividend undex
Which chey are placed, and cheansiver cothac, isthe ArA
Fixure oFche Quorienr; by mhich rou have mulciplicdche
Divisor in che Tarissa, chen deduet che produa ouc oechose
upper Fipures ot ihe Dividend, ond irhac remains must
Be considered in che nexcoperation, iE chere bc more D)2.
ces chenone in che Divisor
4. ThenexcFigure of the Dividend must be caten
dora and sec nexeco ihe Remainder, il chere be any.
andche Divisor muB be2e2in sec under ic, if ihs ralue
lripi
les
one
ird
1
A
ch
enct
AchF
nehP

## Folio 20 — 170380998X:0043
# Source image: https://digitale-sammlungen.gwlb.de/content/170380998X/jpgs/default/00000043.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 39 lines, status machine
20
rithmeticte in Plain Numbers.
nF the uxper Fioures De Tutciene; iFnoc, there inule
a NuIIOr (0) bclet in che ouorient, and chen che nere
Figure ofche Dividend caken donn, and che very same
Operacion repented, cill che work beac an end. Buc one
example inchinos ofchis nature cleariy and distinal,
sec down, is beccer chena chouland verbal directions.
Zec ehie Dividend be chac Number, Wtrich iras las
Found b, Mulciplyins C426) br (327)
Thaciscocay,
ZEC Che Dividend bc 239303 (426
and che Divisor bc 329
308
tlavine poinced che-
Dividend, aud PI2 - 85
cedche Divisor un-
der C1393; ) 100l
FOr 1393 Cor che
327
6G
nearest number 10 1962
IC) in ete Tarista,
327
extrict i5 1308. 1962
Wrheretore 1 sec
chac donn; and sub- 0000
tractino it From 1393, chere remains 85; etien Charinq
sec donn+ Cor che txit Figure oFche Quorient) I cake
doon che next Figure, or Cypher oFche Dividend, viz
(0) etich makes ic (850) Inchis (327) che Divisor bu
ehe atorelaid method is found cvice; WhereFore L Cet
(2) in etie Quorient, and ihien dedue ene Produa.
vi (654) OuE OF ic, and chere remains (196) co irtich
in ehie las place, L cake doion (2) chelast Firure
oE che Dividend, arid make ic (1952) in Which (327) is
Eounds cimes, and s0 che vor is dc end.
carissa
23

## Folio 21 — 170380998X:0044
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 43 lines, status machine
C l
45
reM
cy (at
IIC 0
cine
IOnS.
r
tac
Arithmericke in Ltam Numbers. 4
Che reaton oErtis Mccalib is plain in che subsequent T ab1C.
 Dividend.
Divisor, ertre es auvanced
D tAC XV
3
PlaCCS, ana IB AOC nOV 307. buc
2700.
This Product 15 noc 1308, buc
oboe ienlo 4cimes 32700
CHaL15 A20 Times 327, Wrhich is
uotient in che Margent.
Thacis 32700 being deducted
100, and loss ended che h
Operation
aece bedns a lecona detac
ouc oF 130800, che remainder is
it. aa adeo eo AoC636. bucesde
Thisis ne ouc s, ntictu
beina doublel makes 6540
aolo explelby ihe Quotien
in che MargenE.
eotrich in ena is d cimes
Thac 15, 6540, beisu celluuor
Duc oF850b, there
15 1303
Coends che lecond Operacion
Eere 327 is broughe doWrn 10
asonni racue agalu
IS dc end.
Thac 1s 6 rimes 327 i5 just e-
Hor. 6. +962
qual ro 1962, and (0 che worte
suE

## Folio 22 — 170380998X:0045
# Source image: https://digitale-sammlungen.gwlb.de/content/170380998X/jpgs/default/00000045.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 31 lines, status machine
22. drithmetick in Plain Numbers
Buc non it chis Dividend had been oreater by 20
Unices, chat is, it it had been (139322) che work had
been che Pame, and che Quorient had been ehe Pame num.
berot Incepers, bucchere had been found remainine a
broken pare or Fraction of 20. Which must have becu
Bc set chus 20
laca0
NotatiOn Of FR ACTIOHS
A
Broken Number, Cocherwise called a Fraction) ii
L A PaTE OF an IntegerS FOr example, A FOOC in
lenocti contains 12 Inches. One pound 20 Tillines
One Milling, 22 Pence; One penny, 4 Farthings, 1
The Tarrs of a Fraction.
A Fraction Con(AS OF Z PAEES, The Numerator and che
Denominator, Which are placed one abore che ocher, and
sevgrared by a licile linc; For example, TF P ivould ex
prelschree quarters ot a vard, it must be sec chui
3 Numerator
4 Denominator.
F. Tnch.
Three Foor and nine Inches, chus. 3. 3 Numerator.
22 Denominatore.
OrifaFoor be dirided in- 2, 75 Num.
eoan hundred pares, chusf 3 1OO DenOM.
Or iF a Fooc be divided2. 3 Num.
onelyinio tour parts, chus( 4 Denom
And Poare all octer broken Pares or Fractions exprest
oEwhac kind loever.
CHI A)

## Folio 23 — 170380998X:0046
# Source image: https://digitale-sammlungen.gwlb.de/content/170380998X/jpgs/default/00000046.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 48 lines, status machine
18.
WOrkI
me M1
mainie
lave
100
Thill
uno
Tor aMC
Ocher,
vouls
set
ratoI.
ninai
D et
123
Arithmerick in Plaix Numbers. 2
 uc  
TheReason of Transtatine Fractions from
one Denomination to another, as liberise
of reducine them totheirleast Fearms, and
cherruch of the Operations demonstrated
Fromseveral Propositions of Pvelids. ile-
Ments.
1t
Tarins chus explained chie nacure oF Fractions, L
A MaII in che nexe place proceed co demonstrate
ehe ReaTon OE Tranctacine Fractions From one Denomi-
nation coanocher, as likerrise che Reason oF depressins
ox reducino ehemto cheir lorrest and least Terms. AII
arhich is necessary co be knomn by chiole wrho delire 10
be Masters ot Fractions.
First oE Pranctarins Practions trom ene Denominarion
Co anocher.
FuCI. l. 7. Theor. 26. Prop. 18.
Farsio, 8c.
TF crvo numbers mulciplyine any number, produce ocher
numbers, che numbers producea ot chem, Mal be in ehe
Eame proporrion chac che numbers multiplyins are, vid.
F18. F.
Forthe applyins oechis Proposicion eo che macter in
hand, L lay betore me chele ero Fractions, namely Z
and Z a5 in Fis. F. And Erst L fingle our = and Musciply
ehem by (4) che Denominaror DE chenene Fraction and cher
become = For 4 times 2 i8 (8) and 4 rimes 3 is (12) 25
maybeseen in Fis. B.
2
 113

## Folio  -  — 170380998X:0047
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 26 lines, status machine
APrulsiplicandus- 1
∞N A N N
EA CINFI
=N HEIE
ulsiplicandus = 5.
SA A N A F
ZHAIEIEF
EB DAAL
Wr Multiplicandus = + ad Muliip licanctums
ita Productus. = 12  ad Productum =- 15
F
C
2
HIEE
IF
TIL
Dt
e
ee
M
et
F
D
C
1
e

## Folio 24 — 170380998X:0048
# Source image: https://digitale-sammlungen.gwlb.de/content/170380998X/jpgs/default/00000048.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 41 lines, status machine
Arithmetick in Plan Numbers.
24
Thisdone, I Cay, thac by che afore-mentioned Propo
sition, ehis Mulciplicacion oFche emo numbers (2) and (3)
by a38 number (4) has alcered no proporrion, buc ihc
produas have che lame proportion one ioanocher, as the
numbers (2) and (3) have, by ehich cheyare mulcipse-
Cd, chacisco (ay, 25 (2) is e0 (3) (0i5 (8) 10 (12).
Again, LEingle ouc the orher Fraction, vix: = and L
mulciply chese cuo by a chird Number, namely by (3)
ehe Arst Denominaror. And che Produas are =, a5. In
Fip. H. Neicher hach ehis Mulciplicacion alcered any
proportion, by che lame reason Wich che former. POr aP
(3) is e0 (4) (015 (3) 10 (12). By Whichmeans Lhave
evonem Fractions, viz. =: and= Whichare che tame in
erea wich che Arst _vO, viz. = and 3. And Whereas
chey vere betore ot different Denominarions, they are
nom broughe under one and che Pame Denominarion
And ehus isrhac 1Bih Prop. OFche7ih B0ok oE Euclis
cheerue ground and realon oF alcerins and cranctarina
Fractions trom onc Denominarion ro anocher 3 and Fromi
divers and differene Denommations, eo onc and che Pame
Wrhich errposirion beins once chroustily digelled, and
imprinced in che mind and memorr, all orter Operati
ons ehich relace ro Fractions, (a5 Adding, Substraatine,
Mulriplyins, and Dividing chem, as alto excractine
cheir Square and (ube RoorS) Will admicoE very feu or
nodisticulcies.
Secondly, The may ofreducins Fractions 10 cheir least
Terms.
Bur Foralmuch asic otcen happens in che mulciplving
anderanstacina ot Fractions ehac cher AveIl ineo 100
oreac numbers, Wwhich are nor (0 cractable as Imaller
numbersare. Ic will be propor in che next place, co Mew
chemay ot reducins ehem eo cheir least terms, cicher
besore, or atterchey are chus mulciplied orcranstaced
as che practicioner Mail sec occation. For che berter et
Fectins oE Which, heis dehrred eo consider fome terr
Desinitions and Problems oFche yth B00K oP Euolid S Ele-
ments,
L_Cbo

## Folio 25 — 170380998X:0049
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28
Arichmetick in Plain Nlumbers.
2s. 1
F, NCb. l. 7.
Desino XI.
Iec 705 a5t dud5, 6.
a prime number is chac which is meature d onetr by an
unice.
Thacis Eotay 2, 5, 7, 1Y, 13, exc are prime numbers
Bécause neicher ot ihem ean possibly be divided intoe
qual pares by any chins less chen an Unire.
ses
Defin: XII.
TIPCOTOL vpo 5, 6
Numlers prime che one eo the orter, are such as onti
an unicy doch meature, beins cheir common meature
And Suchare (∞) and (24) For these rvo numbers can
noc be dirided into lels chen Unice pares, (0 a5 chol
Wrhichmeatures onc, may meature che ocher.
For chout (3) il measure srILILIII.
e
Osthac is eo Cay, ic is Found Z) ITTILLEMLMLEML. - I
Eimes in (9) vec ic Will noEmensare (14) cliac i5, atcer
ir has been tound asmany cimes a5 ic can be Foundin
(F4) ehiere will becroodd Unires lefe,
Acainchouoh (2) doméasure (14), chacis colay, i5
Foundiusty cimes in (14) vec it cannoc be Found anx
cerrain number oFrimes in (9) bucchere ill be an odd
Unice or Unices lete
Desin. XIII.
n ZVrdc aecduoq. 16.
a composed number is thac istrich some cercain nunt
ber meaturech.
50is (15) a composed number, because (3) mulcipiys-
ed by (5) makes (15). And (0 i5 (20) a composed
number; because A musciplyed by (5) maties a Drodue
OF (20).
de
2
et
da
vesti

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Yb
enrile
ime
Arithmeticke in Plain Numbers. 26
Destn. XIV.
Z.ui de 20t 85, 6.
Numhers compoled, one rothe ocher, are cher, Whick
Tome number, being a common meature eochem boch,
doch mealure.
ABdThuS AxC (8) and (12) composed Numbers one L
anocher, because chere is a cerrain number, viZ. (4)
Wrhich beinu repeaced, ox added co it Pelf a cerrain num-
ber otrimes, composes bochche one and the ocher ot chele
numbers. Thacisto Car, (4) being repeaced (or added
coir PeIF) ervice, composes (8; che one oEchele numbers,
and thelame (4) being repeaced (or added to ic selF)
3 cimes, composes (12) che ocher ot chele numbers. And
chis (4) is called che common measure ot (8) and 12. 25
in chefollomine Table.
ruo compoled Numbers-
Dirilors oFchele 2 compoled N
Their common measure.
Three compoled Numbers-
Dirisors oEthele 3 composed1
Theix common meassre
Probl. I. Prop.
AVo a educor C.
Pivo Numbers being siren (nor prime che one 1o cBC
ocher) co find out cheir preatest common Measure.
For example, let the Numbers
siven be (A 15) and (B 9)
I cakre che lels Number lES AM
(B= 9) trom che sreace
(A - 15) 250tc a5I can, rhich
B ITTTETTEY
is once: TF noching remains 6C ILTTLE
chen (B = 9) is che greatest 3D LXK
common measure. IF Comethine
Let it bC (C= 6), and chen
25
neal
erset
28 B
11.
une
l 1
ule
os
Pid
De

## Folio 27 — 170380998X:0051
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Arichmericle in Plain Numbers.
EaKC(C 6) OnE OF (B 9) 25 0Fc25 I can, and il
chere remains nochino, chen (C 6) is che orcacest
common measure: and if chere remain Comeching, lec il
De (D = 3) chen Lcake (D= 3) tvice OuE OF (F  - 6)
and because nochine remains, cheretore (D 3) mea.
Tures (C 6) andtheretore ic meatures (B 9) and al-
(0 (CA 15) andistikerise che greacest Numbor chat
mealures Band A, chac isto Cay cheir oreatest common
mensure. Andchis wils be in all ocher Numbers (not
Prime one ro anocher) betore Y ean eome eo an Unicy.
Probl. TII. PrOP. 35.
Apducor Soderrcoi 86
Hor many Humbers soever beins siven, 10 find the leost
Numbers, thar have the same proportion mith them.
P et che Numbers proxounded Bc (A = 6) (B 8)
(C 12) citherthele are Prime Numbers, or elle there
is a certain Number erhich beins repeaced, (or addled to
et TelF) a certain Number oF cimes, compoles cicher ot
ehem, andischerctore cheir common measure.
IF chey De Prime Numbers, Phave granced What Y
detire.
TFnOE, let rhen chCir GrCaECCE Com, SA LI LLZZ
mon measure be D. And I00k ho 8 BLTTLTETI
manycimes D is Found in A, leE E EZ CIRIETLLEEEI
have (omany Unives And lec F have
25 many Unices a5D is tound cime
in B. And C asmany Unices 25 F
D 1 1
3F 1Y+
is Found cimes in C. Thacis, (D 2) +FLTXV
mulciplicd by CF 3) produces EOTTTEEI
(A 6) And (D 2) mulciplied by (F 4) produ.
ces (B 8). And (D 2) mulciplicd by (O = 6) pro-
duceS (C =- 12).
THeN C, F, and C, are che leaA Numbers chachaveche
tame proxorrion ichche tirst Numbers, A, B, and C.
CH A B

## Folio 28 — 170380998X:0052
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ldi
ane
gelu
3) M
1) and
mibor i
E com
bers (
Unii
16) le
tM
2.
se chi
adiled
cicher
d mtit
11
AIII
AIII
11
havet
and C.
EHA
e
Prithmericn Plain Numbers.
CHC C. VI
Addition of FR ACTIONS.
De the siron Frattions eo be added cogether bc
and3
Tixst P reduee them by the 6 Chaprer, t0 2 and 25
Then Ladd 8 c09, hich makesic 27 Or 232
IFcher bemore chen evo. First rednce evo ot chem
Eo one Denominarion. And chen che lum oE chole EWO,
and chenexE, 8C.
For example, Let che Fractions be Z. 7. =. Firsts =
and Z make
fore, matie 
.Then 72 and = beins added a5 bc.
and ES. Which makie  Ox 2
OIA P. VIII.
Subtraction of FR ACTTONS.
Rom Z are cobe deduaed =. Thacis bycheforexo-
Lins Rulestrom  are co be deduated  There-
fore chere remains 12.
GTIAP. Y
e
MulTipliCAtiONOf FR ACTTONS.
VHtis is onely co Multipir che Numerators one by an.
LOcher, For a Nem Vumeraror, and then che Denomi
xacors one by anocher For a Nem Denominator.
FOr
8

## Folio 29 — 170380998X:0053
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20 Arichmetick in Plain Numbers.
For example. T0 mulciply = by 3 is eo mulciplys 2
By 3. (6) FOr anem Numerator, and chen 3by 4 (72)
For a new Denominator. This is = by Z sire =, OF 
Forthe Produa.
Burcomake alI more plain, and co presene boch che
Operation andche Realonof ic, cothe Readers eye, ac
one and che lame instane; lec him consider che lets Ob-
Ions (6) in Fig. L. (made by mulciplvine che Numera-
Tor (2) By che Numerator, (3) included in che greater
Oblons (T2) made by mulciplvine che Denominator (3)
by chie Denominator (4) chen irhich nochins can possibly
bemore plain, or Cacistacory.
CH AP

## Folio  -  — 170380998X:0054
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P92
(11)
01
ch 1
ge, 2
16 0b.
aneI.
reatI
Or (3
OMdi
HA

## Folio 30 — 170380998X:0055
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30 Arithmetict in Plain Dumberst
CMtCL. a
Diviston of F R ACTTOHSo
HC Rule For Division ot Fractions, ischis,
Nulripiy the Denominator of ihe Divisor, By ihc Hu.
meracor of ihe Diridend, for a nem NumeratOr;
And ihe Numerator ofihe Dirilor, By the Deno-
minator of the Dividend, for anem Denominator.
And thenem Fraction is the Guoriene.
For exomple, iF Z becobe divided by 
Then is ? che Dividend.
and = che Divisor.
Then Z into 3 make anem Numerator, viz 92 chac is Y
And Z inco 4 make aneu Denominaror, viz. 8
Phacisto lay  is contained in Zonce, and one
ciohch ParE. 1X
The Reason oEthis operacion is this.
FirH, E curn checivo Fractions 3 and = inco cvo nem
Fractions, viz.   Cas betore has been comn).
Then, a5 it chey vere plain Numbers, L divide (9) by
(8) andche Quorient is (13). Thacisto Cay, che Di-
vidend (3) iscorhe Divisor (2), 25 (, 2) 20 (.2
Bucnon (9) ische Produat ot che Divisors Denomina-
tor Mulciplied by che Dividends Numerator, and is che
Numerator ofche Quorient, And (8) is che Produa ol
che Divisors Numerator Mulciplyed by che Dividends
Denominator, andis che Denominaror oF che Quorient;
etich is consonant co che foregoing Rule, and chac
Wrhich wasco be demonstratod.
Latu

## Folio 31 — 170380998X:0056
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ibe HB
eralbr
Dent
mina
chae
MB
10
Ilii
e
10
D
a
etto
A
edut
Arithmeticke in Plam NumBeES.
Thusit, ? berobe divided by 2
 ineo C matre a nev Numerator
et
24 And 3 inEOFZ make 2 ne De- Z viZ. 50
ominatOs 36
Whieh beins reducedro irs leastrerms, 25
le
Of Decimat FR ACTIONS.
Hete Decimat FractionS ArE Ot AM Fractions che
 most nacural: For che eruch i5, aI plain Num
Bers astherare exprest by che Arabick NoresOEY, 2, 3
src. are noching elle in effect, bac Decimal Fractions
For example, Lec any Number besiren (432) ThelasE
EEigure (2) isreally, 5, and s0 are che las EHO Fi-
vares (32), cruly and proxerly, 8E. And all chrec
QrEA FrACtONOF, 23=. For as chie very propresion et
Ehese and aIl orher plain Numbers is Decimal; chat is
each Fioure on che letchand, is cen cimes che value ot
etre Pame number placed in chenexe place on che RighE.
Xhus in (333) chelast (3) on che lete is cen times the
value oEche (3) nexecoic on the rixhe: And HC (3)
in chemidale, is cen cimes che las (3) on che riphe.
aud buc ehe cench pare OF chac (3) on che letc. And
pheretore aIl, or any ot chem may be pro libitu, cieher
sractions or Integers: TF I vould hare ihem Intepers, I
ec ehem donn wichoucany Line dramn under chem
BBE iE Y evould have che cvo laR a Fraction, I puc a le-
paratins commabecreen chem, chus, 3, 33, Thac i5 3
Inresers, and. 33 For the Denominator istere eo be un-
dorstood ro be an Unice Dfthe MexE plaCC OP DenominA
eion, 28 Was betore explained. And thus 5275 is an
suleeer ox wholenumber, and rhe Inme number mih a se-
Paratino

## Folio 32 — 170380998X:0057
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Prithmetick in plain Numbers.
paracins comma, chus 5, 270 is an Intexer (5) richs
Fraction ot=. Or chewhole is a Fraction Ot1 00
2
CHI AP. XI
Of Addition and Substraction of Decimals
D TrC OperationS OF Addition and Substraction in DC-
cimats, Interers, and Fractions, is che very lame
vich chac oFplain intesens, only che caretul Cercing che
Unices oF aH che inregers in one File, and if chere De any
void places, cherare ra be imaxined eo be Elled up
ich Cyphers.
Examples of Addicion.
26, A3
30, 
Ln b6
109343
35, 25
240, 56
373 032
312, 842
Examples of Suberaction.
58, 00
27,92
30708
3os
22, 203
D, 104
1327
8, 43
18,84
36,890
132943
492
1003
CHAP.
Multiplication of Decimals.
Furris is likerise the verr Came Operation wich ehac
et Mulciplgins plain Intesers, Care onely, When

## Folio 33 — 170380998X:0058
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lioie
eI
e I B
eri
ett
rea
Eille
189C
9156
10
10
696
Prichmeticke in Plain Numbers.
33
all che mork is ended, there must be as many places ot
PATES, OF Fractions in the Produd, as there vere places
boch in che number mulciplied, and in the number mulei-
elving. As in che Eollovins Example, Chete al CM
Dlaces cur off in ehe number mulciplied, and one in ThC
number mulciplrinss Theretore chere are chrec place
cut of in che Produa. And in che second Eixample, De
cause chere are chree places cur of in che Mulriplicand
and evo in the Multiplicator s Theretore there are Aive
cuc oH in che Produa.
Fxample.
2848
64
d
LFXample.
E2
5
95584
4 amC
3 FxamplB.
3132
7
E
332635
734803
d
LxamPIB.
0375
0000
001875
0578
O0
in ihe Laum oecae hete alAB Inlegers, CnC
produa is
83
1000
Inche Cedmble oecacle chere aondeatile out sre
places inche Produe, viz. 0r875 and vet by cheRule
etrere oughero be sxplaces cur ofF, cheretore cvo Cy
pHETS

## Folio 34 — 170380998X:0059
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34 Arithmerick in Plain NumberS.
Phexs must be prelxe comake ux chenumber ot sxpla-
CCs, 2iZ. 001875
1000000
CTIAP. XI
Division of Decimal FR ACTIONS.
X. P F ehc Dividend De greacex then che Divisor, che Gu-
L rient Will be cicter a whole number, or a mixt:
Buc wrhen che Dividend is lessthen che Divisor, the su.
tient must be a Fraction.
2. Whacerer the Dinidend be, ifneed require, chere
must De a comperene number oF Cyphers added coic, le
make room for che Divisor costand under ic, and ehen
e is no other buc ordinary Division, a5 wiil appear by
chefollomins Fxample.
Dividend 1923 5
oisoi
erhich che Dividend beins supplicd wrich eyphers,
tands chus
3, 746
272,500000 (46049, ec
4160
3724. c
Tarissa
CAA

