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# Piece: https://leibnizlegible.com/api/records/606/text
# Catalogue record: 606 — [Aufz. zur Algebra]
# Incipit: Quotiens Divisores Dividendus Subtrahendi qui una cum dividendo
# Date: 1697
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=606&katnr=58183
# Work: https://leibnizlegible.com/work/00068201
# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folios: Bl. 77–78 (from the shelfmark LH 35, 14, 1 Bl. 77-78): 4 pages, canvases 153–156, page ids 00068201:0153 to 00068201:0156
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068201&page=153
# Lines: 348 recognised on 3 of 4 pages, mean confidence 0.71
# Catalogue: Leibniz-Katalog / Arbeitskatalog der Leibniz-Edition (https://leibniz-katalog.bbaw.de/), ed. Arbeitsstelle Potsdam I der Berlin-Brandenburgischen Akademie der Wissenschaften, CC BY 4.0.
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
# Licence: CC BY 4.0, Leibniz Legible. Machine output: do not ingest it as verified text; keep this provenance with the text.
# Wording rule: say "the machine reads it as …", never "Leibniz wrote".
# After the first blank line, page by page: a "## Folio <label> — <page id>" line ("## Canvas <n>" where no folio label is recorded), "# " lines naming its source image and model, then its recognised lines in reading order, one per line.

## Folio 77r — 00068201:0153
# Source image: https://digitale-sammlungen.gwlb.de/content/00068201/jpgs/default/00000153.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 82 lines, status machine
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O2or + XBit XBI + XC1 +, X31+ S  _biF, X E1 + X2 + X 1HY X
L
a
it. rnumgori et Lgnee 2 t hiu vol B8
invpiont sorars pieaad epuvar gue)
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ut. 1E. Ed
is apem myen zurenmr inc ro mmus  in in reof iuo ung gyni
X ognch rossimus hogit. Hgyngets) in rigne ngib hech onn erct
grs ezon B. Smeromi su, mnavenns ds mnnoguabo moe.gi Id1) Jo
hmequars an 6b1n0 mo cmmomur.
9t. n
-
t
89 n evo (99E-dussit  Y) 1
 F. in D 1135. 30) eor =s 
uncum
1+
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2
o
(Xq+ 
i
n F. = T XE) 
X
ED+XXD E
947- BV 4 -3
b∞ + X S∞ + XXD + X evv p + X30 + X9 + X
+93+
2 evvt 176 
a dist
(X) XL2), X9.
XX7, - (1X2)
2 X9 + XX
au
o + Xevo + XX30 +, Xg +, +
0=99. 7 - 3u 1 surenet gus 30 + X qL XX qu abaz
ot-
(X2 XX 
1
10 +. 29 s. X tt
(37- 30) (21
0= 9-
1et
943
E+ 1d
eod rdes
elb nos 0=.
(11 )-
itali Rom relinianr addicti quia in ea ipsorum
diguitas, et in sibem quodoo chustiam regimen quoddum
Lux illi adbisque udit cups

