# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/806933011:0767
# Permalink to this reading: https://leibnizlegible.com/page/806933011:0767?run=74
# Title: Lexicon Technicum: Or, An Universal English Dictionary Of Arts And Sciences (shelfmarks Leibn. Marg. 71; ZEN Leibn. Marg. 71)
# Folio - , page id 806933011:0767
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=806933011&page=767
# Source image: https://digitale-sammlungen.gwlb.de/content/806933011/jpgs/default/00000767.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 108 lines, status machine
# Lines: 108 recognised, mean confidence 0.89
# 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: the recognised lines in reading order, one per line.

and also substractins 50 from it, or ix trom 50,
Wwillmake 16 Dcgrees: Then chis Sum and Ditre.
rence caken trom che half Tangenes, and set cach
Way From P che Pole oF ihie Oblique Circle, ivill
sire che Diameters cuo Exircams a and b, ox the
Poines ot ehe Incerlection ot che Parallel. and then
the Midale Distance becweena and b, is elie Center
otche erue Parallel Circle P a b, wvtich is Parallet
to che siren Oblique Circle AB C, and ae the gi
ven Distance oF 40 Degrees; or che half langene
oF 84 ser trom 8, Wwill sire b, and che halt Tangent
ot 16 Ocerces Pec also trom e, will sire che Poine
a che civo ends ot che Parallel Cireles Diameter.
PR O P. XXI.
Problem 10. Xo measure any Projected Arch of a P a
rallel Cirele.
Eere will bechree Varieries.
P. HF ic Be Parallet to the Primirive, chen a R uler
laid chro the Cencre and che Dirition oF che Limb,
Wwill Diride che Parallel into che lame Degrees, Or
Vecermine in che Limb che Ouanriey oF any ArK
Parallel t0 its
2. YF the Circle be Parallel 10 a RiphE OniC, 25
a b dis, in Cale che second ot the last Propolirion,
and ic erere required eo Meature chat Ark a b, OP1O
diride it inEO PFOPeF DegrCCS : Since ThaL Parallel
Circle i8 66 Decrees, 30 Minutes, dictane From P.
che nearer Pole oF theRishe Circle A B, anid conse
quencle 1Y3 Deerees, 30 Minutes, distane from ies
Othet Pole, rake che halF Tangene OF PL3 DeorCCS,
30 Minutes, or the Tangent ot its hialF56 DCgrees,
45 Minutes, and wich thac Distance, and oh the Cen-
rre of che Primirire, deaw 2 Circle Parallel co the
Limb: And divide chac halF OF ic, wrtieh lies cO-
wards che opposice Pole oF A B into its Desrees
wvtrich is casilr done by a Sector: Thena Ruler laid
From P, and che Pqual Dirisions oF thar Semicir-
cle, Mall Diride a b, or Mealure any ParE
OFIE.
3. FoMeature or Diride che Ark OF a Circle
hichis projected Parallet eo an Oblique onc.
As supposethe Circle a b which is P’arallel eo the
Oblique one AB C, in Case che ihird (Fis. 2.) OF
the preccedins Proxontion: And at che Distanice ot
40 Degrees: this Parallel Circle beins 40 Dcgrces
distant from the Plain oF the Circle A B C must be
be 50 Deerees distane From irs Pole, and conse-
queney r30 Desrees trom thie oppotite Pole. Pake
FherCFOre Fhe HaIF TAnGCNE OF FZO DEGFCCS, OF LMC
Tansent oF its halF65 Degrees, and with chat a5 a
Radius, deaw a Cirele Parallel Eo the Limb oF che
Primirire; Wrhich Circle Divide IE InEO PFOPeF DC-
orees: Thien MaII a Ruler laid chro P, and che c
qual Dirision ot thar Circle, cure the licele Circle
A b intoits proper DegrCes; Or truly sire thie Mea-
Ture oF any partOE ic.
SPHERTCK Trianele, is a Space included wict.
in che Artes of chree great Circles otche Sphere, In-
cerlectins cach orher on che Surtace oF ihe Globe.
and erery suchi Priansle is cirher Duadrantal wticti
harhon one Side (ac le aMt) a Ouadrarit and onc AN-
sle RishE. Or non duadrancat ertrich hach aII
Inche Righe angled Spherick Frianglo YR 83
FT = 54 Degrees 15 Minures, the Suns Longi
eude From the nexe Pquinoctial POInE, OE 24 DC.
Prees +5 Minures OF 8.
B-
S1 Desrees 52 Minures, ihc Suris Rixhe
AsCenSOn.
e
nation.
18 Degices 15 Minutes, ihic Sunis Decli-
S = ehe Angle OF che SunS POTTION.
Y,  che Ansle oF che Suns ercarest Decti-
nacions
lo malee the Triancles
Nich60 DCorCeS OI a LHIC OL CHOTAS, desctiDe
the Cirele Z CIE C Wvhicti is the Limb, or Pri-
mitire Circle, and here represents che Solstitial co-
lure. Deaw che Diamerer PC, wrtich ill be
the Equator e here represented by a Righe Linc, be-
cause the Fye is aF Y Or , in irs Plane. Take
23 Derrees 30 Minutes trom che same Chord, and
set ic trom RroC, (0 Mal C IE be che Bclipriek
utrich wvill be a Ristit Line also for rhie Came
ReaIOn. Then cither etie Suns Place set From Y
on ehe Peliprick, or his Righe Ascension Per From
etience on che Equator, will gire che Point S, Or
R, accordinsly. Then drair Z N at RighE AN
eles ro ihie lquaror, and (0 rou will hare chree
POintS Z S NV, Or Z R HI, chro which che Circle
oE Declination Z S RNI, mas be eatilys dravno
L0 Mensure the dides ana AnCleS.
Tured on the Scale oF halF L’angenes, by Prop. 6. OF
Sphericke Geometry; and che side P ismeasured, by
Andins l, che Pole oF che Oblique Circle Z. 8HI;
and from chence laving a Rulet eo thC ENO Fxrre
mirie softhe Side P, (3. 0.) thro 8 and R, in Or-
der ro reduce ehem to rhe Limb in P and e; che
its Sidesmore or less chan 90 Degrees; and all IIS. Ark P. C, mealured on che Pame Line of Chords,
Amslesbisser oc testet chari Kight Oneo.
ill sire che Ouancies oF ehc hide S H == 18De
BiceS, 15 Minures.
Lhe Application of Sphericke GCOMCEEY, tn
the Construction aud Mensuration of a
tbe Parts os Spherick Frianeles.
The Sides FI and B DeIHS Mall Lhes; aremea-
An