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ets.
bo
Prichmerick in Plain Numbers.
d   
aire, l
TheVulcar Precept for extractine the Square
ROOF Or Sde of any Plain Number.
Taving Ers poinced che siven Number, (suppole 625
chac isto Pay, serr a prick or poine over erery oiter
Figure, beginnine wich che last. Whereby I know chae
ehie RoOChas cmo places andnomore. Pirst, Lenguire
Whecher (6) che last poinced Figure or Figures, De a crue
Equare Number. IF ic bc, chen L Cec donn che ROOC
Certrich is cahiir found by che Folloming Table, and
indeed oughe co be recained in che memory) lome
erhere on che riohe hand ot etie work, and (0 is ene
Arst Figure ot che Squar-Rooe Found. BuciFie bc not
a erue Square Number, then L cake the ROOC OF che
Square next coic, a5 in chis cate, L sec (6) is nOc a crue
Square, Tcheretorerake che ROOLOF (4) Wtich is ehe
Bearest roic, and makce rhacrhe Arst Figure oEche ROOE.
And chen Suberacting (4 che Square chereoF) out ot
(6) Thare lete remainine (2) ertich L sec underneact,
and Coisthe Arst Operation ended.
625
et L 1
19E
ea
ho
a
LHE C, LLaKC DOHn ehe Floures ot che nex
Square Number, viz. (25.) Then L Cerche double oF
chie tirst Figure oPche Roor under che Arst Figure ot
che second Square Number; and I scek out a Digie
erhrich being. inulciplied inco ic CelF, cogecher wich ctie
doublcot che Quorient (Or ArH Figure) may cake a-
rap che remainino Fioures ot the oiven Number, vix
(225) Or ac least asmrch as marbe; erhich Digit, by
a5king hour many cimes (4) che double of che ROOL is
Found in che Fioures Aanding orex ic, a5 in The nATuTO
BE a Dividend (namely 22) ForT And chAE (4) WiHL BC
 (2.)3 times, and enoush orer and abcre 1o
MudeipI

## Folio 36 — 170380998X:0061
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36 Arithmetick in Plain Numbers
mulciply chac s ineo ic PelF al(o. Therefore L Pet donn
(5) For chelecond Figure oF che ROOC, and L allo lei
ehelame (5) under che las Pioure oF che second
Square; and chen L mulciply che double oF che srt
Figure, auomented hychac sccond Figure (5) charis
Imulcipir (45) bi chac (5) and it che Produa becis
cher equalro che Prgures (225) Randing abovechem
or somuch le(s chen (225) a5 che value ot any Num
Berunder (45) chenthe sccond Figure isrighely chalen
ochervile che Pigure next leIs must be taken. Buc in
chis example, che Produa happens eo be just equa
and (o chemorkis ended.
d
00
ete Enceocts ot inc sguate adonad AII 633(253
Been (253) onely chere had been lefe (30) 4
erhichi had been che Numerator oF a Fracti - 255
unice, and chenche Operation had bcen, 25
here you lec.
No in casechis (625) had been (655) utrichis
reacer Number chen (625) by 30 Unites;
on, Wvhole Denominator must evermore De 45
rhe double ot cheRoOc, augmenced by an 225
The Reason and Demonstration of ihc Vulear
Operation of Extractins the Square-ROBT.
d Nd alcer culs verrmanner and mechod mar che
LL Square. ROOF oF any elain Number in Incegers be
extraded
I.
GTTA P.

## Folio 37 — 170380998X:0062
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L alle
de lec
che
(1) itu
ue be
dovecte
any H
Ily ct
D. B1
just
vi
5
- RBI
Mas
IRIeBE
Cxti
Trichmetice in elam Etanols
t
extracted, chongh never so greac; bue ehac ehis and
loche Operacioms oE the lame nacuce inas de alle
vextormea nica anetanune, andlalistaction, it il
denecettary coane lone renections apon ene nacare
and genelis ot a seuate runder, ala ia bidet nele
unco, ihe Lcaclictonet ls denica lo conhider chetol.
Lomins Detinition oEa Square-Number.
FnCl. l.
Desin. XVIII.
TEro.cor a ecuo5 bclv, 86.
ASquare-Number is ihat which is equallu equal; or; rtich
is contained under trvo equat NumDeES.
FTus the Sguare-Number (4) is concained under Ewo
cqual Numbers, viZ. (2; and (2) and che, Square. Num-
ber (9) is contained under evo equal Numhers, namely
(3) and (3) and (0 on 25 in che Follorins Tablc.
A TablC oF Squares wichcheir Oenecire equal
Number.
quare
5) is concainee a
idet
ThuS
no equad Nars, viz. (25) 2nd
25) Thacisto (ar

## Folio 38 — 170380998X:0063
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Sectio
BLIADRATI (625)
in quatuor Plana, a duobus Lateris (25) Segrmentis.
viz (A =20) et (B =5) efecta; quorum tria ordinatim
Cumpta sunt contince proportionalia,
nimirum
)2 (A quadratus =400 = maximus Proportionalis
2 A in B = =200 = medius Proportionalis
3 B quadratus = 25 = minimus Proportionalis
e
+f. B= 5

## Folio 39 — 170380998X:0064
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lis
alis
Arithmerick in plain Numbers. 30
One oF che equal Numbers
beins mulciplyed by che octer equal Number. - 25
Marresche Produt a Square Number, viz.
FUCl. l. 2. TBeOr. 4. PrOP. 4.
Fav codCia 6.
625
r aripht Line be cut any wise into rmo paris, ibe Square
made of the mbole Line, is equal both 10 rhe Squares made
of the Serments, and 10 ivice a Bectansle made of Hc
Parts.
His holds g0od likemise in Numbers. For example,
LeE (25) bethe Number oF a Righe Line, and chac di
vided into rWO PaTIS: ViZ. (20) the grearex, and (5)
chelesser. TCay.
TheSquare oF the Whole (25) is equal eo the emo
Squares oF (20) and (5) more vy checmo Oblonos
made oF (30) mulciplied by (5) a5 in the oppolire Fi
ure may beplainty scen.
For lec (20) becalled A
And (5) be called
I
A9: (Or 20 mulciplyed by 20) makes . 400
B9: Cor 5 muscipliea by 5) mates
a,
A
Mulciplied by B, chac 15
(20) mulciplied by (5)
Musciplied by B, chac is1
MakCs- 100
20) mulciplied by (8) CMakes-100
Thacis eo Car, chele are che pares, Wwhich
Dcing uniced are equalcoche irhole Square s
625
Thelechines being premised, I Cay, chac Whereas che
vulgar Rule direats (atcer che poincins oF che Num-
ber 625 Wrhole Square Roor is to be extracted) e0 find
ouc chesquare-Roocofche las poinced Figure on che
Dete hand, chac is (6) and noc Ainding (6) a crue
Square Number, corake che nexE tO IC, viZ. (4) Whole
Square ROOLis (2.) Y Cay, chemeanins ischis; Thac

## Folio 40 — 170380998X:0065
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40
Arichmerick in lum Numbers.
(6) is in effect (600) itrich is nOE a erne Square
Number, audche nearestco ic is (400) Whole Square
ROdE 15 (20.)
Again, Wwhercas cheruloar Rule dircas eo Tuberaa
che Square-Number (4) ouc oF (6) and loro fnd out
hon many cimes che double of che Arst ROOC is con
caned in che Remainder and che ArH Fioure ot che
NExE Square, ViZ. (23) chacis s cimes, Buc vich chis
provision chac chere may remain a Number equal eo che
square oF chac (5) 25 in che example.
The siven
Rer
Double ofchet
(A - 20) In
B- 3
A
Pehe  A B, Bino.
625 mial a leR00
The meanine ischis, Fraving Suberacted A9, orche
Square- Number (400) ouc oF che Number (625)
chere remains (225) evtrich is (A 20) inco
(B5) or (100) For one ot che su
(A 20) into (B =SI Forcheocher Oblons, aud B9
Ox (25) Forthe lesser Square. AIlWvtich are che very
parrsota Square, expressed in che foregoins Proposi.
eion ot Fuclid. Namely.
(A9) ThCCquare oFthe Greater SCgMEnEZ
intrichis equalco
(B9) TheSquare ot che lesser Segmene
etrich is equalco-
(A) Inco (B) one of che Rectanoles
made ofche segmenes, and equaltos
A) Inco (B) etie ocher Rectangle made
ofche Segmenis and equal 1o
umber–
rec
a 100
Ma
1y
be
1

## Folio 41 — 170380998X:0066
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etB.
dest
S9
s
sine
sC o
vii
2
Arithmerict in Plain Numbers.
The Square made oF che whole (A -j - B) 2
Or (25) mulciplied by (25) is equalcos
c
2625
And bethe Square.Number never Cogreac, boch che
manner ot che Operacion, and che Reason et che Ana-
Iyss, or extraction of ies Square. ROOC, is che very
Tame.
BucFor the berrer understandine oF aII chac hach
beensaid, let the Practicioner consider vellthe Figure
erhere hemay evidentlr sec, hor che ROOt OF everv
lesser Square being doubled, and an Unice added eo ic
makes up che next greater Square.
Thus cvice (3) or the double R0oc oF che next lels
Square, more by (1) beins added eo chac Sgnare (9)
makes up chenexe rreater Square, viz. (16) Andeivice
(5) Or che double RoOc OF che nexe lelS Square (25)
moreby (1) chacis eo CaV (11) being added eo chac
25) makes ic (36) which is che next greater square.
rhe vay and Reason of exrractins thc Square-
ROOT OF FRACTIONHS.
F uho vould riohely comprehend che pature and
LL Reason ot extracting che Square ROOC OF anv
Fraction, lec him consider che Nnmerator eobe 2 lesser
Square.Number, and rhe Denominator 10 BC a greater
Square. Number; and (o che lesser co be included in che
oreater; asFor example, il ic vere demanded 1o ex
Eract the Square-RODE OF = The Numerator (9) is c0
Deconsidered a5 a lesser Square-Numter, and the De.
nominator (25) a5 a grearer Square. Number, includino
or comprehendine chac lesser or (9) And ihen aII chac
i5 codo, is onely co exera a che square- Root oFche Nu-
merator. 9 For a new Numeraior, viz (3) and chen
the Sguare- ROOE OF che Denominator (25) For a ne De.
nominator.
ITA

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42. Arithmetick in Plain Numbers.
nominator, viz. (5) ASiF chey vere Plain Numbers; Thar
is co lay, che Square- ROOEOF =, 15 3
Bueno, it neither the Numerator or Denominator be
Pure-Sguare-Numbers, the Operation is Lomewhaemore
intricare, chough che Reason oF ic be sill the Came. AS
for example, itis ivere demanded to extraat che square
RODE OF 3. RIIIChe Numerator (3) is eo be considered
25 a lesser Square, included in a Breater, viZ. (5)
Thacisco CaY, ThC Square ROOC OF (3) i5 L3
And che Square-ROOCOF (5) 15
FirK, Tbrins ThCENO Fraetions Z and Z EO EIVO FrA-
etions oFche lame Denomination, brche Rule laid doun
Chap. 8. Pa5. 34. and theyare = and  Sochen
The Square-ROOTOF (3) is, 75 Or 2.3
And ThE SGUare-RODEOF (5) 15 22= OF3
 LL220L
The Vulcar method of Fxtractine the Cube-
ROOL.
Orexample, lec 15625 be che Numher Whose R0DI
 isto bc extracced
First, ic is cobe poinced, beginning wichche lastFi-
rure on the Righc haud, and From chence coche Ach trom
che ristie hand inclusire, and (o co the end, POintins
onc and leaving evo. Thus 15625. Where Noce chac
ehe Number eE pricks, or poines signity che places ot
rhe RoOc CoughE.
Second ene adebo lo de enquired et ene
dact pricket Number on che lefe hand, becher chree, cwo.
Or onc) Ashere che Cube-Rooc oF rs isro be demand-
ed, and being tound by che Table oF Cube-Numbers
25. 45. c0bC3. Yler it in che Rorient tor che tirse
dieriber
NI
i
ot
Ar
AI
(d
(A
MC
25
1

## Folio 43 — 170380998X:0068
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he
aa ilainNlumbers
Number oF che Cube. ROOC, and chen serring che Cube
OEchac (2) viz. (8) under (15) and suberacting che
ArR ouc oEchelast, chere remains (7) Andchisis che
tirst Rep, and che rork sands chus.
15625
Inthe next place having Pet (6) checriple oF (2 che
Arst Found Figure OF che ROOE) under etie last Figure
Pare one oEchenexe pricke Number, I Equare che lame
(2) andchen ic is (4) and ehen I criple chac Square
(4) and makeie (12) and ehen L set chaL (12) undex
ehe Remainder 762 justas in Division, and chis done I
askho many cimes, ((2) is Found in che Figures 76
Tust aborechem, and because ic mar be found scimes
Tset (5) ac alladrentures for che second Figure ofthe
ROOE, and chen che work Aands chUS.
25625 (23
This done, T multiply (the Triple oF che Ro0C mul-
ciplied by che srst Figure oF che ROOE) by chis second
Figure; Thac is, L mulciply (12) by (5) and set it
Just under (76)
Again, Tmulcipsy che square oFche last Fioure, by
che Friple oFche hrst, chacis (25) by (6) and set ic
underneach likemile.
Inthe nexe place, Y Cabe chac las Figure, (chacis
TCubes) and set chac Cube, viz. (125) under the
second Cube-number, chat is, Ferring che Unire place
eF che Cube (125,) under che second pricke
L1GC

## Folio 44 — 170380998X:0069
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44 Arithmericte in Plain Numbers.
Figure. And add cosecher chole Produas, andchen che
ork Rands chus.
5023(2
6
50
1625
LaAI, Lcompare chis (3625) wich che Remainder
ehac vas lest atcer che deduaion ot che ArA Cube-num-
ber, (8) and findins chem just equal, Lcurnic oA and
chere remains noching, the morkis ac an end, and (5)
is ehe second and the last Figure ofche Cubc. ROOE.
But vou, ifche atoresaid Numbers 6000, +500, 8
x5 0. had been greater Numbers, and consequenely, beino
added cogecher, had made a Number greacer chen, 7625)
then Lmust have caken a lester Number, and consequent.
Iy chesecond Figure ofche Cube-Roochad been noc (5)
Duc (4)
Roain, iFthe Numbers 6000, 1500 and 1 50. beine
addedcosecher, had nocmade a Number Arst equal 10
(9625) Thacistolar, suppose che Cube-Number given
had been +5645, Wvhichis more by (20) consequene.
Iy atrer the work ended, chere had remained (27)
irhich (20, had been che Numerator oF a Fraction, whole
Denominator is che difference of che Cube oF (25) and
(26) and chac Fracrim had been set donn chuss , 35,
Andchenche ansiver had been chus, the Cube-R0OF
OF (15645) 15 25
155Y
CHAP.
i
ib
Se
10

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Cto
1u 20
C Rou
150C
cuclus 
Den q
conter
Arithmericte in Plain Numbers.
CTIAP. ZIX.
48
The Reason and Demonstration of Lxtract-
ine the CubC- ROOE.
Houghche practick ot ehis extraction may ac Ars
siphc scem Comeching difficule, vec che Realon
and Demonstration DE it, will I doube noc, make re-
compence.
And in order thereunco T MallArH desire the Practi-
tioner coconsider che Detinicion oF a Cube, a5 also the
Sections ot a Cube into its Analyrical pares, accordinq
roche Rulq ot Perspectire.
F.ucl. 1. 7. Defin. XIX
RoCO3 0, 186.
ACube is rhat Number whieh is equally cqual, or, hict
is contained under ihree equat Numbers.
 TuS (8) is a Cube wtich is containe d under (2) aud
(2) and (2).
A Table of Cubes mith their Gene-
tive equal Numbers.
Three eham Number
ClS.
ndc
Renr
CenM
5

## Folio 46 — 170380998X:0071
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The Section OF a CITBE (125) by
aBinomiat Re
L B) d
3 I 2
etio CUB
in Octo Solida
2 duobus L ateribus
le
(Aa B) 1. c. (3 et 2
eRecta
Duorum
latuor ordinatin
Pta, Cunt contincie
Proportionalia;
nimirum
A cubus = = 27
A quade inB = 18
A in B quadr = 12.
B cubus=
e
Xt
(3)
Squ
(2
(12
ana
H
then
edin
bive
ol
it
mnlB
M
ole
OHEI
Tout
Cuct
ihet
par
ett
ot
leles
Mu
NN
pedt
(011
WH
10
che
int
one
de

## Folio 47 — 170380998X:0072
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drithmerice in Plain Numbers.
47
ThuS (3) and (3) and (3) make che Cube (27) FOr
(3) mulciplied by (3) makes che Square (9) and rhe
Square (9) mulciplied 2gain by (3) matces che Cube
(27) 25 ismore elear by che Foresoins Tablc.
And (0 doc (5) and (5) and (5) make che Cube
(125) Thac iS, (5) into (5) makesthe Square (25)
and the Square (25) inco (5) makes che Cube (125) 896.
Wheretoreco Extract a Cube-RooC, is nochine elle
chento find out a number, which beinq Arst muscipli
ed inco ic selF, andchen into the Produa, produces che
siren Cube-Number. Thus co exrract ehe Cube. RODE
OF (15625,) is eo And oue che number (25) wwtich be-
ino Ars mulciplied inco ies PelF (makes 625) and chen
musciplied inco chac (625) makes che siren Number
15625)
Non because chis construction ofthe cube From a Fin-
ole RooE, concribures nochins comards che Aindino
ouc chac Roor trom a giren Cube-Number, cheretore Was
Found oue by che Ancienes, chac admirable ArE OE
curtins or diridins che Rooc inco rmo pares, Which cher
cheretore called a Binomial RoOt; and From chole cmO
varrsther crected 8 Tolid numbers, Whereofche great
elt and cheleast are alirays crro pure Cube numbers.
ot chole rro distinat parrs, and ot the orter SIX ParaL
relepivedons, by wrtich I mean solid Numbers made by
mulciplrine che Sguare ot one Number into anochex
Number, in imitation of che Geomecrical Parallelepi
vedons detined by Fuctid. lib. 1L. Defin. 30. 10 bC a
solid Fioure concained under sx Equilaceral Figures,
Wrhereot chole wrhichare oppolice are Parallel.
The chree oreares Parallclepipedons are equal one
co anocher, and each ot chem made by mulciplyino
che square ot che greacest pare oF che Binomial- ROOF
inco che leser DarE.
And the chree lester Parallelepipedons are equal tO
one anocher, and each otchem made, by mulciplving che
Square ofche lesser of che Dinomiat Roor inco che orcac-
Ex DaTE
Jhus in che oppotire Figure che Whole RODE is (5)
and dirided Or CUF InCO 2 GTEATEF PAFE A=- 3 and
a deseF PaSFB
ThC

## Folio 50 — 170380998X:0073
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50
Arithmerice in Plain Numbers.
The Cube oF che greater A 3 is equat eo - 97
The Cube oFthe leNer B 2 is equal c0--
One ot chegreacer Parallelepipodons, Or (Aq inco B
is equalco
One ot che lesser Parallelexipedons or (A inco B9)
C is equalco.
rhen
Tochose emo Cubes, namety
Addins
THC GTCAEET OF AC- 27
ThC lelter or BC - 8
QTHTEC DE LHE DFEAEEK Paralle-
Clepivedons, viz.
And
CA9) inco (B) - - 18) HheC
CA9) inco (B) . - 18
CAG) inco (B) - -- 18
CA) into (B9) -- 12
ThrCC OF che lesex Parallete-L (A) into (B9) -- 12
LPipedons, viz
C CA) inco (B9) -- 1Z
The cocal summe is che entire Cube. Num -)
Ber oF che BinomiaL-ROOt A 3 more by .-. - - 125
B 2 chac is toCay (5) and amounceth co-
Nomche Practicioner is co conceire che Unices ol
ehe Cube-Number (125) eobe aslomany Dice, OrCu.
Dical Unires, and 27 oF chele being piled one upon
anocher orderiy and equallu eo make ux (AC) and8
oF chem eomake (BC) and 18 oF chem comake one of
ehe greacer taralleleripedons (A9 into B) aud 12 ol
ehem co makre one of the lesser Parallelepipedons (A
inco B9) and rhen aI chese eiohe solid Numbers beine
orderly puc rogecher, co make ux che encire Cube or
(125) Andchisis the Genelis ot a Cube. vid. Fio
atcer chevery Tame manner, lec the ROOE (25) De
made Binomiat and cur inEo LWO ParES, viz. (20) and
(5) and ehe greacer called A, and che leser B
shen
The CuDC OFche OrCATeF A 20 is equal C0- --800C
The Cube oEche lene D is equal c0- - -125
The frearer Paralleiexipedon, ox (Aq inlo B) isc-
qualco
Threc
don
- - 2000
The lesser Parallelepipedon, Or (A inco B9) is equaI
is ch
AMO
AII
irtio
Sgua
F+
lO
gmen
Squa
1
Segen
ibe le
ment.
MEd
15 (2
Pacie
ot F
Cube
(800
10ch.
Thrc
ped
An
A
LaCA
vene

## Folio 49 — 170380998X:0074
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Det
d-
Agin
Kine
e AC
BC
A
2t
pell
d
a
40
Arithmerick in Plain Numbers.
Then
TThCETCATEEOE, ACI+ 8000
eo chese rro Cubes, namely 2 The lester, Or BC - -125
addinq
CA9) inco (B) 2000
Three oF che greatet Parallelexi- = (A9) into (B) 2000
Dedins, viz.
And
lCA9) inco (B) 2000
CA) inco (B9) 500
Three OF che leNer Parallelexipe-L (A) into (B9) 500
dons, viz.
l. (A) into (B9) 500
Summe- 15625
Thecoral Summe nFall cheeiohe Solids,
is ehe summe ot che eneire Cube ewtich .--- 15625
amounceth 10---
e
AII eotrich is ConConanE in cHaE Theorem OF RamUS,
(ertrich is in imiration of chac ot Euclid concerning a
Square Number.
P R A M I Geometr.
Lib. XXTTTI, DC CUbOpaC. 135.
TFa righe Line DC cuc intorvo Scomenes, che CubC
L oFche Whole Mall be equal corhe Cubes oFthe se-
omenes, and chrice che double solid made ot che
Square ot one Seement.
Thus in che las Fxample, che Square oF chegecater
Scxemene, mulciplicd by chelesser, and che square ot
che lester Scomene mulciplicd by che orcater Seg
menc, (tor chacis meane by che double solid made nt
che square of cheonc Seoment into che ocher Segment)
15 (2500)
And, The criple oFchac (2500) 15. - 7500
Towhichaddins chc civo Cubes, Or -- 8125
Checocal is che eneire Cube, viz.
15625
AEcex alI chis, ic will be catre For che meanest ca-
pacierco conceire, chac irhrilu by che rulgar Rules
ot Extractinqe the Cube-ROnE OF 15625, the ArA
Cubeot (8, is Tuberacted out oF 15) ic is indecd
8000) Or AC) chacisthe Cube oF che orcaEEE SCg-
mene suberactcd ouc of (15625, Wrhole Cube- ROOC is
2, 0e

