# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/806933011:0862
# Permalink to this reading: https://leibnizlegible.com/page/806933011:0862?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 806933011:0862
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=806933011&page=862
# Source image: https://digitale-sammlungen.gwlb.de/content/806933011/jpgs/default/00000862.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 83 lines, status machine
# Lines: 83 recognised, mean confidence 0.82
# 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.

det 4 dd d
SIVen Dche Anxle oE che Suris Position, auet P et
ITour trom Midnishe. Required BL eC oun
Distance from he. Po)e.
F. P: R: : c, B: E. BP.
F, P = 10, 0376939
Radius = 10.
t7: B = 9. 5031092
c: BP = 9. 4654053 = 73
C AS F XVI.
Siven as Betore B, the Anele OF Postion, and
che FTour trom Midnishe. Required P A =
the Laricude ot any Place.
S, P: R: : ZB: Z P A.
5, P = 9, 8675151
RadtiuS 10.
Z, B = 3. 4821283 = 97 201
2, P A = 9. 61461 32 = 24 191
Obligue Sphericat Laius, ula) DC Leducec 10
evo Riohr-angled Spherical ones, O) sells laita
Perpendicular, wrtich cicher divides che Oblique
Triansle propoled into trvo Righe ones, ormaties
cvo Rishe ones, by addins a Riehr anse Lrian
Sle 1O IF.
Wohieh (by chis Preparation) may be lolred by che
qrvo ut Adomo, oe bi tules dedueca hou
chem.
A X LO N. III.
In any Triangle the Sines oF the Sides are proporri
onalco che sines ot che oppolice Angles. FOrBY
Ariom 1.
LhecCtOLE d, BC: d, 15:d, D:d, B.
The Cosines Bt che Sides ale proxorrional 10 che
Cosines oF che Bales. Forby Case 1. OF Rishr.
anslea syberick triapeles.
R: C5, P A: : cs, BA: c 5, BL
Esu PA:: cs, C A: CS, DP
es, BA. es, BP:, es, D, A: c s, DP.
D L E HI.
porrionat
The dines oF che Bales are reciproc
c0 chC LAHBCMIS Ot che AB es at che BaleS. LB1
by Axiom 2.
6DA: R:: F, P A: F, B
32 l2.l.. 1,Ca: 1, l
THeretore S, BR L l, D = k X l, A == S, D A X L, D.
Consequeny S, B A: S. D A:: Y, D: T, B.
VL E W.
The Tangemt or che Sides, are reciprocallr pro-
porcional 10 ihc Cohines ot ihe Aneles aC ThC
rella. 101bnse4.
BC: R:: l, l A: C5, DP A
L,DL.l. . L LA - Cs, DP A
Theretore L, BL: L, Ol:: e s, t A. Cs, BP H.
In Oblique Trianeles chere ave 12 Cases, 10 or
S, BP: R:: S, PA: S, B
gs 22. L..d, ll. 0,2
telte.
In lerrins fall joux Perpendicular, obserre chis
Sivd diao,s id po
t t fall from ic end os
site 10 a siven ansle.
For by so doinx, vou have cnouph piven in onc
Criansles ro determine als bt
oF itie Riphe anglec
ics untenonn Latts.
ceration by chechird Axiom; che ocher eistr l ales
ire solred cach by uro Operations.
The tvo sirst Cales are solved each br one Op-
les ac the Base
are P
30
ionalro chesines of che Angles at the Verrex
For b7 Case 7. Ol Rishc- ansled Spheriek Frianstes
R: cs, PA :: S, B PA: c s, B
R: C5, PA: : S, D P A: C5, L
Lhetctere 1o, b. S, BP A:: Cs, D: S, D P A.
The
Obserre also, che Addicion or Subtraction Bortr
OF the Segments OF che Base, and Angles ac the
Vestea accotuus ad the Perpendicular talls wictuu
or rutione be trande
Croportions