## Folio 77v — 00068201:0154
# Scan: The same scan is also registered as fol. 78r; its text is given once, here.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068201/jpgs/default/00000154.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 181 lines, status machine
n
diveuendus
Resii subtrahendi, qui una
cum dividendo consti-
tuunt Residua
evotiens
Ax 1X  divisores
44 uX 
 qu = C 
2eri - D
2
seu f -  26c edr. 2
e
 1
dabit
Ergo si Aad. quadr. de:
(i 122
2x 1X
8
2
a
eX)
-2Besca
MAX
 Ei.
invyx
Hoc absolutum
30 X2, 31xt , 3 A 1 qu 
AA N ARX ACX+
41. 31 3) Rt2. 31 3 2.31. 33 F2. 31 3 42. 3. 25
∞
+1. 327. t2. 31. _ +2 313. 12. 32. 25X
15333 21724 
42. 33. 35X
+1. 24. 34.. 12. 37 XX
175.7K
1, gus ade b) 10X = u X + 1. X - 13X + 14 X r s X abk mto gt ssirrot
10 = 130. 30 1 3
11= 2. 30. 31
12 = 2. 30. 32. = 1. 31. 31
13 = 2. 30. 33 +2. 31. 32
14 = 2. 30. 34+ 2. 31. 33 41. 32. 32
15 = 2. 30. 31 + 2. 31. 34 + 2. 32. 33 + 1. 33. 33
etc
coincidit prioribus pro A, B, C, d, etc
ponendo 30, 31, 32, 33 et
addidi autem 10 vel A, ut primus temunus
et ultimus eodem modo tractentur
31 = 11 L: 2. 30,
32 ~ 12 - 1. 31. 3] (: 2. 30)
33= 13-2. 313C, .
34 = 19 - 2. 31. 33 - 1. 32. 52
35 = 15 - 2. 3134 - 2. 31. 33 : 2. 30)
Hin exigero residtum   ne + c
1
et
2+ 14. Quod si residui
scet et 5
 hoc accuritus ex aminanda
F
X +AK +uX 1BX +14K + 5Xm l + 1X  BX +BX +GA +20X 
X= Bx +Cx +DX +EX rF XS etc 
X + JuX 
Nota 12 non latet in BB sed 11
1 non latet in BCsed 11. 12
19, non latet Ed, CC sed 11, 12, 13
la
Hinc continetur in  hoc calculo modus
etiam altoltend inveniendi potentiam
ex radice generalis, quia est
1 = 2B et 12 = 2C + BB
et B3 = 2d + BB .t 14 = EF 2BD +CC
unde  video potuisse haec erdem obtinesitem
extractione, si modo instituissemus n
cationem. Et quia extractio fuisset incommoda
et laboriosa in altioribus potentiis, pro ea utem
mulliplicatione excitatione. Eademque exrtatio
serviet pro affectis aequationibus; seu pro extrecton
radicis affecta
Residuus constat ex terminis quotiontis pondentitu
multiplicatis per 2. Et (quod notandum, set extra eu ter salis
terminorum7 verb.gratia; erit Ex etiC quotieutis,
sumamus terminos quatuor priores pro
tres sequantes per
Il
l
autim nem , e
icalo soll
EBE B
216
pasietx si ase astes
Haist
 aec radix commode applicari
otest ad Duad
exp
Numeri extractionem, nam
devisio per 2. tantum removet
in gradum sequentem
potest etiam ex pro X, 
substitui X X, X, et
quasi esset Y  1X + uX ex
omniaque privibunt eodem modo
quod aptum d dicis, 
ut
t cum exacte
sucedit
pructio nihil refert auat
unde incipias, ab initio an a
fine, et in 3adicis mneo more
tractatis per periodos columnares
utile est incipi a fine
i tine incipere licet etian cum
resiri sant sid eoanidant
 vel XX
LHt.U
vol de sbrcoX + nosx
+4
mxxtramuxraanu
PIXX + 2 apgx Faaqque
+15)  416d
et 17)
De- 
14 2. 11. 1. 12, 12. 12
1610) 4. 10 1020
+ 1 1
Pa2
17
C18
2+19)
si volumquse non omitti eu et A, quasi
osset 10 X = y X2n.t etc
et AX + BX et
et ft si - 2BCF 13-0
Hiil 13AR. 810 = 2 1011. 12 + 11 = 0
Hae series sunt ex numero maxime
intractabilium, ubi scilicet
4 .. etsi A. cenrafit 14 AA 641 3 - 16. 10.1 0. 12. 12 + 8101.1112 = 1 0 terminus sequens indiget omnibus
A = 10g c = 14
AX+ BX FC AANAEAOxAIACXY
Px ga
E+I5.
410d
AA
10X a  r3 4ei  113 X +4Y
sit his ab taac aequanda qto, posito  m+na. sint m Xx + chamux+ haana
posito y-
+4
vel uesa 
Haec est alia ratro procedendi, ubi primi et ultima termini tactaatur eodem
modo, videndum quomodo duci queat ex priore.
ar ∞to
C pXY + C a P4X +C quqq CpE t p aq X feb pp aa qu ex + 4 pa X A
bem pX
praecedentibus.
.2 s10.14 + 11. 13 = 12 fiol 8. 10.14  e -4. n. 10. 14 + 11. 13 =0
4(10. 14
Haeunqque
b2 ppannx
dest 10X + 1 ∞3
a nnxibrapquanx
apt rox xax a
Et resioni crunt
prout longius
proceditur, quin
semper numerus
terminorum
residui, est
unitate interio
numero termi
norum radicis
ne
fielte prodt
es
B- 20
cc=
si aequatio habet duavamtmet
duas rndices aequanes, videndum
an aequatio factu multiplicave
arthmeticae prog. habeat adhuc
duas radiées aequales. de
i , B, d ntert relip) vel etc.

## Folio 78r — 00068201:0155
# The same scan as fol. 77v (00068201:0154), where its text is given.

## Folio 78v — 00068201:0156
# Source image: https://digitale-sammlungen.gwlb.de/content/00068201/jpgs/default/00000156.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 85 lines, status machine
sunus on sen esst duq
conet ilio ungtur  n in 10 tagul 16
crissin in inn uat en mochgrime qui
+X X + 0X + ac
Ergo ut xx +bx + ac sit quadratus, fiet ac - + bb = 0
i XX (2X) .bb
+X + b X + ac XX t aad X + ae
ac a+ bC
dx + LbX + 2
X B2XY) = LbXX
abx REXX +bX
(x
+ :bx
= (efac. b1)
X + bX .+ ac X + _ aad X + a exx + atfx + a g
acu tbb aad ac bb
X EbXX + Pa
+
 dc H
2
sx
 (xI - iulx
ex + bxx) su u
ac. Hbb
2X + bxX + a
aadb
taad
Cut
fiet aad
ac 4bb
b =0
et ca L 4bb
etf
bb
26
et fit a = 21 (ac - 4bb)+
af= aad (ac. h bb)
c 7b6
ag-
= aad. (ac - Lbb).
aa
b
Continuando prodibit series quaedam primaum, se cujusque extractionis
et series itidem aequationum secundarum cujusque extractionis. Et patet tabore
pro uno quoque gradu valere pro sequentibus. Itaque limisset scubere X bx etc
utile etiam erit facere ut ut uta summi et imi procedant eodem modo sit
 Et quia ubique per 2 dividendum id praeveniatur. sit
oX  X +1X + 13X r19X + isX 16X F9 K X 1BXMyX + 2020
1a il
Dx
bLX
n
+nA
AxI
Extrahendus
10
+ X
+IIX)
+ 14
+13X
+147
TISX
+4X7
et
Aad iste
2lk
- 1 + 13
gnq
otin
∞. 11
X
1
3
et
X
E+ ux nux
 diviscotes ver invertemus sie
a1
nq
i
1
B
11+12
19:
5