## Folio 48 — 170380998X:0075
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Srithmetick in Plain Numbers.
+
(2) Or in appearance, buc in realiey is (20) Or che (3. A.
Breater Segment (A)
Roain, Wrhereas in che next place che ruloar Rule di-
rects, coset dononche exiple of che Aest Found Fioure
(2) ander che last Fioure Care one oF che neXE Cube
Number, viz. (2. and then eo Equare chac (2 and (0
make ic (4) and then eo eriple thac (4) and somate
iE (X2). And ehenco find hoir manv cimes chac (12
ean be Found in che remainder, Ox (7625) 1Wtich
suppole eo be s itimes) wich ehis provition, chac atcep
(+2) has been deducted chus s cimes oue OF (7625)
chere Aill remain a Number, cicher gceater or equalto
ehe Square oFrhaE5). chac is (25) mulciplied by ches
exiple oF che ArA- Found ROOE (2) more by che Cube
oF 5) EbaEIS (125) and ifs0, che mork Rands good.
andche Cube ROOE i5 (25).
Theerue meaninq oFallis chis.
P. The Ars Found RODE (2) is Really (20) and ische
GreaTEF SCOMeNE (A
2. The Square OFchac (20) I5 (400) and is (A Square,
3. ThC Friple oF chac (400) i5 1200) andis (A)
Square chrice.
A. ThIS 2200) is Found in (7625) 5 cimes, Whieh
(5) is chelesser Seoment (B)
5. This (1200) mulciplied by (5) or (B) mates
(6000) andis chrice (A) Square into (B)
6. The Square ot chaE 5) 15 (25 Or (B) Square.
7. This (25) or (B) Square mulcipled by (6 orche
eriple oF (A) makes (1500) and is (A) inco
B) Squarechrice.
8. The CuDe oFchis (5) i5 (725) Or (B) Cube.
AIchele beins added cogether, makes ux che en-
cire Cube.
Thatis to CaY,
Cabe, ote abeoi nefleater sedment...8000
. ASquare into B, or checripleot chesolid
Number made ofthe Square ofthe grear-
ex Segmene mulciplied by he lester Seg
. 6000
tnem
AII
i
BC
2h
egula
Rer
bore

## Folio 49 — 170380998X:0076
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Prichmerick in Plain Numbers. 49
8. A; inco B Square, orthetriple eF the e
Polid Number madc ot the Square of
thelesser Segment mulciplied by thec
Preater Segment.
 2500
B Cube, or the C ubc ot che lesser Segment- 125
he rocal sum is che inrire C ube   15625
Thesiren Cube Num. (ABcheBinomialS
15625) 25 ROOC, 212. C
B
7625 Lemainder
rl200 (A) Squarethrice
AGeregItC OE 600C
chechree For-
mex sums and
(A) CvbC.
60)(A) chsice
A - 20
((A) Square into (B) chrice.
Or checriple ot thegreaLeK
CParalle.
S (A) inco (B) Squarethrice.
equal r0 che +400)) or che criple ot che leser
Remainder a-
borelaid.
Parallel.
2125 (B) Cube
63
CHA

## Folio 50 — 170380998X:0077
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 28 lines, status machine
SC MMcmetiet i 2 outi Ldo
CTIAL. XX.
A plain and easie Nerhod of extractim
Sguare-Rootof any Number, (hor crea
soever) withont the help of cither Mul
tiplication, or Division.
For Fxample.
Pet che Square number be-
VEere are theretore 4 Figure.
 inthe RoOL.
Ihe FrRe, viz. (2) is tound
inspection.
Thelecond is had by che Lariffa
CA) chus,
Take che double OF THE ArHE Fi
Gure (2) viz. 4, and mabe a MuI
siplicaron Table oF ic, mineline wich
che respectire Produas, che Squares
ot the o Digits a5 in A. S0 all vou by inspection
tind chac 276 beins cheneares Number 10 2843
Randsorer against 6 in ehe Margine, and cheretore
(6) is the second Pisure ot The LvOr.
ABC
MI
II
A
Fn
1

## Folio 51 — 170380998X:0078
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 23 lines, status machine
2
Arithmetick in Plain Nlumbers. 5+
4 11, 2 1512,FY 2) 15(2(2(2)
5 1 a 2) 150) 4 1 4 2(1(0(4)4]4)
3)r1219 3) +15 16 19 3151516169
4
Inthe next place, P olter to matie rhe Pariffa
B, For the double ot cherro first Fieures 2 and 6,
2iZ 52. Buc by inspection, Itind chac ic is necd-
lels EoAIl up chespaces, the verr second Produc
beins cooerear tor che Number 854. Theretore (1)
must be chenext Fieure nt he ROOL.
Lasly, Imalce a Fariffa For che deuble ot che
FrA 3 Fieures of che ROOC, 2, 6, and L, ViZ. 522.
And hy chactime Pcomero che serenth place, L
find ehac 6is thelast Figure, For ic gives me 37356,
erhich is che very Numbor 1 ToueheFOr.
This Mechod is che most cerrain, and has che
least ot difficuley in is of any Methods L ever vec
Cam.
F 2
CFLAF.
u

## Folio 52 — 170380998X:0079
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52
Arichmetick in Plairo Numbers.
2222 22 L- L0
OF Proporrions drithmetical, Ceometrical
and Ninsicat.
T. Arithmerical Proporrion or Dabitude; is a
Equaliry of Differences. Thatis to say, wvhen
severat Numbers have one and the lame Diffe-
rence: and this Habitude is 1200. fold.
I. Ontinued: WVhen ot sereral Numbers,
Sche second exceeds the Frst by che very lame
Uniey or Numver ot Uinicies, asthe chird dochche
Tecond, ane asthe Fourth doch the chird; and lo
in infinitum, Thus, 2, 2, 334, 536, 73 8, 61.
dister by an Unic. ANd 1, 3, 5, 739, GSc. hare
their equal Difference (2.) The orderly proccedino
oE irhich Numbers From che lester co thC greater
In a Scala- iray, Is eHat erhich is properly called
Arithnetical Proeression.
2. Disjunet When che second exceeds FhC Hrt
by chelame Number oF Unirs, 23 che Fourch doch.
ehe chird, buc noc 25 che chird dochche second.
Asfor Fxample, 2, 337, 9, are Four Disjunet ariih.
merical Proporrionals. FOr (3) excceds (1) by che
same Number oF Ulnits 25 9) doch (7). buE not
25 (7) doch (3). And ThuS, 2, 7, 10, 15, dre
tour Proportionals ot the Pamme kind, FOr (7) ex
ceeds (2) by 5, Units, and (0 doch (15) excecd
 to

## Folio 53 — 170380998X:0080
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eti
IHI
Arithmerick d Plain umbers. 53
2. Geometrical Proporrion or Habicude, is th
Rqualitus of Ratio8, thatisro say, it is ibat
Wvhich sheros wohat part or paris one Number
is of another
Thus, (23 2, 4, 8) (234,8, 26,) (3, 6, 12, 24)
438, 16, 32, 64) arc Geomerricat Proporrionals:
For in the frse Fxomple, 25 (1) is chehaIF OF (3). 10
15 (2) chehaIE oF (4), and ognin, (4) che halE
Ot (8), as may beseen in che tolloins L’ables.
3. Musical Proporrion er Habitude: Is. When the
first Number Barh ihe same Proporrion 10 the
tbird, Wvhich the Difference beroeen ihe first
and the second hathothe Difference between the
second and the ibird.
A5 in (3, 4, 6), (3) is chehalF OE (6), and
Tois (1) or che Ditterence berween (3) and (4) che
halE oF (2), or che Ditterence berween (4) aud
(6); and 10 in (638, 12). But ot chis in iES
proper place.
That which is ac presene eo be hardled, is the
Nature, Properties, and Similicuide oF the evo
Aestkinds of Proporrion, Namely prithmericat and
Geometricat, Which may be vieed in cheir sereral
Progressions, by chetollomins Tabses.
Aritb.

## Folio 54 — 170380998X:0081
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7
d
TC
TT
22
23
14
2
2
128
TC
2C
27
23
23
2c
2C
2C
2C
31
3
32
33
34
Arihmetical Progression.
d
12
7
81 9) 10 117 12
14 16) 18 20 22, 24
25) 18 25 24 27 30 33 36
26) 20 24 28 32 36 4 44 48
2.3
3=
30
25
30
35
40
45
eC
30
35) 40 45 50 55 60
36 42) 48 54 60 66 72
42
49 56 63
48 56 64 72
54 63) 72 81
70 77 84
80 88 96
90 99 108
60) 70) 80 93 100 210)120
66 77 88 99 129(225, 132
72 84) 96108 120132244
78 92, 1042F7 133) 243 256
70, 34) 98, F22T26 2402542(8
90(105(F20(135250(165(180
83, 96T12 F28)T44 160276 297
F+68) 8510129 136153 170]187204
9010d+26 144262 180198216
95, 114)(33552(272(190(209(228
143 160]280, 20012 20]240
=)(+T47168(189(220(23+252
005 50++L5 C54F761298220 242264
230 253,276
144) 268, 192]210 240 (264, 288
130(T751200(225250275300
256 182 208234 260(2.86312
162 139 226243270 297324
168196224 25 2
283308336
174203232261290359348
1802 10) 240
270
100 1724827G
64 96528]560192 2 24 256,230
SC
3yL32265(290,231526429
300330,360
310345,372
320
330
352 384
363,396
68((022361173204238272306340(3741408
35 70T05)540)275(210245(280315350385420
36(72]508(T44 180216252288
3
324
360396432
74(IIL(F46(185222259, 296333370407444
3876TT4)T52]5902282661304342380418456
3978227)256)295234273312355
Ac (30)120)260)200(243(230132
390429468
360400440480
creoine
2
2
3
3
44
3
C
52
24
2
40. 50
55
75
39
44
48
52
42 56
6C
64
72
t
54.
57 76
60 80 100, T23
63 84
69 92c55 256) 1651284]207
72 96)C20
13200225
78204, TZC
6+6813
84) 1F2  E4C
87 T16]245
9022025C
B4
93224) 155

## Folio 55 — 170380998X:0082
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611
Geometrical Proeression.
163
f553
eb
15
68
340625
1703(125
4
32 76E
262 144
2197 152
167772 16
+12 13728
43a
16F O5F
1(772561
19487 57F
6(561
59049
531+AI
A(782(969
430467218
823(5
764, 801
13
360)
0
100
21003
10030
100000
15000000
10000000
1100000000
201489 150001003000
2
244
F 728
20 726
248, 832
2935984
35(831808
1264
2 197
28561
711292
4826809
62
748527
214(358882 129987696, 815730(721
2517(947(691 511591780352 20604499. 373
E
ArisB-
EC
0
511776
117(64

## Folio 56 — 170380998X:0083
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 62 lines, status machine
Arichmeticat Progression.
19
5C
24
43040,=L.
T29
387
2(162
1401
486784 43 1 4
10460
353
2034.
31(3850596094
34243
178(827
28242953648T4G
847288609144. 351
2541365828(329,53
62559.
464987
2. 2, 876792 454,96F(57
68630377364883
205891232 394649(6
62767339628394
21853920288851584 TC
5(559960566,555523
26677 181(699666,56c
50
0311545(098(999
348
A20 481
26216.
a
L
di
l 46
496
8(19214
26384
32 768T
E 65(5367
1320721E
D 262 E4. 4
524 288
11048(576
2097252
A 294(304
b
13
20
.1
22
388160824
26 777226
29
33(553220
essedojeda
34)217
26
+35145.(129
AriiB

## Folio 57 — 170380998X:0084
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hmetib L
1011
20
100C
26000
20000C
1000000
000000100
100000000000c
1000000000700
200000000900003
11030000000(000000
C3001000300030000
100303030000000000
110000000000001090000
10000(000700000(0001000
1003000000006000100000c
15000000(303(000(00000000c
20000300000070300(00000c
1700003000000000(001000000
2000000003000(0001030000900
2
24
2000002000010000300001000100325
In this Progression ic is more vilible chen in any
other, hou sddivon and Substraction in arithmeri-
cal Procression ansivers eo Mulciplication and Divi-
sion in Geometricat Prozression. For, a5 in Geome-
tricat Progression, 2000 Mulciplied by 100,000
produce 100,000,000; S0 in Prirhmetical Progres
sion, the Numiber anlverins e0 1000, and 100,000.
eiz. (3) and (5) beins added rogecher matie (8),
Whien ansvers eo che Produet 100,000,00O, A92IB,
25 in Creometrical Progression (100,000000) beine
dirided br (100.000) the Ouorient is (1000.) 50
in Arithmericat Progression, it trom the greatelt ol
their Corespondene Namibers, V1Z. (8) vou Sub-
Araet any one ottheocher, 212. (5.) theremainder
is (3) and anlwcrethto (1000.)
Arith.
1000000000c
100000000C

## Folio 58 — 170380998X:0085
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 41 lines, status machine
Arithmetisat Proportion
I. Refection.
AIORANTOT AAELANAPESEZ HEPI
HIOAIEONSLN APIOMSLH.
ProP. Terria.
B. a.. 7 .. d.. E. B. A.. G.. D. . F.
AV coV aed, ESC. IF Numbers (hoV
Lsmony soever they be) exceed one anocher by an
equal Interval, then ile Intereal between the oreat.
est, and theleast, is atultiplex of tbat equal Interval,
accordins 1othe Mulcitude of ehe Numbers propoune.
ed, less by one.
Pec che Numbers provounded be FOUT, viz
IB A) (B C) (BD) IBE) wrhose common In- IAC
3 1I5 117 cerral is equal e0 2
By he Hypothesiss is che InerraL Bermeen
ete ereateB  and che leaB): And sibemile
che chrec Nuniber, (2O) seD) (DF
2
2 and erery ot
chemequal co the Common Ditterence, and equal
ehe one coche ocher. And che multitude of them
equal ro che Mulcieude ot che Numbers given lels
by onc (viz. chelealt.) And lasly che ABereenC
OFchese chree Numbers is equal cothe Incerra
(che partsuniced beins equal roche Wwhole.)
AF
Thac 1510(ay,
sTor the Interral between che greatest
DEand
che least  sis Mulciplex orche common incerval
A
i
Ie
lI5 8
ThI
Ib
Wpe1
1
1) 16
1.

## Folio 59 — 170380998X:0086
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et
Ceometrieal Proportion.
I. Restection.
E Numbers (Boro many soever they be) conrain
the one the other by an equat Kacio; Then the
greutest of those Nwinbers is Multiplex of the P’orvers
ofthe Denomination of that equat Ratio Multiblyed
Byihe least, accordins rothe Mulcitude of the Num-
bers siven; less by one
This Refection I hare framed For Geometrical
Proporrionals, in imiracion ot chac Diophantus FOr
Arithmeticat Proportionals.
Lec ehe Numibers eiven DCFOUr, 2 Z. 2, 6, 18, 54.
And lecche Denominator ot che Ratio DC 3.
Thenby che Hyporhesis, che first Mulciplyed by
(3) is equaltothe second; and the second MuIT-
plyed bY (3) isequaleo che chird; and che chird
Mulciplyed by (3) isequalroche Fourch: And (0
in Infinitum.
Thatisto lay
ad S  xX.
00
0v 
a
 et
d
5.3
 2c
O H   55
i   8
F. ThCHr TerM (2) is equalEO 2 C
2. Thc2d Term (6) is equalto 2 into 3
3.
l
core
u
e 8 et
Su X
The 3d Term (18) is equal t0 2 ineo 3 into 3 Vre
2. The +th Term (54) is equalrO 2 inEO 3 IIO 3 IHtO 3
Llat 10 COTa)3 1I1 a∞)Modba 1 at.
Lec chere be any Number ot Proporrionat Num-
BerS, AS, A, B, C, D, C, F, C56. And Ehe DenOmi-
marion ot che RariobeR.
A-

## Folio 60 — 170380998X:0087
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60
AC
Arithmerical Proporrion.
accordins cothe Dultitude oF che Numbers
propounded lels by one, Whichwas tobe Demon-
Araced.
In 2 Symbolicat w2y, ThUS,
Then let the Terms be A, B, C, D, and che
Common Difterence F.
Thus,
Or thus,
C = = A. )- F. 1
D
=A. ). F. 1- F
In plain Ensliss chus,
A Term (1) is equaltOL
2dTerm (3) is equalro L More by 2.
3d Term (5) is equalro r more by 2 more by 2.
ath Term (7) is equal cor more by 2 more by 2 more by 2.
Thac is eO Pay, by the Hypochesis, the sreatest
Term is equol rotheleast, and as many Differences (i
25 chere are more Terims behdes the Jealt; chere. (d
Tore theorearest Term less by che leactis Multiplex
oF che Difference accordins co che Number ot
Terms le(s by onc.
AS Was eo bC Demonstrated.
=
3= 15
TF
e
d. 
l
AL CA

## Folio 61 — 170380998X:0088
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A = A
Geometrical Proportion.
B= A InEO R
C = A INEO R inEO R
e D = A inco R inco R into R
D E= A INEO R INEOR InEO R INTOR
F = A InEO R into R inEO R inEO R inEO R
G = RInIO R IEOR InEOR inEO R into R into H
pA  
Oxthus,
B = A IntOR
C = A INEOR.
D = A InEOR Cub
3) B  A ineo R Squared Square 4
F = A inco R Squared CubC- 5
LO  A into RE Cubick C ubC. -6
A5 this Retlection carrres ies eridence alono
rich ic, s0 is ic ot admirable Speculation and Use,
ashereatter will apPCaF.
POrVerS
Deone.

## Folio 62 — 170380998X:0089
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 27 lines, status machine
Trichmetical Proportion.
TT. Restection.
ere nee Numbersare three Aricimtelical
Proportionals, the Sumof the ravo Fxtreams
is equalto the Double of the Mean.
Tecthechree Numbers DC (2, 4. 6)
Andche Common Difterence De (2)
Then by che First Rerection.
The FirA TermI 15 2
The second Term is 2 more By che Difference once.
The chird Term is 2 more by che Difference erice.
Vhence it is erident and obrious, Thaccwice (2)
more by cvice the Ditterence, is boch che sum ot
he telt and chird Terms, and alto the doubie ot
che lccondor Mean.
Wrhich wasco be Demonstrated.
letr
tetec
 
MM
HI
llIent
la
na
esed
1t. L.8.
AFith

## Folio 63 — 170380998X:0090
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LIeI
lu
Ceometricat Proportion.
II. Reftection.
FuCt. Lib. 7. PFOP. 20.
AV YBCIIS aecDpo, (5C. I ihere be threc
LNumbers in proportion, ihe Number contained
under ihe Extreams, is equalto the Square made of
the Mean; And if the Number contained under the
Extreams be egnaliothe Square of the Mean, those
obrec Numbers pall be in Proporrion.
Let chechree Numbers DC (23 6, 18)
And the Equal Ratio (3.
Thenby che tirst Refection.
The Frst Term 15 2
The second Termis 2 into (3)
a
AXI
The chird Term is 2 ineo (chC SGUATE OF Z) AXRXR
Whence it is evidene and obrious in che ArI
place, chac ehe srst Term dramn inco chechirdis
equalto 2 into 2, into theSquare ot 3.
Again ic is eridene, Thac the Square oF che
second Term is equalro che Square ot 2 inco the
Square ot 3.
Buc these tro are equal; Thatis colay
(8) into (2) into (theSquare ot3) -36
(The Square ot 2) into (theSquare ot3) ==36
Fr9O
The Product of che FirR Bultiplyed by che
Third, is equal co the Square of the Second or
Mean. Wrhich masto be demonstrated. Vid. Fis.
BCOMC.

## Folio 64 — 170380998X:0091
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 23 lines, status machine
Ariihmetical Proportion.
TII. Reftection.
XY Fiere four Numbers are four Arichmetical
Proporrionals, the sum of ihe first aud
fourth, is equal io the sumof the second and thira.
First, let chem be tour concimied Proporcionals,
212. (43 12, 20, 26)
Andcheir Common Difterence (8)
Then byche second R eRection.
The ArA Ter 15 4
The2d Termis 4 more by once che Difference.
EThe 3d Term is 4 more by cvice che Difference.
The ath Termis a more by chrice theDitterence.
Secondly, let them be Four discontinued Propor.
tionalS, 2iZ. (43 72, 30, 38.)
Andtheir C ommon Difference (8)
Then by che second ReRection, and che Hy-
pothest 5..
Thie first Term IS 4
CThe2d Termis 4 more by once the Diference.
e Thc 3d Term 15 30
The ach Termis z0 more by once the Dilference.
TI

## Folio 65 — 170380998X:0092
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Geometrical Proportion.
TTI. Restection.
Fuct. Lib. 7. PrOP. 19.
AV arSES, XC. If there befour Numbers
in proportion, cho Number produced of ihc first
and fourth, is Equat so ibe Number Wwhich is pro-
duced of the second andrhird. And if ihe Number
produced of the first and fourthbe F. qual1o that pro-
duced of ihe second and chird: Zhose four Numbers
sall be inproporrion.
First lec ehem be tour comtinued Proportionals.
2iZ. (23 6, 18, 54) and chcEqual Ario (3).
Then byche Second ReAection.
The srH Term 15 2.
CThelecond Term iS 2 Into (3).
eThe chird Term is 2 into che Square oF (3)
The Fourch Term is 2 intothe C ube ot (3).
Secondly, let them be Four Disjoyne Proporcionals.
viZ. (236, 54, 162) and che Equa) Raio (3).
Thenby thesccond Refection, and rhe Hy potheliS.
The ArI Term 18 2.
The second Term i5 2 into (3)
eThe chird Term 15 5+.
The Tourch Term is 54 Inco (3).

## Folio 66 — 170380998X:0093
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66
Arichmetisat Proportion.
Inchehra Example ic is erident,
Thaterice (4)more by chricetheDifference (24),
is boch che sum ot che Extreams, and allochesum Ia
oF the second and chird, 2iz. 32.
In chelecond example esasenues
Thac (4) more by (30) more by once che Dif.
serenco, is bochche Sum of che Furreanis, and allo 
et the second andthird PerHS, 3iZ. 42.
i
sII
Vid. 5
1. Restection.

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en
stdi
Ceometrical Proportion.
67
Inthe Arst Example it is eridene by the Mulci
plicarion ot POrerS.
Thacche Square oF (2) Nulciply ed by the Cube
OF (3) is both che PrOdvE OF thC ExTrCAMS, and
allo ut rherOMCAnS.
Inthesecond Example ic is as eridene,
Thac (2 inico 3) Multiplyed by (54) is boch hC
Produe oE che excreams, and allo oE che Means.
Via. 618
 16
4. Reftection.

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Prichmetical Proportion.
IV. Restoction.
N ast Conrinued srichmoricat Progro (sions, (hou
many soever thc Terms B0) ihe Sum of ihe Ex
ercams isequat to rhe Sum of any ravo of the other
i
Terms oquidistant from the Eurreams, and 1o ihe iulla
double of the Middle Torm, in case the Number of
Terms bcad8.
Let the Number oF Terms be Seren.
VIZ. 3, 6, 9, 12, 15318, 2F, and che Common
Disterence (3).
First By the Hypothetis.
TheFoUF NumberS (3, 6, 18, 2Y) are FOUT PrO.
porcionals.
Theretore by the Fourch ReRection.
Theircrotums, viz
3 moreby 212
(6 more by x8F arc Egual.
Secondly, by che same Hypothets.
The Fcur Numbers (6, 9, 15, 1B,) are Four
Proporcionals.
Theretore byche fourch ReRection.
Theirtro sums, viz.
56more by 187
9 more by 15C arC F qual.
Lasly, by ehe lame FCypochesS.
The chree Numbers (9, 12, 25) are chree
LHere
pH1D
3
Proporcionals.

## Folio 69 — 170380998X:0096
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Geometrical Proprotion.
IV. Restection.
N al Consinne d Gcometrical Progressions (horv
many soever ihe Terms he) the product of ihie
Fxereams is equal ro ehe Product of any tuo of the
other Terms equidistant from the Extreams, and 10
the Square of che Midale Term, in case the Deumber
of Termsbe odd.
Tet the Nuriber oF Termsbe Serens
ViZ. (2, 6, 18, 54, 1623 485, c458); and che
equal RarIO (3).
First, by che Hypothests.
Thetour Numbers (2, 6, 486, 1458) arc FOuF
Propertionals.
Theretore by che Fourch ReRectiOn.
TheirFwO PFO. S2 INtO 1458
duCtS, viZ. C6 into 4865 arc F. qual.
Sccondir, brthelame Hlypochelis.
TheFour Numbers (6, 18, 162, 486) are tour
Proporcionals.
Theretore by che tourch R eRection.
Their cmo Pro-58 Inco 4867
ducts, 2iZ. C18 into 162f are Fqualo
Lastly, by che Tame Hypeche(S.
thc Thce Numbors (18, 54, 162) ne thsee
eetca e
TherE

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Arichmetical Proportion.
Theretore by chechird Rerection.
39 more by 152
Cr2 doubled Care Equal.
Theretore by thC TA AX. F uctid.
C3 more by 277
Smore by 18 are aII Equal one 10 8.
o more by 15
nother.
C 12 doubled As as tobe Demonstrated.
Vid. Fig.
18 21

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Ceometrical Proporrion. 7+
Theretore by thechird ReRectioi.
18 IntO 162)
e
and TareEqual.
(C54 Squared, D
Wheretore.
= 2 into +4587 do matie 2916; and con-
6 into 486C. sequenelr are aII Equal one
18 into 162C to anocher: Which ras to
54 Squared be Demonstrated.
Vido Fi8.
62 436 14: 8
54
1E 4
A Table

## Folio 72 — 170380998X:0099
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Be 
TheForegoine Reections applyed co the
Golden Rulo, Or Rule of Three.
1II.
(1
le
The Rule of Threc, or the CoIdon Rule.
Prelis Rule is cither Sinele, or Compound;
Y. The Single Rule of Three.
The Sinele Rule of Threc, is irhronchree Num-
bers arc Ciren, and, a tourch Proportional De.
manded.
Non ehis Single Rule, is cither Direct, or
Inverse.
T. Direct.
The Single Rule of Three Direct; is when chree
Numbersare Given, and a Fourrh is Demanded,
rnich bears the lame proportion eo che Third, at (lo
ene Sccond bears cuche Firlt.
Fxemple.
IF 4 Acres of Ground cost 80 Pou d, irhat
iil 8 Acres of chelame Cround cost:
T0 underttand. chis Operarion, look back 10
chechird R. A ction upon Geomerricat lroporion,
and yon MaII H. Id ic Demonstraccd, chic et chere
betour Proportionals, the Produet ot cheFirst and
buct
Fourch is egualio che Product ot ihe Second and ds
Third.
Wheretore in this P xample.
IF che Product ot ehe Second and Third Term,
Vi2.
D
1
n
e
Me

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2
viz. (640) be Dirided by che First, namely
(4) The Ouociene, 2iz. (160) is the Fourch
Proporrional louche.
And For a Proot oF this-
Lecche Fourch found Term (160) beine Mul
ciplyed by che krA (4); ehe Produet rist be che
Tame wich che Product oF che chird Mulcipived by
the second, 2i2. 640.
The Rroumenration is plainly ehus,
IF the Produet oF (80by 8) be equal eo che
ProduetoF (4 by cheuntnoon Number.)
Then,
The Quociene wil be che very Came eherher
PDiride ihe Product ot (50 by 8,) or Wwhecher L
Diride che Produet et (q by che untinonn Num-
b. r) by 4. For cicher ot che Products beine 64C3
checuorient mult necds bc 160.
Buc non ie is monifest, chat il
TMulcipiy 4 by 160, and Diride the Produet
back again br 43 ic will gire 160 Forche Duotient.
Becaule, wharerer Muiciplicarion doch, is again
undone by Dirition. And this is che crue and
eenuire Reason oF che Operarion in This Rule ef
Three.
Thac

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Thacis,
A5 (4) is foutid in (80) just 20 cinies, (0 is (8)
found in (160) just 20 TiImCS.
Or thuo,
A5 4 Mulciplyed by 20 matces 80, (0 8 Multi-
elyed by 20 Malies 160.
20 Fxamp. c.
The Anliver Willbe tound as betore.
F 801. Win das  ecr a 100. bus:
Het
ite
1
i
115
1be
1
se
b
Bo Dividino che Product oF (4 IBEO 160) viz. I
(640) by (80) For chen che uoriene ill be8: Ni
Lor ac S0 contains 4, tweney cimes, (0 160 b0- M
ins Dirided by 20, clie Ouorient is 8,
2. Inverse.
The Single Rale of Three Inverse is when chere
arechree Numbers giren, and a tourth deminded.
Wrhich bears the lame P’roxortion ro chelecond, as
chechird dochroche hrlt.
Kxample.
TF 2 gi Ancity oF Tley riil kecp S Horles 12
D295, Elom mans Days will chelame quanticy licep
I6Hor(Cs.
Here

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Here il ls oblerriere, at Mmose ot thole rhohare
hitherto Tresced of this Rule of Three, puzzle
boch vouns Learners and chemlelres, rich ehis
distinction ot Direct and inverse, as though they
verecrodistinet and difterene chines, irhereas in
eruth cherare chevery Pame ching, only care must
be catien hor eo place chem. For the erue un-
Foldins ot this queltion, is chis,
L.Ook Wrhac proxortion 16 Ilorles bear 10 8
Horles, (0do r2 Days bear 1o a Tourch Number
oE P 2y5. And chey cuphe co be placed thus,
And ehen the operation is thebery Pame as be-
iete e cheProduat ot 8  (96) ntricte
beine irca e16, S (6), nhica
is the fourrh Number (oughE.
The

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0
2. The Double Rule of Threc.
and this is
I. Direct.
2. Inverse.
2. Direct.
PPHe Double Rule of Three is when more chen
chrce Terms are siven; as che ordinarr
Boolsot Arichmerick teach u5.
lo Lultso
IF 4 Men spend r9 Pound in chree MonHS,
hon many Pounds vill 8 Nen spend in niné
MontHS3
The Retolurion oF ehis Quection is ehus per-
Formed.
1. IF four Men spend 19. Wrhac rill 8 Men
spend.
na
Men. Pounas.  Eoms
2. L

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1
2. IF 381. Bet S) al aiber oF Nen in
Monchs, homans onit be spemeby lucl
aNuniber ot Men in 9Monchs:
Monchs. Pounds.
Monchs. Pounds.
2. Fxample.
IF 9Bustels oF Odes serre B FTortes T2 Day5,
hon many Days will 24 BustreS lost 16 Horles.
Read itthus,
2. IF 9Busels laA 12 Days, hon many Days
nill 24 Buctels laAd
gels. 2475. Onstbis. n73o
It

## Folio 78 — 170380998X:0105
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1026 Day5.
DaM
f
Medi
OL
be3
rii (
 iha
B
ida
19, 42
calleds
1 (0
de PB
And this is the whole Tnerigue of the Goldem polei
Rule, Or che Rulo of Three. Thc irhrich beino Iu
righely understood. (together with the forogoins ((I.)
RcAections on arirhmerical and Geomorricat Pro vect
porrion) chole orher Rules oE Fellorostix, and pno
Be ac aII disficult. And cheretore L chink ic Ma
necdlets ro mulciply Examples.
(8a
ist
2. A5 16Hores is ies; (0 is 32 Daye
AI
sett
lose
1I
1
s
Uousa
idt
Horses. orses. Dus. Dus.

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Vin
he Diamerer of any Cirele beirrs piven in Tntepers;
10 find rhe Peripherie, and ihe Square- Root of ihe
Area, in infinicum, vithont the help of cither
Mulciplication, Dirision, or Fxtraction of theRoor.
Or Fxample, Lec the siven Diameter ot a Cirele
bC 35F. And let it be required co And che Pe-
ripherie (or Circumference.) FirstI Per donn (300,)
under that (50,) and benearh thac 13 25 in the (0)-
lomine Operation. Thisdone, Pfrst seck the Peri-
pherie oF a Diamerer OF (3) intha sublequene Table,
riZ. 9, 42477795, and because it is che placa ot
Hundreds, I add chereco on chetiphe hand eno ci-
phers (00.) Then, under chac Sum I set che Numbex
ot che Peripherie oF (5.) addins c0 ic one Cypher
because ic is the place ot Tons (viz. For 50.) L aAIY
Iplace under theeuo Sums aborelaid che Peripherie
ot (L.) withour addins any Cypher, becaule ic is che
place ot Dnirs. And addingthese 3 Sumstogether,
(erermore distinguistrins che inlegers trom cha
Fractions, atrer the 8th place trom che riohe har.d
wich a Comma, or Line ot Seperation) che Sum, Ox
segregare (viZ. 11O2, 6990215,) is che true Pers
pherie ot chac Circle, Whose Diameter 18 35F0
300- 942 (4777,9500
50- 257 0796,3250
2
3 11425,9265
35F sums +FO2  6990, 2015
Alcer e tely lame manner, it ic ere required ia
sire the square- root otthe Area ofchat very Circles
erhose Diamerer 15 35F. I add che 3 Follomins Sums,
and ehe Apgregare is WhacI detire. For F. xampe.
300-- 265 18680,7700
50- 44 3T13,4620
I
∞18862,2692
EE I sam ZTF 06c65012
IF che hrit place ot che siren Diameter be ot
honsands, chere must De 3 Cyphers; it oF Tens oC
Thousands, chere mult 4 Cyphiers be added on cha
riehit hand, and (0 in Infinituma
∞
Aia
o
cal

## Folio  -  — 170380998X:0107
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Diamet.) Peribherie. (Squar
1
312415,926
6283L,c
d 42472)
2(56631706
15(7079163
18(8495,550
2F991F, 4.
25 F327.4
283
s
5449,0770
4322,3462
273,6T5C
20350884
0898, 1540
7(9760,4232
Buc in case ot Fractions, asFor Fxample, it che
Diameter had been siven 3517, and the Peripherie
ivere demanded: The WaY 15, 10 take 2 oE 3,
x415,9265. (212. 037853,9816) and to add it ro
X202, 6990, 20r5, Whichmakes 1103, 4844, 183Y
For the Peripherie ot thac Circle irhole Diameter is
15 35r=. And chelame method is tobe uled for
any Fraction Whacloever.
The Circumference of a circle beine siven to find the
Diameter, aud the Square. roor of ihe Arca, in In-
Finicum, virhout ihe help of cicher nsulriplication,
Division, or Extraction of the ROOI.
Circum.
Diameter. ISquare. roet of ihe Area
3183,098
6366, 2c
1549, 2
27
925
9098
c228F.
54643
13
2820,9479
5641,8958
8462,643
X282,7916
4204,7395
6925,6875
3746, 6354
2567,5833
215388,5312
This Table is ceDe iled atcerthe very same man-
ner richche Former.
21
of the ArCa
6862, 2692
7724,5388
0618077

## Folio  -  — 170380998X:0108
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MM HI
ilb
i
16. d0
13 8
li
6d 41.
b1
eri
Pui
2bli
Iti
AMII
uli
fo
lin
0,91))
1.895
b184)
2.7911
4731
168)
66H
15d)
M

## Folio  -  — 170380998X:0109
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erpctualt Almanack invented by
S. Norland 1650.
oFind the DOm: TCHCF FOF eVer.
B
GF BA DC  FE AC CB ED
1000 1200) 1400 1600) 110O 1300 1500
1516 20 24 28 32 36 40
44 +8 52 56 60 64 68
72 76 80 84 88 92 90
1700 4
8 12 16 20 24
28 32 36 40 44 48
52
2400 1900) 2500 2300) 18001 2000 2200
FoEind what dar ofthe Weck cach Month begins.
X
3
l
D
H t C
Octob: 31 May. 31 August 31 March 31 Lune. 30 Septem 30 Aprill. 30
Canu: 31
Novem. 30
Febru. 2.9
Decem: 31 Tulis. 31
Totind the day ot y Monite
T 8 15
TO
16
4 TI
C
12
TE
14 12
23
a
i
A
IC
ie
M

## Folio 1 — 170380998X:0110
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e
LNLLNAY
OE THF
erpeluat Almanact.
is Almanack was tirst incendu
ed c0 bc a8 Thorc and compen-
dious a5 vas posible, and cO
be Graren on a (maiI place, ot
Silrer, about che breadch et a
Stilline, and (o portable coxe-
cher rich moner: buc harins
nom delien dic For a mais pockée
B00h) L have chouche ie nore
conreniene co divide ic incochree
distina lables, istricteare muchmore plain and catie
ehac (orhre use chercot may beobriousco che meanest
capacier. And irhen, che chrec Follovina Tables and
theix usc are chronehis understoods This Almandek
ill necd no explanarion, and may, beuled Coihecimee
as Well ac the ochet chreo Fables.
Thouse oF theTable in Pagc 6.
By ene Table in Page 8. Vou may immediaeely And
ehc Dominical Lerter From eHe Arst pear ot Our LOrd, es
the vear 3400, _c. (olong as ihe orld MaII LaH.
For example, For anx rear ot Our Lordunder 100.
cheyare exprest in che Marginal Cotumnes oF Numbers,
and arc ansivered in che Ark Cotumne ot LecerS. Thus
For che rears of Our LOrd 28, 56, and 84. The Domi-
nieat Certersare DC. For the rears X, 28; 57, and 85.
etie Dominieat Peuor is B. FOF che vears 1L; 39; 67
ead 95. ho Donihieat Fetter 13 D.
or
I

## Folio 2 — 170380998X:0111
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Nom tor ait ene eten Munaceas or ThoulandsFron
100. c03400. (Which are aHI L cap. VearS) che Domi-
nical Lerters arero be found abore chem in MMEL, 2,
3, 4, 5, 6, and7ih Columne.
AndFor any ocher Numbers, ehie Rule is FOF ever
ehis; Wrbere the Marginal Number (equal to ibe Fracti-
on or parr of an Tundred Souxht) meers with ihe columne
rhere that Number of Hundreds or Thousands (which is
be other parr of ihe Number soushr) is exprest: That is
the Dominical LecteF (Or Letrers) for that sear.
For example, Ler ehe Dominical Letter he demanded
For chevear oF Our Lord 1672. Thenumber oF Hun-
dredsis, 1600. and is Found in chechird Columne. and
chebroken pare (72) amons che Marginal Numbers
meets wich chac chird Columne in che Lecters GF.
Wtich are che Tominicat Perters For chac pear, namely
ehe Axs oE ehem CG.) Fromche Arst oF fanuary 105.
Marthias Fve, che cvener Courch oF February and the
Ocher Certer. F. eo che vears end, erhich is a constane
Rule For alt Lcap-V: ars
TE ehe Dominical Lerter De demanded FOr 148L. The
FTundreds arc 1400. and are Found in che Arst Co-
sumne, the broken pare of an Hlundred (81) mé̂cis
evich chac Columne in G. Wtrichis che Dominical Lerter
FOr chaL VCAY.
S0 iF ehe. Dominical Lester De. demanded FOr 1348.
1300. is Found inche y Columne, Where che broken
Dart (49) amons che Marginal Numbers; mects in.
ehe Lester D. Wtrich is che Dominical Lerter For chae
vear.
.
ABain Lecche Dominicat Letier Be demanded For che
vear 1729. 1700. is tound in chea Columne, 2nd29.
meces wich chac Columne in F.
And (o For any vear pastor to come.
The ulc oF the Table in PaSC7.
The usc oF chis Table is eo sind resdily, boch uxon
etrac day ot chewreck any monech oF che rear begins
Eor ever. Buc allo hon mans days each monch con-
EaLBS
i
s

## Folio 3 — 170380998X:0112
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eains, ivhich is eobe Found under chename oe cachre
specire Monech.
For example, L desire coknon uxon whac day of che
Wweck chemoneth oF April begins, in che rcar 1623.
Pirst IAnd by che Table in pagc 6. chac che Domini-
cal Lerrer For thac vear is F. Then I quide my Fyc
sonn chac Columne of cheTable in pazey. Where e
is ac ehe cop, and ac che Came cime obterve ivtere
aril is in ehe Margene, and Wvhere che Line oF April
meoes wich che Columne F. chere I And (Tuesday)
which givesme co understand chac Aprit in che vear
1623. begins on a Tuesday.
By che Pame Rule
The moneth OF NCay in the ycar 1615. bcoins on
amundar.
The lame moncch in the vCar 1616. beTAn On S
Wednesday; erhere ic isto be noced chac Forasmuch as
1616 is a Ccap vcar, L make ulc OF thC 2 LCTTEF (F. )
for che Tadle in page y. Which must alvars be ob-
serred in L Cap-YCaES.
ThemonechoF Sepiember in che ycar 1537. bexan
on 2 Saturday.
The monech oF fuly in che vCar 247L, began on
aMonday.
The Monech oE December in chercar 1642. began on
eThursdas.
Themonech oF Angust in cherear 17BF. Will begin
on a Sunday.
And Co in alIehereK.
TheUse oFthe Table in PagC8.
The use oF chis Table (having Arst Found upori
Whac dar ot chereck auy Monech begins) is coknon
readily che day ot che Monech.
Suppose ic co be Thursdar, and che beginnins o
October in che vear 1672
By cheervo former Tables IFind, ehac che Monech
ot October 1673. begins on 2 Tnesday; Wheretore L
look

## Folio 4 — 170380998X:0113
# Source image: https://digitale-sammlungen.gwlb.de/content/170380998X/jpgs/default/00000113.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 41 lines, status machine
lont amans the Tebles in pase 8. siII. L End a X2
Ble chac besins wich a Tuesday; and Andine hAC
che Thursdars ot char Monech ara 3, 10, 17, 24, ind
31. qnd chZC iC is yet ouc che pexinnins et che
Moneth, I conctude chac ie must needs be the 3 day
et che Monech.
Where ic isco beobserred charis Lcannoc by some
Martes or Circumstances help my memory, co knou
AF leaA Wvhac weck pt che Monech iEIS, no AIM2
nacke in che Wortd can intorm ox cel me whac day
ot rhe Monech it 15.
Euo excellent Ises ot cheTa
blc, in Pa8C8.
c. By ic may bereadily found whac dav
ot ehie meek, any day ot cheMonch
WS, or Will BC, OE any YCAF PaA OF
EOCOmE.
e
For example; Such 2 man was born, or tuch an 3ai-
on 1gs done; or such a Letcer 1r25 Wrrirten che
Fourch ot Seprember in chercar 1518. and ic is demanded
erhac day ofche vecke ic ir25 d
 By che Table in Page 6. Y Find che Dominicet Let =
ter Forchacycarrobe D.
L. By che Table in Pasc y. I find chac Seprember in
chac vearbecauon 2 Tuesday.
3. And by che Table in proc 8. I And chacche Fourch et
Seprember Wasche first Friday ofchac Monech. And
(o may any: ocher day ot ady weck, ot any ocher
Monch, ot any octer year PaH, Os c0 ceme, b0
LMONBI.
p. B
d
Toret
Aa
AFIB
si
15C
es
1
1BIMI

## Folio 5 — 170380998X:0114
# Source image: https://digitale-sammlungen.gwlb.de/content/170380998X/jpgs/default/00000114.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 17 lines, status machine
(5
2. By it may bereadily Foundirhat
dav ot che Monch, as or will be, ot
any dar, ol any weck, ot any monch, ot
any ycar paH, Or to come.
For example; Suppose sucha Man was born, or such
an action done, or such a Lercer vriecen, uxon che
trs Friday oF September, in che ycar 1618.
Hlaving Found by che foregoins directions, chac Sop-
tember in ehac vear bexan on a Tuesday, I And chac
ehe Rest Friday oFchac Monech, as che Fourch dayot
che Tame Monech.
And (o may bereadily Found whac day ot che moncho
as or will be, any day ot any weck, ot any monch,
Ot any rear, paItOrEOCOME.
M rhiebare of excellent and daily use for ait Ministers
s Stare, and for all Merchantsin rheir correspondencies

## Folio  -  — 170380998X:0115
# Source image: https://digitale-sammlungen.gwlb.de/content/170380998X/jpgs/default/00000115.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 145 lines, status machine
ATable Theine theDominical Letter trom
theCirlt rcar ot Our Lord to therear 3400
t mar bc continced for cver
DEEDEECETACBa (CD
000) 100 200 300 400 500 600
700) 800] 900,1000]1100,120011300
1400) 1500)1600)17001800590012000
2100)2200]2300 2400, 2500]2600, 2700
2800(2900300051001320077005400
DCI ADSEELOFL AO) BA CF
B
C  D) F C.F C  A
A B C D  F E C
A B) C) D
X
F
88 FE OF AC BA CB(DC)EF
D
F
c D
B C
F
C) a B
F E C A
D F F C
C
B
A
8 (3616492 AC BA CB DC ED  FB CF
F C
E
E
a B C
D
C a B C
D F F C A B
F
C
CBDCIED EE, GFIAC BA
a
B
C
D, E F
C
C A B C D E F
F
C
A B C
D
F
ED EE OF AC) BA CB DC
B
D
C
B
F
D
C
F
F
Ce
F
a
C
D F E
B
A
C
GF AC BA CB (DC ED PF
F
d
F
F
D
C
F
H
a
B
C a
C
B C
E G A B
ACB(DCEDEB CF aC
A
e
A
C
C
B
D
C
B
D E
a  81C
1
2 28
2
5
4 13=
5
6
55
34
35
9 (37
10(38
ET
39
1240(68
13 4T69 97
14 42 70 98
15 4.3
16(44
1
18
10
20
2F
212
24
2C
4
4
4
5
0(28,56(84
5i7
58
6C
6T
62
83
86
B
89
90
93
94
7T
72
9F
de
30
e

## Folio  -  — 170380998X:0116
# Source image: https://digitale-sammlungen.gwlb.de/content/170380998X/jpgs/default/00000116.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 21 lines, status machine
etro
34
ATable
Stemins brthchelp or Dominical
ut dar ofthe rcek anr Montho
tnc rear Begins forcver
Tete
lan (Sund. Satur. Fryd: Thur. Wedn Tuesd. Mun.
Feb Nedn. Tuesd. Mund. Sund. Satur. Frrsd: Thur.
8
Mar (Wedn. Zuesd: Mund. Sund: Satur. Fryd: Thur
Apr Satur. Fcyd: Thur. Wedn Tuesd. Mund. Suna
Mar Mund Sund. Satur Fryd: Thur: Wedn. Tuesd
Tun Thur: Wedn. Tuesd. Mund Sund: Satur Frya
10
Tul (Satur. Fryd. Thuc: Wedn. Zuesd. Mund Suna
AaSTuesd. Mund Sund. Satur. Fryd: Thur: Wedn.
Sex (Fryd. Thur. Wedn. Tuesd. Mund Sund: Satu
Oet Sund: Satur. Fryd: Thur: Wedn: Tuesd: Muncs
Nou Wedn: Tuesd: mund. Sund. Satur Fryd: Thuc.
Dec Frydsthuc. edla ruesc plume duna datu.

## Folio  -  — 170380998X:0117
# Source image: https://digitale-sammlungen.gwlb.de/content/170380998X/jpgs/default/00000117.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 61 lines, status machine
Thc, Varicties a
the laAtTable Pas
For tindins Y dar ol
theMonth.
Wcdr: 1 8 15 22 2)
Thursdays 2 9 16
Fry days
Saturdays
Sundays
Mundays
3 10 T
4 TI IC
5 12 13
6 13 2
Tucsdays 7 14 2
Scnd: (T) 8 15 (2229 THErId: ) F (8 (25
mundays 2 9 16 23 30 Frydays
Tuesdays 3 20 (7 24 3F Saturdays
Wednesdays 4. TT 18(25
Thursdays 5 T2 T9 26
Frydays 6. 13 20 27
Sacurdays 7 14) 2F 28
2 9 10
3 10 F
Sundays 4. II
Nundays 5 12
Tuesdays 6 13
Wednesdays 7 14 
Mand: ) F) 8(15 (22(27 Frvd: F 8 15
23
2
Tuesdays 2 9 16 23 30 Saturdays 2 9 16 2
Wednesdays 3 20 17 24. 3F Sundays 3 10 17
Thucsdays 4 II 18 25
tiris days 5 12 19 26
Saturdays 6 13 20 27
Sundays 7 14 21 28
TECId:  E8 15 2229
Mundays 4 IE TE
Tucsdays 5 12 L
Wednesdays 6 13 2
Thuesdago 7 14 2C
Saturdi) E) 8 (15 (22
Wednesdays 2 9 16 23 30 Sundays 2 9 16 27
Thursdays 3 1017 24 3C Nundays 3 10 17 24
Frydays 4. II T8 25
Satuedays 5 12 T9 26
Sundays 6 13 20 27
Mundays (7 (14)ZL 28)
Tuesdays 4 TF 18
Wcdnesdays 5 F2 19
Thursdays 6 13
trydays
E4
3C
2
24
ri
23
24
3C

## Folio 9 — 170380998X:0118
# Source image: https://digitale-sammlungen.gwlb.de/content/170380998X/jpgs/default/00000118.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 27 lines, status machine
So findout thelrime or Colden Number
for ever
Divide che jear ofthe Lord by (29) and to the
Remayndce after theDivision addlL) the sum
1sthe Prime for thatyear
Example
Thus (1672) divided by (19) leaues (18, torhiete
adding (5) nalees it (19) for thetrime of is yeac
Diviend  167F (87
Divisor 19
T52
Dividend 15 T
Divisor 10
33
Remaynder- 18
Tontich add 1
TheSu: is the Prime T9
uotient
Sable of Multiplication serving for the
dividing os any year ofthelord
L.-
bs 19
T91
6 - - 114
 33
3
l17I

## Folio 10 — 170380998X:0119
# Source image: https://digitale-sammlungen.gwlb.de/content/170380998X/jpgs/default/00000119.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 70 lines, status machine
ATable
for thereadis findinis
os the
PrIme Or
GoldenNum ber
for euer.
T (20(39(58(7
2 2T 40 59 78
D
3 22 4F 60 7998
4. 2342 6T8099
5 24 43 6281
6 25 44 63 82
26 4564) 83
8 27 4665 84
9 28 4766
10 29 48 67
TI 3049 68
85
12 3T 50698
(3 32 5F
14 33
15 34
16 35
17 36
18 5
52
5
a
55
70
(9(38(577C
n rosiose soita
0 00d
000000
6 1I 16 2 7 
O
1 1 N) n
t
O
1 W
0 O
4
00
0100000c
7 12 T7 3 8 13 L
8 13 18 4 9 14 19 5 TC
9 14 1O 5 10T5 I 6 II
1015 I 6 TT 16 2 7
TT T6 2 7 12 T7 3
8
1
12) 17 38 T3 18 4 9 14
13 18 4) 9 T4 T9 5 20 15
14) 1O 5 10I5 E 6 II 16
15 T 6 IT T6 2 7 12
1
16 2 7 12 27 3 8 13 18
(7 3 8 13 18 4 9 T4) 79
18 4 9 14 T9 5 10 15
19) 5 10) 15 E 6 IF 16
T6IT 16 2 7 1Z
2
7 12 17 3 8 13 TE
3 8 13 18) 4 9 14) 19
I
4 9 14 19 5 1OT5 E) C
51015 F(6 TI 16 2
6 11 16) 2
7 12 17 3

## Folio 11 — 170380998X:0120
# Source image: https://digitale-sammlungen.gwlb.de/content/170380998X/jpgs/default/00000120.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 59 lines, status machine
The Table
s Primes
Continued.
 1 
n
eA
o
5100
13 18 4 9 14 29
O
O
∞ 14 W0) co 10) W visve
0 O) M N W X
O
0 000
0 O
0 000)00
F(20(3958(77(96 14 (59 5 [20(15IY
2 2140(59789
15 T 6 TT 16 2
O
7
5 2242607998 16 2 7 12 27 38)1
4 23 426T809927 3 8 13)18) 4 91
5(24 43628T)
6 254467(82
26 45(648
82746658.
9 28 4766 83
10 29 4.8 6786
1I 304968(87
12 315069 88
13 3251708G
14 33 53
15 34 5
16 35 52
17 365.
18 3756
19(3857
76
D
18 4. 9: T419 5 1O TC
19 5 10I5 I 6 TT (16)
F 6 IF 16 2 7 T2 1
2 7 12 C7 3 8 13 18
3 8 13 T8 4 9 T4 T9
4 9 14 19 5 2O15 I
5 10T5 T 6 TT 16 2
6TT16 2 7 T2 27 3 8
17
7 12 17 3 8 13 18 4 9 14
8 13 18) 4 9 14195 2O 15
9(T4 T95TOIS I 6 TF 16
10T5 T 6 II. 26 2 7 T2 17
IF 16 2 7 12 17 3) 8 (13(18
12)57 3 8 (1318) 4) 9 (14)19
231O49 14 19(5 (1015
F
0000000

## Folio 12 — 170380998X:0121
# Source image: https://digitale-sammlungen.gwlb.de/content/170380998X/jpgs/default/00000121.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 64 lines, status machine
APble 1o Finde the moveable Feacts For ever
br Jhe Dom: letier es Colden Number.
Domin. Golden Erom Chrictmas Shrove Facte
LCter Nemiber 10Strrove Pand: Cunday
2 5 13 16 6 mects
7 10 15 18 7 mects
2 4 9 12 8 oeets
3 6 11 14 17 0 mecto
8 19
20 mects
day
Febe 5 Mar
Febr 12 Apr
Febr 19 April
Febr 26 Apr
Mat
5 Apr 
2 5. 13 16 6 vects 2 das Febr 6 Nar
4 7 10 15 18 7 wecks
2 9 12 17 8 wceks
3 6 n U 0 rocets
 19
10 meets
1 dais Febr 13 Ape
2das Febr 20 Apr
1days Febr 27 Ape
+dais Mar
6 Apr
25 10 136. 6 vects 2 days Febr 7 Mar 2.
4 7 15 18 7 vects 2 days Febr 1 April 
+69 12 7 8 mechs
5 11 14 19 9 occkes
2 days Febr 21 Apr
2 days Febr 28 Apr 1
20 mects 2 days Mar
7 ApF 2
5 nectes 3 das Febr. L Mar 2E
2 5 10 13 6 wecks 3 days Febr 8 MaE 25
4 7 12 15 18 7 rocetis 3 days Febr. 15 Apr
26 9 17 8 wects
3 days Febr 23 Apr
38 11 14 19 9 nects 3 days Mac 2 ApF 1
16
5 vecks a days eebr 2 Mar 2
2 10 23 18 6 mects 4 days Febr 0 Mar 3
24 7 12 17  vects a days Febr 16 april
6 9 14 17 8 vectes 4 days Febr 23 apr
3 8 H 19 9 wectes 4 days Mar 2 apr 2C
10
5 vecks 5 days Febe 3 Mar 24
27 101518 6 wecks 5 days Febr 10 Mar
1 4 12 25 7 rectes 5 days Febr 18 apr
369 14. 17 8 wecks 5 days Febr 24 apr V
8 1 1
5 13 16
3 apr 2
o occls 5 days Mar
5 vecks 6 days Febr 4 Mar 2
2 7 10 18 6 weckes 6 days Febr u apr
249 12 25 7 vecto 6 days Pebr 18 apr
36 14 17 8 nechs 6 days Febr 25 apr 1
1 19
0 wechs
6days Mac 4 ape 22

## Folio 13 — 170380998X:0122
# Source image: https://digitale-sammlungen.gwlb.de/content/170380998X/jpgs/default/00000122.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 46 lines, status machine
Thelable for the Moreable Fedsts Continued
Dom Colden Rogat: asenC: Whit: Triniiy sadven
Letter Number Sundi dar Sund: Sund: Sund
2 . 5. 23. 16. Apr. 30 May. 4 May. 14 Mays. 21 Dec.
1
20. 15. 18. Payy . 7 Nay. 1 May. 21 May. 28 Dec.
. 9. 12. May. 14 May. 18 May. 28 Tun. 4. D ec. 
7. 6. 1. 14. 17 Mayy. 21 Nay. 25 Tun. 41 TuM. IIDec. 
8. 19.
Nay. 28 Tun. 2 Tun. I Tun. 28Dec. 7
2. 5 . 13. 46. Nais. 2 Mays. y May . 15 Mars. 22 N0v. 217
4 7. 10. 25: 18. 1TaY. 8 May. 12. May. 22. May. 29 Nov. 27
2- 9. 22- 27. M(ay. 25 May. 29 Mays. 29 Tun. 5 NOV. 27
7 - 6 - 21. 14. May. 22 May. 26 Tun E TUM 12 Nov. 27
8- 29 L
May. 29 Tun- 2 Tin. 22 Tun. 29 Nov. 27
2. - 5 - T0. 17. 16 Mayy. 2. Mays. 6 Mays. 16 Mars. 23 Nov. 25
4. 7.15. 18. Mas. 9 May. 13 May. 23 Mais- 30 No2. 20
C. 6. 1. 9. 22. May. 16 May. 20 May. 30 Tum. 6 Nov. 28
3 - 1L. 14.. 29. Mays. 23 Mays. 2.7 Tun. 6 Tum. 13 Nov. 26
d
16:
May. 30 Tun. 3 Tun. 23 Tun. 20 N0v. 28
Apr. 26 Apr. 30 Mais. 10 May. 17 Nov. 29
2 - 5 - 10- 13. Mars . 3 May. 7 Mays. 17 Mars. 24. Nov. 29
4 7. 12. 25. 18. May. 10 May. 14 Mays. 24 Mais. 31 Nov. 29
1. 6.9. T7. Mays. 17 May. 21 May. 71 Tun . 7 Nov. 29
3. 8. IF. F4,. 19. May. 24 May. 28 TWI- (7 Tun. 14 Nov. 29
5. 16.
Apr. 27 May. F Mais: 11) Mays. 18 Nov. 70
2- 20. 13. 18. Mars. 4 Mais- 8 Mays. 18 May. 25 Noy. 70
F. 4 . 1. T2. L5. Mays. 11 May. 25 Mars. 25 Tun. 1 Nov. 70
6. 9. 14.. 11. Mar. 18 May. 22 Tun. 1 Tun. 8 Nov. 70
3. 8. 11. 29. Mays. 25 May. 20 Tun. 6 Tun. 15 Nov. 30
5. 16.
Apr. 28 May. 2. Mar. 12 Mar. 19 Dec. I
2- 7- 20, T7. 18 May . 5 Mays. 0 May. 19 Mar. 26 D ec. 2
- 4- 12 - LG. Mays. 12 Mar. 16 Mar. 26 Tun. 2 Dec. 1
3. 6. 9. T4,. 17. Mays. 19 May. 27 Tun- 2 Tun . 9 Dec. 1
8. I1. 19.
May. 26 Mai. 30 Inn . 9 Tun. 16 Dec. 2
5- 13- 26. Apr. 29 May- 3 Mar. 13 Mars. 20 Dec. 2
2 - 7- 10. L8. Mais. 6 May. 10 May. 20 Mar. 27 D et. 21
L. 41. 9 - 12. L5. Mars. 13 May. X7 Mar. 27 Tun . 3 Dec. 2
3: 6- T4 - 17. Mars- 20 Ma. 24 Tin . 5 TuM . TODec. 2.
H. 19. Mars. 27 Mas. 31) Cun. 10 tm. 27 ∞ec. 2

## Folio 14 — 170380998X:0123
# Source image: https://digitale-sammlungen.gwlb.de/content/170380998X/jpgs/default/00000123.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 67 lines, status machine
14
Plable Continued Cor  moveable Termes
Dom)Oolden Kaster P acter Trinit Trinit
Nuember
ad
d
Terme Terme Terne Terme se
besins endo beomo ends
2. 5. 23. 26 Apr. 12 Mar. 8 Nar. 26 Tun. 14
7. 20. 25. 26 Apr. 19 Mar15 Tun. 2. Jun. 2 P
2. 4. 9. 22. Apr. 26 M 2Y. 22 Tuv-9 Tun. 2E
3. 6. 21. 24. 27 Nay. 3 Mar. 29 Jun. 16 Fulr. 5
25. 23. 26 Apr. 13 May. 9 May. 27 Tun. LE
4157. 10. 25. 18 Apr. 20 May. 26 Tun. 3 TuM. 2.2
29, 12. 27 Apr.. 27 May. 23 Tun. 10 Tun . 29
1Z. 6, 22. T4 Mar. 4. Mar. Z TuV. V7 TuIV. C
8 20 May: It Tun. 6 Tun. 2.4 TUIy. 23
2 5. 20.27. 26 Apr. 14 May. 10 Nay 28 Jun. 16
A1. 17. 1B. 28 Apr. 22 May. 17 Tun. 4. TMm. 2
1. 6,9. 22.7 Apr. 28 May. 24 Tun. 11 Tun.. 3C
3. 21. 24, 29 Hay: 5 MaY. 32 TUn. 28 Tuhs. )
26
NCay. 12 Tun. 7 Tun. 25 Fuly. 1.
Apr. 8 May. 4 May. 22 Tun.. 10
2. 5. 20. 23 Apr. 15 May. 1 May. 29 Tun- 1
407. 12, 25. 18 Apr. 22 Mar. 18) Tun. 5 Tun.. 2
L.6.9. 27 Apr. 29 Mar. 25 Tuin. 12 Tutr. 1
3. 8. 11. 4.19) May 6 TuI. 2 Tun. 29 Tuly: d
5. 26. Api: 9Mar. 5 May. 23 Tum. . 2
2. 20. 23. 28 Apr: 16 N aY. 22 Mar. 30 TMM.. 18
N
l
p
L
e
dd:
d0
dA B 1
0L. 1
P d. 3 ls
d
d
1D
0
e
ad
a e
Di
2.47. 12. 15. Apr: 23 Mar. 29 Tun. 6 Tun. 2510
6.9. 14. 17. Apr. 30 Nar. 26 Tnn. 13 Tuliy. 2
3. 8. 11. 19. MCar. 7 TIn. 2 TUI. 20Tuly. C
5. 16. Apr. 20 May. 6 Nay. 2.4 Tun. 12
227 20. 13 18 Apr. 17 May. 13 dlay. 31 Tun. 29
e
1
ud
2. 4. 12. 15. Apr. 24 May. 20 CM. 7 Tun. 26 _ R
1
3. 6. 9. 14. 27 Mays. 2 May. 27 Tun. 24 Tutr. 3 2 d4
8. 1L19. May. 8 TUN. 3 TIn. 22 TuH. 208
5. 27. 16. Apr. 1 Mayy. 17 May. 25 TIM. . 23 2 18
21- 7. 2018 Apr. 28 Nay. 24 Tun. 2 TIIM.. 20 
1. 41. 9. 12 25. Apr.. 24 elary. 2.2 Tu. 8 Tun.. 275.FX
3. 6- 14. 17- Mas. 2 May. 28 TUN. 25 TuI. 4
8.X1. 19. (alas. 9 cum. 4. Tum. 24 Lut. 1
1t
Lettes

## Folio  -  — 170380998X:0124
# Source image: https://digitale-sammlungen.gwlb.de/content/170380998X/jpgs/default/00000124.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 44 lines, status machine
    e v
ATable of the Fixed Feasts, and orher
Solemn Days 1o be observed in iBe
Church of Enslando
AII SundayS.
TFW-gears. day, or Circumcision - Fan. i
LNTvelf day, or Epiphany
Marcyrdom ot R. Charlest.-
Fan. 5
Fan. 30
Purificarion ot che Virom Mary - Febru. 2
LADY-P AY, or che Annunciation
oF chevirem Mary Mar. 25
Mark F~anE.
Aprit 2E
May day, or Phillip and Facob May e
Birch and recurn ot Charles II. May 29
MIDSUMMER or ZohB Baprist. 
fames Apostle
Bartholomero Apostle
Marhero Apostle
Fune 24
Falus 2E
AUg. 24
Sepe. 2X
MTCHRELMAS, Or Mich. Archanset -- SepF. 29
Lute the F. Vangelist
Simon aud fude
Au saints.
Porder Frealon
Andrero apestle
Thomas Aposle
Ost0. IB
Oct0. 28
10V. 21
0D. 5
100. 30
DeC. 2F
CFTRISTMAS, or Birib of our Lord Dec. 25
DE. SlephenDeC. 26
de. Fohn FvanG. Dec. 27
Innocens Edec. 28
3
Ochet

## Folio  -  — 170380998X:0125
# Source image: https://digitale-sammlungen.gwlb.de/content/170380998X/jpgs/default/00000125.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 38 lines, status machine
Other Remarkrable DayS
aleniine
Equal day and nish.
idt. Ccorge
Longelt day, Or Bayn
drrichim
A. AMaS
Rgual day and niphe
Shortes day
AITLLAAr TERM
D FgInS
DEnds-
and hach Four Reca
7. Octab. HTil.
2. Ouind. HIil.
3. CraIC. PuF.
4. Oa ab. Pur. 
ANCHAEEMAS TFR M
Begins
Fnd.
and hach C
X. Tres Mich.
20 MenC. Mick
3. Crat. AM.
4. Cral. M21
5. OEt. M2
6. Qur. Ma
c
15.
Febr. 2C
1.
e 1V
1
3.
B. 20
1t. 
10
Lue

## Folio  -  — 170380998X:0126
# Source image: https://digitale-sammlungen.gwlb.de/content/170380998X/jpgs/default/00000126.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 6 lines, status machine
1
i
eeeue
111 1t
1
1t11t1ttt

## Folio  -  — 170380998X:0127
# Source image: https://digitale-sammlungen.gwlb.de/content/170380998X/jpgs/default/00000127.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 123 lines, status machine
14
LY
12
a ATable sor the ready finding rohat Sion theMoon is in or shall be for euer
Androhat part ofMans body evers Sion doth govern
E(27(26(25(22(23(22(22(20(19]28 (27 (26)15 (14)13112)er (10(0(8[71615
a
2 L 27 26 25 24 23 22 2C 20) 19 18 17 16) 15) 14) 13) 12 TC 10 9 8 7 6 5
3 2 T 27 26 25 24 23 22 2F 20 19) 18) 17 16 15 24 13 12) TT 1O 9 8
4 3 2
5
A
3
LicT
2 I
65 4 3 2
6
8 7
8
S 4. 5
7
6
26 25 24 23 22 2c) 2019 18 17161514 13 1Z TT 10 9 8 7
27 26 25 24 23 222120 19 18) 17 16) 15 14 13 12 TT 10 9 8
4
6
17
l27 26 25 24 23 22 21 20 19 18 17 16) 15 14) 13 12 T1 10 9 8
2 C 272625 24 23 2,2 25(20) 19 18 17 16) 15 14 13 TZ) EI 10
d
5
6 5 4) 3 2 X27 26 25 2425 22 21 20 19) 18 17 16 15 14) 13 12 CF 10C
7 6 5 4 3 2 Y2726252423 22 21 20 19 18 17 16 15
10 9 8 7 6.
14 13 12 TI 10
5 4 3 2 C 27 26 25 24 23 222F 20 19 18 17 16) 15 14 13) 12) T1
4 TT 10 9 8 7 6 5 4 3
12 TE 10 9 8
15 13 12) TF 20 9
7
2
6 5 4 3
8 7 6
5
127 2625 241 23 22 21 20 19 18 17 16 15 14 13 12
2 Y 27 26 25 24 23 22 2C 20 19 18 17 16 15 14 TZ
4 3 2 X (272625 24 25 22 2T 20 19 18 27 16 15 14
71413)12)FE 10 9 8 76 5 4 3 2 T(2726 (25(24)23 22(2C2029(18 (17 1615
15(14)1312) TT) 20 9 8 7 6 5 4 3
2 1. 2726 25 24 23 22 21 20 19 18 17 TC
1816T5) 14) 13) 12) T1(10)9 8 76 5 4 3 2 T (2726 25 24 23 22 21 20 19 18
1
10C7 16 15 14) 13 12 TF 1099 8 7 6 5 4 3 2 Y 27 26 25 24 23 22 21) 20 19 16
2 18)17 16 15 T4) 13 TZ TT( 20 9 8 1 6 5 4 3 2 T27 26 2524 23 22 2T 20 20
13
19)(18) 17 16 25 14) 13 12 TT 10 9 8 7 6 5 4) 3 2 1 27 26 25
2019 18 17 16 15 14) 13 12 11 109 8 7 6 5 4 3 2 Y 27 20
24 23 22 21
25
2C 20 19 18 17 161514) 13) 12) 1T 2098 76 5 4 3 2 1 2726
22 22 20 10) 1827 26) C5 14) 23 T2) TF 10 9 8
7
1623]22 2520)19) 18)17 16 15 14) 13) 12 TT(10 98 76 5 4 3
Can: Oct. 8 2423 22 21 2019 18 17 16 15 11 13 12 T1 10 9 8 7
19 26 25 24) 23 2221(20)19 18) 1716) 15) 14) 13) 12 11) 109(8 7 65
26 25 24 23(22]2120(19)18) 1726)15) 14)23) 12) 41 20(9 (87
4
25 24 23
I
27
2C
2
22
24 23
I 27 26 25
2524 23 22 2T20 19 18 17 16) 15 24) 13 12 TT) 10 9 8 7 65 4 3
2127
241 23 22
6 5 4. 3 2 X 27 26 25
6 5 4
2
3
e
26
2
2A
23
2C
27
C
Head de Face
8Necte de Throat
Uems strouldees
ana Hanas
6.
Breast and
somact
eart and
Back
l
Borvels d
Belly
2
Reyno di
Loyno
1
Secrets
de
tegho
nees
Leg95
Hect
FCOr: NO 3
Mlarch
December
AprI
Aruisutt
Scplembe
V
th
est
1M.
1

## Folio  -  — 170380998X:0128
# Source image: https://digitale-sammlungen.gwlb.de/content/170380998X/jpgs/default/00000128.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 32 lines, status machine
1
b _ hee k e c. e  
The2 se of this Table.
c. CFek ehc name oF the Month in the lete-
Dhand Margene, and eviding pour FyC EO
(1) in the Table, find out the day of che Monch
prhich rou MalI Aind cicher abore, or beneath in
thac Column.
2. From thac day ot che Monch, guide pour
ere back cothe Number in che letr-hand MargenE
thac Rands against ic in che Column under che
Ticle (Day of the Month.)
3. From ehac Number guide pour Byc 10 (1)
in the Table, and in thac Column And rhe Number
ehar is the Number oF che Prime For thac TCaF, and
trom chence puide pour Rye co che rixhthand
Margent, Coharerou jour detire.
Fxample.
The Tenth day oF May, 1665. I desire toknom
Wrhac Sion che MoonIS, ESC.
1. The Prime For thac Tear i5 13.
2. TEnd May in che lefc-hand MargenE, and
uidins my Fycto (1) inthe Table, and in thar
Columineo ro che Day oF ihe Monch, LErins my
Eye back r0 (27) in che detr- hand MargeHE.
3. Ilook For 13 amone che Primes, and From
thac guidemys Fycco (1) in che Table, and Anding
theatorelaid Number (17 in thac Column, 1d0
trom chac, suide my Eye co che richc-hand Mar-
gene, and find chat che Hoon upon the Tench ot
May, 1665. is enerins into Leo Sb, and BOVerNS
che Borels and Bell70

## Folio  -  — 170380998X:0129
# Source image: https://digitale-sammlungen.gwlb.de/content/170380998X/jpgs/default/00000129.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 57 lines, status machine
 V d 
AT able Bemine the time of ehe Moons com-
ens tothe Sonth, and quantiey of her sinins.
2he IAToons Moons
asvons sourhine ase for
ageo e5 sim. ber stii.
C 16
6
y
18
19
20
2F
22
23
24
O 25
+
20
es
in
CZ 28
O 48
F
4
4
6
O
a
8 oc
8
AC
20
14 29 11 V
25
3
22
tc
24
na
1
The use of ehis Table.
Ind theMoons asc in the sirst Column; and
nexe against che lame rorards cheriehe hand,
35 che cime ot her comine to che South; irhich
TromtheNem Hoon to che FuII Moon, is alivays
in che Atternoon, buctromthe Fullrothe Nem, ic
is in chemtornins.
Fxample.
May 12. 1072. ChcMoonIstouiceen days olds
erhich CEnd in ehe firs Column, against which.
Forrards che riphe hand in che second Column is
YF. 12, Wrhich being beforethe FuII oF ehc Moon,
conclude Thatthe Moon commes to Touch May 12.
567 T. aEFE BClock aE Niphr, and J2 Minures pal.
u
V

## Folio  -  — 170380998X:0130
# Source image: https://digitale-sammlungen.gwlb.de/content/170380998X/jpgs/default/00000130.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 26 lines, status machine
20 knou horu lons the Moon Shinerh.
Enter the third Column with thC MOONS aeC,
and againstit, on che lete hand, vou have cherime
oF her ining, Which aIl che rime ot her Fncreate,
beins added to che hour ot sun rilins, sires the
eime ol her ritine: Bur if added eo the cime ob
Sun sertins, siresthecime ot her serrins.
But after ihe Full.
Talce the time ot her Mining From che Suirs ri
sins, and ic sires her risins; and chenrate che
lame tromthe Sun Petrins, i sires rhe time oF her
Tercins.
Example
MCay 12, 267T. the Moon is rg days old, and I
find Ex hours, 12 minures, For che time ot her
Miming, (ehrich beins added eo che Suns rising)
upon checrelt et May. 1672. (viz. Tour hours)
matres z oF che clock, r2 minutes, Cor che rime oF
theMoons rilins che next Mornins.
Rgain cochelaid IF hours, r2 minutes, add
Bhours trom che Sun serrins, it sires y HOUrSi
L.2 minures For the cime ot his serrine.
Thouohthese Rules are not alcogether exact;
vec chey come near enoueh checruch, For ordinary
ulc.
arat

## Folio  -  — 170380998X:0131
# Source image: https://digitale-sammlungen.gwlb.de/content/170380998X/jpgs/default/00000131.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 42 lines, status machine
Aride Table ot cerrain Hlarens in and abour. Fng-
land, Wherebr may be lnomn whac noon mates
2 FuII-Sea in any oF che laid places; and hon
many ho. and min. are to be added eo the time
ot theMcons comine toche sourh For che rime
OE High- avater.
SonttDuconborongh, Sonthamton Poris- HL. M.
and mouth, iste of Wicht, Spits, Ken - 0 0
Norch cistr Knock, halF. Tide at Dantirik.
S by W, Rochester. Maldon, aberdeen.
NBy F. Redband. West end oF che Nour, 0 45
Blackrait.
S S W Gravesend, Dorons, Rumney, Te
NNF vet, Sity halte. tide, Blackness, L 30
Kamkines, Senehead.
SW By SiDundec, Sc. Andreos, Lisborn
N E BV N SC. LucAS, Bell IstC. Hoty Iste.
SW IFondon, Timmonth, Haritetool.
N F. IWhirebay. Amsterdam, Ga scoign, 30
Bricain. Galicia.
SWBy U Barrwick. Zlambrough.he
NEBy F linston bay. Burdeux, Oste
W S W
Flahine. Founine(5.
Scarboroush quarcer de, L
bebtc
F N F inas, Severn, Horkhave, Onngarum,
NTounts. Bay. King sale, Calice. Creete
WV By S) Nerocastle Humber. Falmouth. Sal
Eby N Gy. Darrmonth, T0. bay, St. Mal
Eas
and
NeA
10205, Foy, C arsy. L. 12.
elimonth. Wegmouth. Null
4
3
Davids head. Ancverp. Landy6
Folms ot Bristol.
Fby S forisol Fouless AE chC DEAVE
e
1

## Folio  -  — 170380998X:0132
# Source image: https://digitale-sammlungen.gwlb.de/content/170380998X/jpgs/default/00000132.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 36 lines, status machine
ESE. Pasilford, Bridgewarer, Lands-end, (AI. HI.
W NW Wacerford, abermoricke. Cape- Cleer, 7. 30
Texel.
SF by F seorcland, Peterpori, Harstewo, uie
NWbyW Clasue, S. Magnes. Touch, Dublin, 8 15
S E
N W
Lambay. Macenels Cape-
1P00t S. Hellen, Cames
Fair-Istes, Kilden, Man- Iste. 18
Bass. Istands.
SE By S(Accales, Laisto, Norrh de
NW By H Foreland.
SSF. (Tarmouch, Dover. Parwvic
N NW de Luce, Calice Rond, Bullein
Sby E IRe Winchelsey, Force Thames
Nby W Xhodes.
Thelse oF the Tide. Pablc.
Example.
Ay 12, 167T. Twould Hnom che FuII Sea
VL ac London.
c. By che Foregoine Rules I Find the NOOM
comesro South ae Ls oF the clock, and L2 Minutes
Ppast, at NighE.
There L Seck For London in ehis Table, WHere
PEna chac a S. WV. Or N. F. Hoon maties a FuII
Sea, and on cheriehc.hand L find 3 hourso minutes,
rhich mult be added ro che Moons Souchino: ThAC
is 3 hours, ominures, added t0 rE ho. 12 mino
makes 2 a clock and 12 minures ERC RexE MOrninO,
Cor Hioh Warer ac London. Bridee.
Sochactor anr place and doy, the hours and
min. inthe Tabile, are cobe added eo the NOOnS
Southine, irhich sives che erue cime of High-
pacex Fex chat place and dos.
BC

## Folio  -  — 170380998X:0133
# Source image: https://digitale-sammlungen.gwlb.de/content/170380998X/jpgs/default/00000133.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 86 lines, status machine
Thetime ot the suns Risino and Serrino
D) fannany i l’obruarr 1) Mcarch.
e
e
o Sun sun  Sun Sun ( Sun(sun
rises. Pets. riles. TerS. ( rises.  TeTS.
ad
e
2
4
s
8
10
H. M C NC. (I H. MC ET. M,  HI. AL. (H. MI.
d
9
3 5F(7 184 42 6 20)5 40
8 835c(17 27 4 43 6 185 A2
8
8
8
8
537 254 45(6 26]544
63 54 3 234 47 6 24 5 46
A
8 0
50
7 56
3 55
3
14 
15
5+
3 214 49 6 F1(5 49
356 7
94 5T( 6 8(5, 51
3 58) 7 74 58 6 65 54
4. O
4 +
7
7
5455 6 45 SC
3
4 57 6 25
58
4 3)(7 2(4 596 660
XF l 7 554 5
Z
4
6595 XI 5586. 2
6 6 575 3 5 566 4
7 52 4 8 6545 61 5 546O
7 5T4 96525 8 5526 E
504 10(6505 101 5 506 70
16 3 484 X2 6 485 +2 5 48 6 F2
27
18
19
20 
27
7 46 4 24 6 465 24. 5 46 6 24
7 44 4 166 445 16 5 44, 6 16
7 43 4 27 6 425 +8 5 426 18
7 42 4 19
39 4 21
6 405 20 5 406 20
6 38522 5 38622
22 7 37 4 236 365 24 5 36 6 24
23
24
35 4 246 345 265 34 6 26
7 344 266 325 28 5 326 28
25 57
26
7
32 4 28 6 305 30 15 30,6 30
304 50(16 295 311)5 286 32
27. 7 28 4 3T1 6 275 3315 26) 6 34
28 3 26 4 34(6. 245 36) 5 24 6 36
29  7 24 4 36622
30 7 224 38
3+
7 20
5 226 38
5 20 6 4
5 1816 42

## Folio  -  — 170380998X:0134
# Source image: https://digitale-sammlungen.gwlb.de/content/170380998X/jpgs/default/00000134.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 129 lines, status machine
e
Throushout the Whole Tear.
April. ) May. II.
0 Sun Jhun dun (Sun ( Sun (3
2
3
4
5
10
1
12
13
14
15
16
17
28
29
20
27
22
23
24
25
26
28
29
rises. PeFS. rIICS., PCLS. riles. PerS.
A. M_ N. IH. NC. E. NI. TI. M H. MI.
5. 166 44
5 146 46
5 126 48
4 19(7 42 3 42 8 18
4 17 7 43
4 15 7 45
5 10(650 (4 147 46
8(6 52 4 X2 7 48
5 66 54 4 22 7 49
5
5
5(655) 4 107 50
3657
26 58
07 0
4 577 3
4 55 7 3
4 53
A 517
4 497 IF
4 47
7 13
4 45 7 15
4 43
7 27
4. 4L 7 19
4 39 7 22
438322
4 36 7 24
4 34 7 26
4 32
7
28
4 307 30
4 28 7 32
4 27 7 33
4 8 752
4 3 7. 53
4 6 7 54
4 4 7 56
4 37 57
4 2 7 58
4
O8
3 59)8 L
3588 2
3 578
3
2
53
8
e
3 528 8)
3 5F8 9
50(8 10
3 49(8 XF
30 4 21(733
3 428 18
3 42 8 18
3 428 19
3 4C)8 T9
3 4+(8 29
3 4+8 29
3 42)8 19
3 41(8 1G
2 A2 8 EG
3 428 19
3 A1(8 29
3 AF 8 X9
3 458 29
3 A1 8 19
3 AT)8 1G
3 42 8 18
3 42 8 18
3 428 T8
3 438 1.
3 448 1O
3 44 8 2C
3 48(8 12 3 45
3 478 13
3 46(8 14
4 25 7 35 3 458 TC
4 237 37
3 428 19
3568 4 3 418 19
3 55.(8 5
2
3 45(8 T5
3 44 8 26
43
8
3 46
3 47
8 T5
8 24
8 13
3488 12
41)
B 1Y
3506 13

## Folio  -  — 170380998X:0135
# Source image: https://digitale-sammlungen.gwlb.de/content/170380998X/jpgs/default/00000135.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 74 lines, status machine
Thetime of the Suns Rilmo and Secrine
O
fuly. 1 Aueust. ()Seprember
( Sun ISun ( Sun Sun I Sun I Sun
 rises. PetS. riles. Pets. rises. Pets.
C
2
HI. AC. A. AC. IIH. MTHT. AL. H. AT. H. ML.
3 57(8 9(l4 35 7 265 356 25
3 51(8 84 367 245 376 2:
528 8 4 387 22 5396 21
4 3 53
5
8
9
10
TF
2
13
1A
26
17
18
19
20
2L 
22
23.
24
8 74 407 205 4F6 19
3. 54)8 6 4 417 1915 436 17
568 4
5
3 58
3
52
4 43(727 5 45(625
8 34 457 15 5 476 13
8 2 4 47 7 135 496 2L
8 X(4 487 C2( 5 5F6, G
4 0(3 94 50(7 10)55316
4 2 7 58
4
3
7 57
4 527 85 566
4 54 7 6 5 586 Z
4 4 7 56 (4 567 4 6 06 C
4 67 54 4. 587 2 6 2 5 58
4
7
7 53
S
07 0l 6 415SC
4 8(7 525 26 58 6 655
4 207 505 4(6561 6 955L
A TF 7 495 66. 54 X X15 49
4 12 7 48 5 86 52 6 235 47
4 14 7 46 5 10(6 501 6 1515 45
4 15 7 45 5 226 48 6 27(5 43
A 17 7 43) 5 24(6 461, E 195 4L
4 187 42
5 166 44 6 255 39
4 207 405 18(6 426 235 37
25 4 22 7 58(15 206 4086 2515 3
26  4 237
27
37 5 226 3816 275
A 25 7 35 5 246 3616 2953
28 (4 27 7 335 266 34 36 31520
29  4 287 32 5 286 32 +6 33 5 2
304 307 305 306 30)16 3552.
2
+327. 281 5 32(6 28

## Folio  -  — 170380998X:0136
# Source image: https://digitale-sammlungen.gwlb.de/content/170380998X/jpgs/default/00000136.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 102 lines, status machine
chroushout che Whole Year.
October. ) Novemb. ((December
Sun (Sun ( Sun Sun  Sun (dun
2
a
6
3
20
T1
x2
1
24
15
26
T7
18
29
20
2.F
22
3
24
25
2C
7
28
2.9
30.
rises serS. riles. Pets.  riles. PeES.
H. ML MC MI. FI. MC EL. AC.  IT. MT II. MI.
6385 22 7 38 4 228 16 3 44
6 405 20
7 39 4 22 8 163 44
6 425 18)7 42(4 19((8 57
3 43
6 445 16 7 42 4 18 8 X7 3 42
6 465 24 7 44 4 16 8 T8 3 42
6 48(5 X2 7 464 F4 8 183 42
6505 20 7 47 4 238 18 3 43
6525 87 494 TF 8 19, 3 4F
6 545
6
7 524 9
6565 47 52 4 8
6 585 2
615
O
2 4 58
44 56
64 54
8 4 52
104 50
T2 4 48
7 54 4 6
7 554 5
7 57
e
8
S
8
58
4 3
4 2
8 19)3 aC
8 293 AC
8 193 41
8 19.3 42
8 193 41
8 193 41
04 08 193 4L
2(3 59) 8 28. 3 42
3357
8 T8(3 42
4(3 56 8 28, 3 42
7 144. 468 5(355(8 17343
7 26 4. 44
S
3 53, 8 273 43
7 18(4 42 8 8(352(8 263 44
7 204. 40((8 93 5F) 8 16,3 44
11
22 4 38
23 4 37
7 25 4 35
7 27 4 33
7 29 4 37
7 37 4 29
I
33 4 27
7 34 4 26
7
36 4 24
18 10(3508 153 45
8 15(3 49 8 143 40
8 X23 48 8 14 3. 46
8 123 48 8 13, 3 A7
8 23(3 47 8 12 3 48
8 243 46 8 123 48
8 143 46 8 XT(3 49
8 25
3 45 8 20357
935E

## Folio  -  — 170380998X:0137
# Source image: https://digitale-sammlungen.gwlb.de/content/170380998X/jpgs/default/00000137.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 33 lines, status machine
 Z able Bermine the lenet of the loncese
Artificial Day, in alt places from the
Equinoctial 10 the Poles of ihe Worid.
Heig. )Long. day(Feic. pCong. day (Feis.) Longest day
Pote. II. AL. (Pole. HI. AT. Pole. D. HI. M
0012 004715 42168 42Or16
06 22 2046)15 52(69 541625
12 12 42 4916 0070 641340
16 12 585016 1071 740000
20 (13 125216 2072 820636
2413 3052(16 3073 890458
27 13 4253 56 4274 961700
30 (13 56 5416 5475(104O1O4
32 14 06 55 17 0876 120072)
3414 1656 17 2277 C16T422
35 24 22 57 17
3678122 1706
36 14 265817 52791270955
37 14 34 5918 1080(1340458
3814 38 6018 3031(1393136
39 14 44 62 18 54 82 1450643
40 14 52 62 19 20 831520206
42 (14 5863 19 5084 1560303
42 15 04 64 20 2485 1610523
4315 12 65 2T 10 56 166IT23
44 15 18 66 22 28 87 17T2147
4515 2666224 0088(1760529
46125 34 67 2462y5 89(18+2158)
90l1870639
5
neti
net
Epst

## Folio  -  — 170380998X:0138
# Source image: https://digitale-sammlungen.gwlb.de/content/170380998X/jpgs/default/00000138.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 41 lines, status machine
The Follorrino TABLEC
ArC OFexcellene use, and doreadily discore
exact cime oF che Nem Moon, Pull Moon, As litewise
che First and Second duadrats; And consequencly
hererue AgC
And chis trom chie rear oF our L ord 1673, 10 the year 1700
E X A M PL F.
In che MonetHOF April 2673, and ché cAth day oF che
Monech, che Table For chac vear, Wvill discover, over
acainst che laid Monert, April
First. Thac che Nem Moon happens co beche txch dayoF chac
Monech, andche 13ch hour ofthat day: Thac 15, 1C
Minures Past e ofche Clock ac niohe (remembrins al
varschac che dares are eobe accompred From NoOn.)
Secondly. Phacche Airc Ouadeac is che 13Th day, 10min.
PaCtO ac nighe.
Tbiraly. Thac The Full Moon is che 20Ch day, 1L min. paA
12 aC niche
Fourchly. The Second Ouadrat is che 28ch dar. LMin.
DaCt L2 ac niote.
Fisibly, And LasIV, Decaule ehe Moon changes on che
Sixch dar, and 8 added c0 6 makees 14, cheretore chC
Moon is B dares old, upon che Caid sach dar ot April.
Bur iF you willbemore exact, rou must AccompE
Lde lel
(First Ouarrer OFche MOOn.-- 7 - 09
FuIl Moon.-.-
L aC OuarE.
Time FrOM MOON EO MOOn--29.
An Explanation of the double Numbers in the Table
F X A M P F F.
Enthe ArK Ouarcer oFche Moon, in che Monech ot May
incheyear 1674. C And che 2 NumberS, 3i2.
d. b. M.
2 12 45
32 16 30
he ian nreot 1o clacnee lata monem ota)
che Axst quarter oF cheMoon happenech co be boch upon che
Exst day, 12ch hour, 43chminure, And likemise uxon che
3Tch dar, 16 houres, 30 m. OFche lame Monech. Theirhich is
eobe (0 read, and 10 underAood in any ocher ycar or monch.

## Folio  -  — 170380998X:0139
# Source image: https://digitale-sammlungen.gwlb.de/content/170380998X/jpgs/default/00000139.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 55 lines, status machine
Vem 3
T. Quar. FWIb D, 2
a
O. TI. M. (D. TI. M. D. IT. M. D. FI. NI
Fanuar) (7 14 0 (15 15 3722 0T 102905 2C
Februa. (5 06 25]13 20 5820 120627 23 12
March  00 2215 04 062T 23 3829 18 12
Aprit (5 23 20(1309 1420 12 1F28 12 L
May
5 23 11(12 24 1220 0T 3528 10 26
Funo (t 07 101O 2F05 28 25 5726 1820
fuly
Aueust
3 14 091006 382506 592603 42
3r
20 4
1(5 29 2426 22 2124 25 OY
Septem. 29 15 257 ZF 17 (5 13 4222 22 22
October (29 3 587 55715. 4 2522 4 A5
Novem. 27 19 37(5 F59(13 18 620 TF 47
Decem. (27 9 27(5 22 33l13 6 19(19 20 59
167L
Nen d c. Duar. FUIb D 3. QW
D. TT. M. D. II. HI. D. H. M. D. H. M
Fanuarr (26 08 414 26 27, LZ 27 22180909
Februa. (15 03 +53 095F1003 15 26 23 47
Marcb (26 28 524 22 44, TF 12 45]18 16 12
Aprit (25 09003 07 199 22 2617 09 25
ay
12 459 06 27 27 02 54
30
24 21 O2 3E 16
f. 1.I)
22 24 2229 04 247 08 405 IF32
Aueust (20 2F 5827 24 475 23 1224 X5C
eptem. (19 0 526 5 04 25 49 12 24 25
October (1825 4025 22 474 8 15+2 + 9
Novem. (17
3
724 19 33 F 18(70 945
Decem. 16 17 14: 4 15 542 27 267 17 14
Ma
A
M
s
sut
e
Ma
A1
Ma
f
S0
O
N
De

## Folio  -  — 170380998X:0140
# Source image: https://digitale-sammlungen.gwlb.de/content/170380998X/jpgs/default/00000140.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 39 lines, status machine
New D
2. Duar. FUII 3 (2. Dwat
D. FI. MI. D. FI. ML. D: FI. H. D. TI
anvarYIS 93623 72 26E7 22d 6
FebrHa. 24 3 4 (22 6 38NIOFWII 76 9
c77 205.
Maroh (E5 20 5023 22 2730 18 54
Aprib 24 23 2822 8 152823 416 20 35
May 24 4 232C 24 2128 6 186 L 1O
Fune 12 27 2619 79 4926 25 344 27 2L
Fuly 12 4 1618 233T26 2 474 20 2L
usust 10 25 4627 4 3924 16 253 3 27
Seprem. (5 22 5415 12 4423 8 30+ 1957
October 6 7 4715 X X123 2 2232
+1
x 47
Novem. 6 27 241327 622 21 8,29 13 27
Decem. (6 4 1013 12 23]2F 25 228 22 49
16763
Nem D 1. Duar. FuIb D 2. Qua
D. FI. M. D. H. M. D. FI. HL. D. FI. N
fanuary 4 26 33+2 85720 65827 C
Februa. 3 0 6 391F 4 43 16 2F 5625 22 58
Marcb (3 22 722 0 4319 7 925 2050
Aprit 2 24 XTIO 17 4(7 14 5924 6 40
May
(3x 21 2620 6 716 22 2723 18 29
Fune 13 27 188 27 3625 5 2622 8 44
fuly
7 22 2314 (3 2322 033
30 0 37
Ausust 28. 9 326 2 59T2 23 2(20 1810
Seprem. 26 23 564 7 48F 2T 3229 2234
October 26 3 393 24 15 EF 2 3919 6 4
Novem. (24 19 522
Decem. (24 6 14=
0 69 20 49180 2
X4
6 579 26 4(27 15 5

## Folio  -  — 170380998X:0141
# Source image: https://digitale-sammlungen.gwlb.de/content/170380998X/jpgs/default/00000141.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 46 lines, status machine
16
s
Nem D T. Quar. FUII D 2. Qua
D. EI. H. D. FI. M. D. HI. M. D. FI.
PanuarY 22 77 3030 3 F8 TF 16F6 2
Februa 2F C 2728 2F GF7 14 17 EA EF TV
March (22 14 530 27 598 19 815 17 19
Aprit (2C 7 5329. TF 107 6 3013 22 30
May 20 22 3429 5 96 25 2523 5 20
unC 1913 1527 13 234 22 45 EE 14 LL
Fuly
9
3 357622 564 5 30TE L 40
o
+
Aucust 17 19 525 4 1232 0 259 1622
Seprem. 16 9 1823 FF 5730 8 448 9 43
Octaber 15 23 222 27 5129 22 498 4 3.
NoveM. 14 ZF 52F 2 72)28 13 467 0 2
Decem. (13 22 820 13 2328 10 566 26
26
38.
Nem D T. 9uar. FuI D 2. Quat
D. FT. M D. FT. M. D. EI. M. D. H. N
Fanuary 12 + 2YY9 33627 6 145 13 4.
Februa. 20 28 5217 29 58260 204 4 22
DCarcB (T2 5 24 59 22 3427 25 515 24 33
Aprit (10 26 2828 8 826 4 303 2T32
May (1O 2 5078 + 2925 24 4+3 2
Fune 8 25 252627 4423 22 40(30 12 30
fuly 8
9 5216 8 1823 6 2(29 212
Ausust (6 20 3+24 20 57 2F 13 2628 10
Septem. 5 22 4+23, 7 3019 2F 5227 TA0
October 5 5 722 26 419 5 826 20 52
NoveM. 3 2F 210232017 20 5325 1730
Decem. (3 TT 24150, 6 3977 T2 2525 1433
Re
M
AF
M
t
S
O0
A
D

## Folio  -  — 170380998X:0142
# Source image: https://digitale-sammlungen.gwlb.de/content/170380998X/jpgs/default/00000142.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 39 lines, status machine
Nem D (2. Duar. FUI 3 2. QHa
D. II. MI. D. HI. M. D: H. M. D. H. 3
Fanuary 2 0 178 25 2016 6 124 9
Februa. ONeW)y 2 2625 0 2823 2 2
March
April
May
i
20 488 25 47 26 26 824 15 15
5 32
29 7 267 65624 23 4522 2357
26 23 256 23 4,15 0 23,22 22 33
fune 27 9 595 25 58+3 25 5420 9 E
Fuly
26 22 375 8 5122 22 4319 13 22
Ausust 25 13 144 L 6+F 6 25 27 20
Septem. 24 5 55 2 26529 24 3526 6 17
35
October 24 3 3732 28 38,8 23 16,15 2035
NOvCM. 22 25 43(30 4 13,7 9 1O14 24 2C
Decem. (22, 10 2629 12 206 21 9(14 10 35
1680.
New D X. Duar. F uII D 2. Quat
D. TI. NI. D. EI. M. D. FI. M. D. TI. M
Fanuary 2T 0 59,27 19 195 10 6,+3
Februa. 19 22 5726 3364 2 2, 12 03
MarcB (29 22 2026 TF 264 1839 T2 2F5
Aprit 18 6 1725 L523 2L, 25 TE 12 54
May
27 23 5024 24 593
3 9TE 2 5
Fune (25 2T3723 6 27, 2 28 139 7:
fuly
(25 26 3922 23 T230 15 278 22 F
August 23 7322F 26 4729 5 436 15
Septem. 22 65720 10 3227 8 84 2F20
October (23 25820 X3027 2 194 5 2:
NOveM. 1O 18 7328 18 50, 25 IF 202 16 1G
Decem. 170 23 33]28 7 3424 20 22(2 9 34

## Folio  -  — 170380998X:0143
# Source image: https://digitale-sammlungen.gwlb.de/content/170380998X/jpgs/default/00000143.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 35 lines, status machine
1681
Nem 3
T. Quar. F WII D
2
D. HT. MI. D.ET. M. D. FT. M. D. HI.
Fanuary 9 7 5216 27 2523 20 632 0
Februa. 7 23 48,25 0 37 2F 23 6102. Ou
20
March (9 22 43 16 6 4523 13 2431 25 1
Aprit 7 23. 324 232422. 4 2930 7 30
Nay (7. 7 FT 13 2T 472T T9 5829 20 45
Fune (3 23 712 8 53, 20 10 4528 624
Tuls (4 2C AFEF 22 4020 X 1827 24 28
Ausust 3 4 57 10 14 318 24 2025 20
Seprem. E 24 43,9 8 917 4 524 2
October 30 28 43(8 3 2076 25 4(23
E
NOvem. (29 +2 567 22 3825. 5 82F27 5
Decem. 29 8 267 26 3614 13 5221 8.
Neo d F
Quar. Fult D 2. 8
D. HI. HI. (D. IT. M. D. TI. M. D. II.
Fanuary 28 3 326 8 2123 0 1219 232
Februa. 26 20 484 20 56 2F 2F 25, 18 2757
Marcs (28 20 566 5 TE22 2L 45, 20 12 3)
Aprit (2622 94 105IZF 9 3419 645
ACay) 26 7 23 15 2910 22 2718 23 45
Fune 24 24 52)C 20 499 2F 5717 24 5C
Fuly (2321 3230 24 239 23217 35
AuSust (22 4 4426 63+7 17 625 24 3C
Septem. 20 13 59)26 0 26 9 34 13 23 C
October (20. F15(27 29396 F 413 5 5d
Novem. (1d 15 2226 26 274 25 3 +Y 24 53
Decem. 11d 8 3226 72 204 5 710 20 37
10

## Folio  -  — 170380998X:0144
# Source image: https://digitale-sammlungen.gwlb.de/content/170380998X/jpgs/default/00000144.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 34 lines, status machine
1683
Nem T. Quar. FuII D 2. Qusr
D. YT. M, D. FF. M. D. FI. NI. D. IF.
Fanuarr 17 3 1025 6 222 18 289
FebrUL. 25 2F 5723 2L 6F 2 397 20
5d9 1X 3:
March 17 25 3925 7 36 27 40
April 16 6 4623 24 2830 7 58 A E
May 15 15 2622 28 3729 17 407 21 3.
Fune (14 5 4020 22 3128 5 126. 24 34
Fuly 2314 25 20 5 4027 29 36
dueust TF 22 918 12 4326 103T4 22 3
Septem. 20 5 5517 L 725 3 233 22
October (0 24 5526 27 2724 20 523
NoveM. 8 Z 26, 25 +2 2523 23 4230 27 4:
Decem. 7 24 2625 9 25(23 5 2(30 234
1684.
Nem) 2. Guar. FuII D F. Gua
D. H. M. D. E. M. D. FF. M. D. H. 1
Fanuary 6 5 34 E4 6 25 2F 20 3)289
Februa. 4 22 2613 2 5120 4 4926 29
March 5 25 25+3 1S F320 X4 027 729
Aprit 4 9 I12 7 618 2F 5525 2F2C
May 4 O 5T LF 16 328 5 3425 12 32
Fune (2 4 429 2F 50+6 14 2524 5 TC
fuly
32 24 39 X37 16 03F23 2X52
Aucust 29 22 207
7 35 C4 22 5222 25.
Septem. 28 7 335 T2 2013 8 02F 7 40
October 27 26 464 2F 2022 2F 520 23
NOveM. (26 2 583 24 TFTF 25 3729 IF 18
Decem. (25 24 32(3
6 27TF 20 18 18 23

## Folio  -  — 170380998X:0145
# Source image: https://digitale-sammlungen.gwlb.de/content/170380998X/jpgs/default/00000145.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 48 lines, status machine
Vem d F. Quar. FWIl D
D. FI. M. D. TI. M. D. FI. M. D. FI. M
Fanuary 24 3 385- 23 420 3 34 +7 
Rebrua. (22 T8 19)NO L. Ou8 X7 5225 235
Marob 24 9 45 2 20 420 5 49 26 2058
Apri
May
Func
Fuls
AuCus
23 F35]F 9 445 24 58+5 5 25
29
22 18 2(30 24 57.
2F 7 49(282 3 706
22 4d24 25 59
5 023 4 40
20 22 2228 4 505 23 412 19 AF
1920 1026 9 793 21 422L 22 37
Seprem. 17 2F 53(24 24 572
8 3910 9. 55
22
October r7 8 45(23 22 503F 25 2610 L3L
NOVeM. (25 20 1622 20 5230 20 248 1942
Decem. 125 5 27122 2 2030 5558 8
168
Nem D T. Quar. F uIb D 2. Quar
D. EI. M. D. II. M. D. H. M. D. H. M
Fanuari (T3 TF 5920 2050,28 22 127 2 12
Februa. (12 T 2620 15 3727 26 205
1 5+
March (13 14 2)2F IF 129 6566 1835
Aprit 22 4 3220, 5 1327 25 15 O
May
Fune
Fuly
TT 16 929 22 182623 04 5 4L
(10 92626 TX 4225 5 552 22 sC
9 23 5927 21 5724 X2 4032 24 22
Ausust 8 25 716 4 2522 20 5030 4 Z
Seprem. 7 5 5824 13 152T 6 4628 2 32
October 6 20 1(23 19 1820 19 2228 2817
NOveM. . 5 9 16C2 2 2319 2F 2427 14 30
Decem. 4 2F 41F 13, 51O 5 2527 921
Ma
s
M
A
V

## Folio  -  — 170380998X:0146
# Source image: https://digitale-sammlungen.gwlb.de/content/170380998X/jpgs/default/00000146.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 35 lines, status machine
Nem D T. Quar. FuII D 2. Dua
D. FI. M. D. TI. B1. D. II. MI. D. FI. P
Fanuary (3 7 55)20 024 1802726 12
Februa. (L 28 23(8 22 3826 29 2622 22 4
Maroh 3 4 3(10 8 4918 +2 7725 22 4
Aprit (X 24 80 2 2527 2 18(24 4
Mar
40(3 1955(16 24 423 81
30 22 24
Fune 29 5 297 52 56C4 22 30(22 22 52
Fuly
28 16 47 4 5124 6 2420 20 12
Aneust 27 7 595 28 382225 XL 19 2 56
Septem. 26 0 294 6 210 2T 3057 21 16
October (25 20 503 14. 1020 6 49(27 24 53
NOveM. 24 8 352 0 228 18 2616 10 SC
Decem. (23 22 30(30 25 108 5 3226 8
1688
Nem ) T. Quar. Fubl 2. QHa
D. TI. H. D. FT. MI. D. FI. MI. D. TI. M
Fanuary (22 +0 Z2(290 577 E X225 4 sC
Februa. (20 20 2427 72 39(5 19 423 22 30
March (2F 5 1528 2 296 13 58T4 1314
April (19 15 2726 18 745 6 473 0
s
May (18 16 25(26 F0 414 2F 3622 6 sC
Fune 27 8 525 3343 9 5610 5 4C
Fuly 16 19 47 24 20 34(2 20 389 25 10
40
Aneust 15. 9 10(23 12 3430 24 267 20 45
Seprem. 24 0 4922 3 4228 23 06 4 28
October 13 18 402F 26 5928 8 +25 26 56
NOvemM. 22 22 5420 4 826 19 54 2 5X
Decem. (72 66829 13 226 7 424 6 25
6

## Folio  -  — 170380998X:0147
# Source image: https://digitale-sammlungen.gwlb.de/content/170380998X/jpgs/default/00000147.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 41 lines, status machine
Tero D2
Quar. FuB D
D. HT. H D. FI. M. D. FI. M. D. HI
fanuary TO 22 20)F7 20 2624 22 123
Februa. (O XF 2T26 3 42 23 14 T2E ZF
March (1O 2T 5727 22 27(25 16 43 +7
Aprit (9 6 3225 22 42 23 23 02
Mai
8 13 3415 IF 2T23 T4 79E 22 2
31
7
4c
Func 6 22 824 X 5222 4 1829 1350
Tuir
6 5 28, 17 13 54, 2T 165828 18
Ausust 4 25 2x12 TE 13(20 4 1726 22 38
Septem. 3 3 39, IF 5 17 18 +7 4625 8 12
October 2 18 552023 018 0 4024 14 2.
Novem. (C X2 359 25 35T6 1030(23 522
Decem. 13+ 3 29 6 025 22 2122 22 42
169C
Nem D F. 9uar. F ulb D 2. Qua
D. TT. M. D. FI. M. D. IT. M. D. HI. N
Fanuary 29 20 177 26 5314 15 382F 18
Februa: 28 FF 46 E 49, 12 20 3920 1424
March (29 22 817 8 624 101422 940
Aprit (28 6595 24 2 13 21 34223
May
Fune
Fuly
27 24314 21 012 15 1920 1753
25 21 213 6 30TT 4 13 19 5 4)
25 4 422 262710 2F 28 18 14 45
Ausust (23 13213c 2 239 21 45 26 2132
Septemo 22 0 3229 21 128 X 4225 3
October 2E 13 2029 25 297 14 26 14 1035
NOvCM. 20 7 3428 9516 02522 2652
Decemb. 20 2 42,28
5
55 23F1 T2 4 25
CC

## Folio  -  — 170380998X:0148
# Source image: https://digitale-sammlungen.gwlb.de/content/170380998X/jpgs/default/00000148.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 39 lines, status machine
Neo D I. Quar. FuI D 2. Qua
D. TI. MI. D. EI. M. D. EI. M. D. HI. N
Fanuary 18 22 826 19 203 23 4010 18 55
Februa. 17 26 2825 5 392 9519 12 8
Marcb (19 7 5226 13 363 20 25 IT 630
Aprit 17 2C 4024 29 42 7 2210 2
May
20
Ey 62925 2T50317
22
549 27 37
Func 25 14 3822 4 24 29 22 268 10 46
Fuly
24 22 492T 13 4329 13 298 2 2
Ausust 13. 4 5020 2 2228 5 166 136
Seprem. LF 23 23 28 18 1326 2T 54 23c
October (EF E 418 23 926 T2 294 6 42
NoveM. (9 22 2527 9 44, 25 2 302 13 42
2∞ 54
Decem. (9 2 5I(T7 633(24 25 9Z2 4
16C
28
Nem D I. Duar. Fulb D 2. Duar.
D. TI. M D. TT. M. D. TI. BI. D. II. M
Fanuary 7 2F 52 16 0 45(23 2 3(29 27 3
Februa. 6 26 3224 28 262F FF 48287 3
NarCB (7 20 30,15 2 422F 20 5328 23 30
Aprit (6 3 623 25 3320 5 49(27 16
May (5 26 48(T2 20 48 29 25 4027 9
Fune 4 4 28TT 0 3718 2 2226 2
Fuly (2 262550 5 24 27 25 925 175L
Ausust
3F
25 42
c 498 2T 4416 5 5524 9
Seprem. 29 24 246 22 44 22 2622 2T 13
October 29 0 366 22 3014 15 5222 9 32
NoveM. (27 TF 485 6 46 13 9 4620 18 43
Decem. (27 F35(5 2 40113 F50(20 0 40

## Folio  -  — 170380998X:0149
# Source image: https://digitale-sammlungen.gwlb.de/content/170380998X/jpgs/default/00000149.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 56 lines, status machine
69
Nem D (I. Quar. FUII D 2: 21
D. FT. M. D. FI. HI. D. F. M. D. FI.
Fanuary 25 27 384 O XTF 16 018 9
Februa. 24 20 502 19 5320 3521620
Maroh (26 4 24 14 27 EF 1332285
Aprit (24 20 203 4 529 21 4416 27 5
May
fune
Fuly
(24 IF 73E 3
479
5
5 3726 7 5G
22 23 5630 3 447 23 3624 23 37
22 IY 729 7 336 22 40(14 16 22
Aueust (20 21 2627 T2 395 95013 95
Septem. 29 65725 2 163 2334, 12 1
October (18 26 5725 9 143 25 4I TF F9 23
NoveM. (X7 2 924 0 422 9 161O 10
Decem. 76 ZY 1723 20 3132 23 24(9 22 28
16940
Nem r. Quar. FuIL , 2. Quar
D. II. HI. D. TT. MI. D. HI. M. D. TI. B
Fanuary 15 X 1422 29 3930 15 348 y
Februa. 13 24 502T 23 +NO FuILD6 25
a
+
March (15 5 4F23 7 5230 24 377 2F 4C
Aprit (232T 622 0 528 22 736
May
4 3C
(23 X2 42 21 13 1228 5565 14.
Fune (12 3 2229 23 2226 TF 5F4 L 2
Fuls IT 18 616 6 125 20 503 25
Ausust 10 7 2717 TF 1224 6 302
3
Seprem. 8 20 1025 27 722 19 330 10 4
October (8 7 3214 22 4d22 20 3430 24 36
NOveM. 6 18 2013 8 4621 4 4229 8 14
Decem. 6
4 43 22 22 202F 0 8(28 2331
s
O
N
D
P
MI
7
M
f
A
Se
De
e
De

## Folio  -  — 170380998X:0150
# Source image: https://digitale-sammlungen.gwlb.de/content/170380998X/jpgs/default/00000150.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 43 lines, status machine
Nem D T. Quar. FuI D 2. DWa
D. FF. N. D. FT. ML. D. H. M, D. FI.
Fanuary + 25 5IY 24 5929 17 42 27 13
Fiebrua (3 X 5220 9 40 18 +2 2325 20
MarCB 4 23 22 +2 5 320 2 5027 LL
Aprit 3 EA12O 23 46+8 13 5725 9 +
May
fune
Fuly
2 24 5910 16 5457 23 824 X2 8
4
sC
30 18 429
7 5616 6 T722 2L 20
30 10 528. 20 2015 23 2022 8 4.
Ausust (29 2 137 6 20 13 20 33)20 23 10
Seprem. (27 26555 24 512 5 3029 16 30
October (27 6574
NoveM. 25 16 73
9 26TT 16 45 29 TF 56
5 1010 7 018 10 37
Decem. (25 6 TT(32 24 43(8 23 59(18 4 25
1696
Nom D T. Quar. FuII D 2. Qua
D. TI. MI. D. FT. M. D. FI. NI. D. FI. N.
Fanuary (23 27 3630 TF 495 18 3676 2F 55
Februa. 2F 3 2028 3 437 24 1015 F2 2L
Maroh (22 T2 5929 2F 228
7 5T15 22 25
Aprit (20 23 025 24 416 23 1024 5 42
May
(20 9 5228 8 126 IF 45 T3 FO33
Fune 18 22 3227 0 54. 2T48 CF 24 42
Fuly 18 FF 5226 24 564 65620 29 54
3
3
Ausust 17 31025 4 253 22 220
2 36
Seprem. 25 19 4623 25 2930 5527 27 17
October 15 2F 3623 05229 16 307
9 23
Novem, (14 5 122F 8 2628 5 226 4 35
Decem. (13 20 4(20 15 49(27 20 496 0 42

## Folio  -  — 170380998X:0151
# Source image: https://digitale-sammlungen.gwlb.de/content/170380998X/jpgs/default/00000151.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 38 lines, status machine
26
Nem D 1. Quar. F.WII D 3
D. TI. NI. D. TI. H. D. TT. HI. D. TI. M
Fanuary 12 8 59(19, 0 126 1353,4 22 20
Sebrua. EO 2F 34(27 203025 8 103 17 43
March (12. 5 142S 23 2427 L 235 20 2C
Aprit (20 23 3257 23 5225 27 273 23 C
May (9 2E 3927 5 3723 7 133 7 4
Func 8 63615 22 2623 185930
IY
20
27 2
Fuly 7 26 58)2525 223 5 129 2F 10
Ansust 6 5 2724 8 T2F 23 5428 348
Septem. 4 20 2712 23 561922 1026 24 C
October 4 13 712 24 4029 7 44 26 T4 28
Novem. (3
7 46FL 3 13 T7 17 5E24 22 24
Decem. (3 2 0(+0 73 25(27 5 3+24 18
1698.
Nem 3 r. Duar. Fubl D 2. Qit
D. H. M. D. FI. H D. HI. M. D. HI. M.
20
Tanuary 3E 23 15d 21 24 15 +9 723 15 2C
Rebrua. NONemD7 4 2224 20 222 2233
25
34
March (3E 8 255 22 4 16 4 1824 5 20
Aprit (29 14 246 22 824 18 T9,22 2955
May (26 2T 206 3 24 14 9 5522 7 L
Tune (27 4 584 27 32730 40)20 14 5C
fuly (26 13 514 22 55 12 24 20 19 2030
Ausust (25 0 523 5 40)2T 2 25 18 0 2C
Seprem. (23 14 29) L 23 369 233016. 5
32
October (23 7 2432 22 209 0 225 14 
NOvCm. (22 2 2030 3 167 9 5914 2 3
Decem. 125 21 3729 2606 29 5413 17 48

## Folio  -  — 170380998X:0152
# Source image: https://digitale-sammlungen.gwlb.de/content/170380998X/jpgs/default/00000152.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 40 lines, status machine
Nem D T. Quar. FuII D 2. Qua
D. II. H. D. FI. M. D. II. M. D. TI. D.
Fanuarr, 20 25 5828 2 205 6 5912 72 10
Februa. 19 7 5226 9 423 14 49) TY 7 58
March 20 20 5427 25 +35 7 24T3 3 45
Aprit 19 6 4625 F 43 20 50TL 21 44
May
18 24 4325 5 73 IF 13 TF 14 FO
FunC 26 21 3223 TF 45 2 0 1210 3 10
fuly
16 4 38(23 4 533E
27 229 24 27
Aueust 14 22 32, 22 20 4929 22 227 22 TC
Seprem. 12 22 2920 15 428 24 106 4 1E
October (12 20 45)20 20 43280 265 9 4
NOveM. TE 2 43(79 63726 T2 33
8 2
Decem. (10 20 51(19 0 5625 22 582 20 TY
17C
Nem D T. Quar. FuII D 2. Qua
D. II. M. D. TT. M. D. II. M. D. H. M
Fanuary 3 16 2627 24 324 9 43+
7
Februa.  2F 3F16 5 922 29 21 NO2. Ou
Marcb (2O 4 2517 23 34, 24 5 393+ 30 3
Aprit 3 18 X825 29 322 27 030 23 27
May
S
5 32(24 23 2225 5 630 6
Func 6 14 2623 4 3420 28 25(28 22 20
Fuly (5 2C 4222 72 F320 9 2 28 +L
Ausust 4 5 71023 20,19 0 4226 22 2
Seprem. 2 22 549 1333 27 26 4825 4 20
October 3.
27 50
5 369
7 12 17 8 5424 2545
NOveM. 29 23 508 3 1016 0 1(22 2T38
Decem. 29 13 07 23 44, 15, 23 622 9c
C

## Folio  -  — 170380998X:0153
# Source image: https://digitale-sammlungen.gwlb.de/content/170380998X/jpgs/default/00000153.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 99 lines, status machine
A Cataloque oF aIIthe F clipses oE che sun an
Moon rrhieh wili berisible in Fneland, From
the rcor 1672, 10 the VeaL 170O.
rear. Moneth. ID. H. M. L. Un. DI8. M
1674 Fanuary EL 17 22 D E 2I
2674 Fuly
2675
1675
May
1678 October
268F Ausust
2682
2684
1684
1685
1686
1687
Aucust
26 25 30 D
3F 2F 200
29 8 X7 D
16 14 22) D
n 2756 D
3 20 C
November (30 10 26 D
NTOVeMber Z9 FF 22 D
E X 25 ()
5 6 4
25 6 47 D
Seprember (18 24 46 D
2690 March
Fuly
14 1O X4 D
17 15 9
D
February (CF 16 24 D
1693 Fune
2694 Fune
23 0 60
26, 12. 50 D
1695 November (TO 7 0 D
1696 May
6. FF 45 2d
2696 Octob er (29 2630 D
2697 October 29 7 44 D
2699. March
1699
22 77
18 5i
15
4 Sc
22 20
10 38
18 SC
19 40
17 4 27C 20 3C
Fune 16 24 17 D
May
1689 March
1693
6 25 25
FebruArY EE IF 28 D
Fanuari
fuly
2688 Apret
1659
7692
7. 18 39
Fanuary E 7 29 D
Fune.
1676 May
1677
7682
2663
D
D
8
5 1 7 24 D
Seprember F2 2L 30 C3
F. 35
E
2F 43
7
35
L 4
6
4
22 10
20 35
12 2
19 32
2
6 47
6
22 4c
22 45
8
9
10

## Folio 1 — 170380998X:0154
# Source image: https://digitale-sammlungen.gwlb.de/content/170380998X/jpgs/default/00000154.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 30 lines, status machine
cegocgoccho csocoo se chich ao uc snso aos
A T able serine the becinnine of everz
Kines Reien fromthe Conquest; Zoget her
rith the rear of C’hrist, ansmerine 10
everi rear of eachKing er Ducens Reien
from Henry S. 10 Charles 2. inclusive.
Iherear becinnins on the 25chof Mareh.
WTL F Y A ML the Conquerer.
DPgan his Reien che Fifreenth ot October
R D1O56. Ended ic the Nineh oF Seprember
1087. Reisned 20 Tears, 10MonthS, 2L (2y5.
WILLTaM RDEDS.
Besan his Reien Seprember che Ninch, 1087
Reigned 12 Lears, sTMonchS, 18Day5.
H F. XY R V I.
Began his Reien che Firs ot August, 110O.
Reioned 35 TearS, 4 MOnEhs, T2 D 4y5.
ST F PHP HI,
Began his Reion December the Second, 1135
Reigned 18 PearS, E F MOnchS, 20I 2y5.
HI F N R Y TI.
Beganhis Reien October che Fvency Filch, 1154.
Reigned 34 PearS, 9MOnTHS, S DayS.
RICH AR D I.
Began his Reion Fuly che Ninch, 1F89. Reigned
DVears, 9 MonthS, 19 D2y5.
FOHN,
Besan his. Reien April che Sixth, T199. Reigned
17 VCar  5 MOnTHS, OD2yS.
enru

## Folio 2 — 170380998X:0155
# Source image: https://digitale-sammlungen.gwlb.de/content/170380998X/jpgs/default/00000155.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 35 lines, status machine
(2
AF. N RY III.
Besan his Reion October che Nineteenth, T216.
Reiened56 YCarS, LMOnCH, ODaYS.
E D W ARD I.
Bexanhis Reion November che Sixceenth, 1272.
Reigned 34 Pears, 8 MonchS, 9C 275.
E DW ARD II.
Began his Reien Futr che Serenth, 1307.
Reiened 19 Ycars, 7 MonthS, 9 Da95.
F DWARD III.
Bexan his Reion Fanuaryche Tvency Fisth
1326. Rcigned 50 Tears, s Monhs, 7 Day5.
RICHARD II.
Besan his Reien Fune che Tweney First, 2377.
Reisned 22 Tears, 3 Monchs, 14 I 275.
HTR NR Y IV.
Beran his Reion September che Twency Ninth,
399. Rcigned 13 Pcars, 6 Months, 3Day5.
HIF. N R Y V
Besan his Reion March ehe Tvenciech, 14120
Reigned 9 PearS, 5 MOnThS, 2 4 D2y8.
HF N R Y VI.
Degan his Reien August the Thirey FirH, 2422
Reigned 38 PearS, 6 MonchS, 16Day8.
F D WA RD IV.
Besan his Reion March the FOurFK, 2460.
Reigned 22 PearS, LMOncH, 8 DayS.
RTCH ARD ITI.
Began his Reien Zune che Tweney Sccond,
483. Reigned 2 PearS, 2 MOnCHS, 5I 275.
AF NR Y VTI.
Pegan his Reion Aupust che Tveney Second,
(485. Roiened 23 LCaIS, 8 Monh 19 DayS.
HENR)

## Folio 3 — 170380998X:0156
# Source image: https://digitale-sammlungen.gwlb.de/content/170380998X/jpgs/default/00000156.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 58 lines, status machine
L3Y
HLAAt VITI
Beganhis Reien April che Tveney Second, 1509.
Reisned 37 Tcars, 10MOnchS, LDaV.
rears of
his Reign.
TC
II
I
1
1L
I
18
1G
20
2 1
22
24
2C
48
10DOu.
Mar. 25. 16720
10- 162
1-
12-
17-
18
 16L
160
159
18
57
6
155
254
519 153
520152
522  15L
522 mamnena 150
23 149
24 148
25  manmmm 24
526 unoua 146
7
 245
528  144
 1529a 43
80 142
8tum 1g
32- 140
1533.
35-
8
137
 1536ma onmamum 236
28na 1537 manm 135
29re  cn Y538mn amalo eoata X34
Tearsexpired;

## Folio 4 — 170380998X:0157
# Source image: https://digitale-sammlungen.gwlb.de/content/170380998X/jpgs/default/00000157.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 27 lines, status machine
(47
anno Doms
Pears of
his Reign.
I
E. DW ARD VI.
Began his Reen Fauvary the Piveney Fighch:
2546. Reigned 6 Tears, 5 MOnthS, T9DayS.
Pears of
Bis Reign.
MIAR X,
Becan her C Fuly che Sixth, 2553. Reigned
Tears, 4MOntHS, 22 V ayS.
Tears es
Ber Reign.
rears expired.
MLar. 2.5. 164
Lears expirea
ar. 23. 1672
Auno Do.
Antoom.
rearsexpired.
Mar.. 1672.
R. L I Z AB F. X Le
Began her Reion November the Serenteenth
558. Reigned 44 Tears, 4 Months, 15 DayS.
TeAES

## Folio 5 — 170380998X:0158
# Source image: https://digitale-sammlungen.gwlb.de/content/170380998X/jpgs/default/00000158.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 46 lines, status machine
Pears of
Ber Reign.
1
10
E
20
2T
23
24
25-
26.
27
28.
29
30
3F-
(5
d Dom.
559.
560.
167
562.
563.
564
56
36
c
156
5
78
1580
158F.
1582
1583
1584
-+58
 1586-
2587
2588BA
1589.
32man Y590  
Tears expirea.
MTar. 25. 165
d
8
de

## Folio 6 — 170380998X:0159
# Source image: https://digitale-sammlungen.gwlb.de/content/170380998X/jpgs/default/00000159.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 72 lines, status machine
rears of
her Reign.
(07
Anno Dom.
33.. 0 1591
34. .. 2592
33 0 0 0 2593
36.  . 1594
37. 0 0 1595
38... 1596
39. 0. 1597
40. . 1598
AF. . 0 1599
42 ... 1600
43. .. 16OI
44. .. 1602
Mur. 25, 2672
 BF
. 80
..0  19
. 0 . 78
. 17
... 75.
 74
0
73
72
.0. 7I
0.0 70
7 AATFS
Beoan his Reign March the Tweney Fourct.
2602. Rcipned 22 Tears, 0 MOnChS, 3 DayS.
rears of
Bis ReigM. Anno Dom.
1
3
4
0 . 2603
Tears expirod.
Mar. 25. 26720
.. 69
.. 1604. . .. 68
.. 1605
. 1606
0 1607
. 1608
.  1609
o 1610
. 16TY
. 16T2
.. 1613
.. 1674
 2615
 1610
 2677
. 67
... 66
.
63
. 64
. 63
. 62
. 67
. 60
59
. 58
e
55
Tears expired,
26
Pet
bit

## Folio 7 — 170380998X:0160
# Source image: https://digitale-sammlungen.gwlb.de/content/170380998X/jpgs/default/00000160.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 75 lines, status machine
rears of
hic Reion.
L7
Anno Dom.
16... 1618.
rears expired,
Mar. 25, 1672.
a . 54.
. 1619.
53
18 ... 1620.. . . 52
19 . . 5 162T
20
2 0 0  5_
.. 1622 0.  50
2I 0 0 = 1623
22
 40
0 1624   a 48
CH A R L. F S I.
Beganhis Reiga March the Tweney Seventa,
2625. Reisned 23 Pears, EX MOnChS, O D2yS.
Tears of
his ReIgH.
e
1
+I
22
13
24
15
16
17
Anno Dom.
.. 1625
rears expired,
MLar. 25. 1672
. 1626. . 0 0 46
 1627.. 45
 1628.. . 44
 16290 0 43
0 2630.. . . A8
 1631
. 2632
.. 1633
. 1634
 2635
.. 1636
-. 1637
. 1638
. 1639
0.. 2640
. TEAC
18... 2642
19 0 .. 2643
2C
 0 A1
. 40
.0 . 39
.... 30
e
0
37
.... . 36
o
35
0 . 34
.. 33
.. .  32
000
31
. a 0 30
0 0 0 - 29
0. 1644..  28
A

## Folio 8 — 170380998X:0161
# Source image: https://digitale-sammlungen.gwlb.de/content/170380998X/jpgs/default/00000161.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 70 lines, status machine
Tears of
bis Reign.
(87
Anno Dom.
E . 0. 1645
22 ... 1646
3
. 1647
24.. 1648
Tears expired,
aLar. 25. 1672.
. 27
 26
CH ARLF S TI.
 25
. 24
Beganhis Reion Fanuary che Thirrieth, 1648,
and is nom Reisnine.
Tears of
Hlis RetgM.
E
26
1E
2C
22
0
Anno Dom.
. 1649.
165
.. 2654
. 1655
. 1656
. 1657
 1658
. 1659
. 1660
. 166T
. 1662
. 1663
. 1664
 1665
. 1656
1667
. 1668
...
1669
. 1670
. 1671
0 1672
Tears expirod,
Mar. 25. 1672.
... 23
.. 1650...
. 1651
.2652
.
 22
e 2
0... 20
19
..- 18
77
10
25
 L.4
13
22
17
. 20
AdricO

## Folio 9 — 170380998X:0162
# Source image: https://digitale-sammlungen.gwlb.de/content/170380998X/jpgs/default/00000162.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 30 lines, status machine
 e   o ge e eae e u ase gasse aec  c ecte ete 
Advice touchine che POSTS, and
ROADS, more exactly chan
hach hicherto ocen publibbed.
I. Concerning Letrers, Which may be
sent from L. O N D O N.
On Mondays.
P3O France, Spain, Italy. Germany, Flanders
 and Sveedland, Denmark. Kent and chc
Dowons.
On Tueldays,
To HTolhand, Germany. Sroeedland. Denmarke.
Treland, Scorland, all Parrs oF Finsland and Wales.
On Wedncidays,
T0 all ParrS OF Kent and che Dorons.
On Thurldays,
T0 France, Spain, Ctaly, all Pares OF. Enslanc
and Scortand.
On Fridays,
To Elanders, Germany. Iraly, Sueedtand, Den
mark. FTolland, Kent and The DoronS.
On Saturdays,
AII pares oF Fingland, Wales, Scorland, Treland.
Lecrers are returned From alI pares oF Fncland
and Scorland, cerrainly erery Mondar, Wednesday,
aud Friday; trom wales every Monday and Friday;
and From Kent and che Dorons erery day; Buc
trom ocher paris more uncerrainly, in resard ot
the Sed.
a

## Folio 10 — 170380998X:0163
# Source image: https://digitale-sammlungen.gwlb.de/content/170380998X/jpgs/default/00000163.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 52 lines, status machine
10
OST STAOFS.
NORTHERN-ROAD.
Miles. ITorat.
Rom London to W alcham- erots 12 - 12
Erom WV alcham. CroIsIOWarE 8 = 20
From WareroRoyston
From Roystonio C axton
From Caxtoneo Fluncinocon
From Tluntineron to Srilion
From Sciltonro Scamtord
From Scamford 1o Scurhmitham
From Souchritham eo Grancham
From Crancham eo Nemarte
From Nerarkeo Tuxtord
From Tuxtord eo Bautry
From Bautryso Boncalter
From Doncalter r0 Ferrybrige
From Ferrybrigs eo Tadcaster
From Tadcalter io Tork
From Torkro Burrombries
1.
3
2 
8
20 -
10 - 107
12 = TTG
6  12G
10  135
9
8  152
12  164
From Burrombrixe ro North. allerton 12 - - 176
From Norch. allerron ro Barlington 10 - 186
Erom Darlinocon eo Durham
From Durham ro Nercastle
From Newcasle toMorpech
From Morpech 10 Alnmile
From Alnrik ro BelFord
Erom Beltord io Berwick
From Bermick ro Cockburnspeth
14 - 2C0
12 = 212
12 = 224
12 = 236
12  248
12 = 260
24 . 274
From Cockburnspech eo Hladdineron 14 = 288
From Eladdinscon to Pdenbroush 12 - 300
From

## Folio 11 — 170380998X:0164
# Source image: https://digitale-sammlungen.gwlb.de/content/170380998X/jpgs/default/00000164.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 65 lines, status machine
L+IY
NORWLCH-ROAD.
From Ros Cambridee
From Cambridee 1o Nemmaiket
From Nemmarkee toBury
From Bury 1o Thertord
From Thertord ro Arelebrouph
From Acxlebrouph eo Normich
CHESTER. ROAD.
From London t0BarneE
From BarnCE +O SF. AIBanS
From SI. AIbans eo Dunstable
From Dunstablero Fenistrattord
From Feniltratford to Toserer
From Lolleter to Dainrry
From Daintry 1o Corentry
From Corenery ro CoMrail
From ComraII +0 Lichtield
From Lichheld to Stone
From Sconc 1o Nampemich
From Nampemich eo Checter
From Chester 1o Norchope
From Norchopero Denbeioh
From Denbeish to Comvar
From Conray io Blenmorris
From Blemmorris eoHTollyhead
DARET-ROAD.
From Tosseter 10 Northampron
From Norchampron ro Hlarbrouet
From Hlarbrouph ro Leicecter
From Leicester 10 Loubrovea
From Loubrouoh ro Darby
Mites. (Foral.
10
10 .
10.
10 -
10
2
10 rC
10
10
6
12
10.
14
8
12
16 - 1Y
c
16 - 126
24  5
18  158
22  1
24 . 184
20 unn 19A
24  210
6
12 - 18
12  30
8
(2
38
c
110221

## Folio 12 — 170380998X:0165
# Source image: https://digitale-sammlungen.gwlb.de/content/170380998X/jpgs/default/00000165.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 61 lines, status machine
12
WNESTERN-ROAD.
Fom Londonto Stanes
From Scones to Flarrtord bridoe
From Hlartford bridse ro BasingAoke
From BalinoRoke 10 Andover
From Andover 10 Salisbury
From Salisbury 1o Shatesbury
From Shatesbury ro Sherborn
From Sherbornro Crookhorn
From Croolchorn to Fluniton
From Hlunicon 10 Pxeter
From Fxerer ro AMburton
Fiom ACburton 1o PIymoucha
From Plymouch 10Foye
From Foyeto Trovro
From Trorro 10 Merkejen
Miles. 201al.
16 -
16 
9
18
19.
16
13
32
A
l23
19  14
5
20 -
PORTSMOUTH- ROAD:
From Stanes io Hlartford bridoe
te
16 - 16
From HlarrFord bridee 10 Pererstieid 10  26
From Pecersteld ra P’ortsmeuth
24 -
TA RMOUTH. ROAD.
From London 10 Burnerood
From Burneood roWicham
From Witham eo Colchedter
From Colchelter io Iplwich
From IpErich 1o Sarmundum
From Saxmundum to Bechles
From Beckles 10 Varmouch
16
18 m
P2 
5
16
34
46
26 - 62
16.
78
16  94
10  104
BRISTOL
e
d

## Folio 13 — 170380998X:0166
# Source image: https://digitale-sammlungen.gwlb.de/content/170380998X/jpgs/default/00000166.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 44 lines, status machine
13.
BRISTOL KOAD.
Fi om London te FTuncsto
From Flcincso ro Maidenhread
From Maidenhead 1o Readine
Erom Reading 10 Nembercy
From Nemberey toMtalbrouet
From Malbroughio Chippentam
Erom Chippentam to Bristot
Miles. Fotat.
16  2C
12
16
15
From MaseLad to Abbinecon
Prom Abbinecon 2o Farrington
Erom Farrinocon io Cirenciltei
From Cirencilter io Glocecer
From LohuontoDartford
From Daretord 1o Rochester
From Rochester 20 Sictineburn
Erom Sictinsbuen to Canterbury
From Canterbury 10 S DOrer
54
C9
15 - 84
20 = 204
GLOCESTER-ROAD.
RENTISH- ROAD.
Deal
1O
36
16  16
5  31
15
18.
4 
24 
12
40
6+
2 8
23
Forret

## Folio 14 — 170380998X:0167
# Source image: https://digitale-sammlungen.gwlb.de/content/170380998X/jpgs/default/00000167.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 41 lines, status machine
L. 14
deaabe ace ase o cse e a     q   u
Forreien Weiches and Mlcasures, carefully
compared withthe Enslitr, by the creat
pains and industry of the famons, and my
vorthy Friend, Sir Jonas MOOr, nigh.
ted _ Bs_ a S 1]  s
∞ D
38
Ores
2o
D
v
e
8
3
i
en n
n
LOndOn FOOL . . (1000 (0. 12. 0 10C
France.
Paris, che Royal FoOc, X.068 1,00, 80
LiOnFII
0
3. 976 3. IX. 7 1.0G
Boloyne FII . . 2.076 2.00. 8 0. 89
The 17 Provinces.
Amsterdam FOOE. (0942 O. TY, 3 O.9
FII : (2, 269 2, 03. 2
AMEWVOrPFOOE...9460. I1. 3 0.9
EII..
2. 273 2.03. 3
BriII FOOE.  P. 103 I, OT. 2
DOrt FodE... 1. 184 T. O2. 2
Rynland Or L eyden (oOr T. 033 2. 00. 4 0.5
EII (2,260 2. 03. F.
e
LOrain FOOE.. 958 O, TI. 4 0.98
NLecalin FOdE...919 O. TT. O 0.98
Midaleboure FOOr. 1. 99r (0. 11. 9 1098
Germani.

## Folio 15 — 170380998X:0168
# Source image: https://digitale-sammlungen.gwlb.de/content/170380998X/jpgs/default/00000168.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 56 lines, status machine
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nain Fo0t. 5.948.XI.40. 93
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o
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1. 826 X. 09.9
1.905 1. 10. 8 0.9
2.260 2. 03. F X. 1
1.903 X.69.8
1.006 X.00,L 0.94
2. 227 2.63. 3
954  O, IT.4
1.053 1.00.60. 8:
Palm ot Castite. 5 75I 0, 09,0 O. 9
The Spanist VarC Or 7
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Their FoOt is 3 oFC 7. 3OY 1. 00.C
the Vare.
0
Lisbon Vare.. 2.750  2.09.0 T.OC
Cibralter Vare..2.760 2.09. 1) 1.0=
Toledo Fo0t... . 899  0, 20. 7l F. OC
Vare... 2.685  2.08. 2
Traly.
Roman Fooc, onthec
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Ot Statolius.
Roman Palm, Cor
buildins, where. 
et ten matce thel
Cauna
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972 O, TI. 7
.732 9.08
Biu

## Folio 16 — 170380998X:0169
# Source image: https://digitale-sammlungen.gwlb.de/content/170380998X/jpgs/default/00000169.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 57 lines, status machine
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. II. P.
100P.
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2. 147 2, O1.7
12, 04012,00.5
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Naples Palm,..
BFDCC..
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2, T00 2. O1. 2
Cauna .. 6. 8d0 6. 10.5
Cenua Palm,..
aTantoua FOOE.
asidan C alainus..
Parma Cubit....
Venice FOOc...
Orher. Places.
Dantzick FOOC.
FII. ....
Copenhazen FO0E,
Prague (in Bohemia) C
FOOE. e
RICAFDOL..
Chrora Cubit.
Turin HOOc.
Cairo CubiE.
Persian AraM..
Turkist Pikre, at Con. 
830 09. 6 1
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6.544. 6,06.5 1. 4C
1.866 2. 10. 4 1. 43
F. 162 L.02.9 1. 53
. 944) C. TL. 3 T.
1.903 T. 10. 8
.965,. TL. 6 0. 96
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7.016 T.0O. 2
1,062 X. 00.7
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3, T97 3. 02.3
stantinop. Thegreaters 2.200 2.024,
The Greck FOOE . . 1,007 X.00,1
Mourons Unirertal FOOE 0.675,08. 11
A Pendulum oE che juAt lensch. Whereot wilt Vi
brate 132 times in a Minute.
Fx. by meu JonasMOOrC.

## Folio  -  — 170380998X:0170
# Source image: https://digitale-sammlungen.gwlb.de/content/170380998X/jpgs/default/00000170.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 7 lines, status machine
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## Folio  -  — 170380998X:0171
# Source image: https://digitale-sammlungen.gwlb.de/content/170380998X/jpgs/default/00000171.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 1 line, status machine
Ir: OD-A

## Folio  -  — 170380998X:0172
# Source image: https://digitale-sammlungen.gwlb.de/content/170380998X/jpgs/default/00000172.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 2 lines, status machine
:OD. A2
6, (17

## Folio  -  — 170380998X:0173
# Source image: https://digitale-sammlungen.gwlb.de/content/170380998X/jpgs/default/00000173.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 1 line, status machine
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## Folio  -  — 170380998X:0174
# Source image: https://digitale-sammlungen.gwlb.de/content/170380998X/jpgs/default/00000174.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 1 line, status machine
l

## Folio  -  — 170380998X:0175
# Source image: https://digitale-sammlungen.gwlb.de/content/170380998X/jpgs/default/00000175.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 7 lines, status machine
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