# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/806933011:0846
# Permalink to this reading: https://leibnizlegible.com/page/806933011:0846?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 806933011:0846
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=806933011&page=846
# Source image: https://digitale-sammlungen.gwlb.de/content/806933011/jpgs/default/00000846.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 88 lines, status machine
# Lines: 88 recognised, mean confidence 0.88
# 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.

2. AS Radius is ro che Sinc :: (0 is c)
Can
Called a Fansene: And il a Righr Lie De ataton, Wo che langene. lhacis, CO: OR:: C S
insich che Langene MM Sy at LICSCIs Callee
a Secant, and they boch limit one another, (0 25 rO
bc etic Fangent and Secant oF etie AFKEOT: F N
is the Con Parigent, and C N che Co- Secanc oFcte
Tame Ark; but rhey are che Lansent and Secan
ot the Complimental Aek O F.
6. The Line I L’intercepred berreen cheRish
Sine and che Tangent, is called ihe Versed dinc
and by some sasitta.
7. Wiaterer Number ot Dcorces an Ark wan
oF a Semi circle, is called iis Supplement.
8. THC L Ine C R, Which is che parE OF the R a
dius C T lving Delheen che Centre and che RigHE
Sine, is alvars equalro, and mar be catten for chie
Co SinerO; and Cr is equal ro che Rishr Sine
DR.
the Radius and Co. Sine, I ie Versed Sine: Thus
DF, O.
Ehe C0 decatitu Mahe a ti B a 1
etie ruvo tormer.
dut
3. A5 the Sine is to the Radius:: (0 is che R a
dius corhre Co-Secant. THat Is, OR: OC::
L C: CN.
. Aeche Taneentioro ehie Badius:: Sois Ra.
dinsro che Co. Tansent; dd ST: IC : : F N.
Theretore che Rectangle berween the Tangent
and C0. Tansenc oF any Ark is equal coche Square
Ot che Ladius.
FI. Lvery Prianslehas Ex Parrs, oF Whichchrce
are Sides, and chrec Angles; and ot thele iti ve
have chrce siren, we can tind che Fest, (except in
the Case where the chree Angles only oF a Plain
Trianste ace Biven.)
For From chence the Sides cannor be found, be-
cause ro Friangles may be Equiangular, and vet
hare che Sides by no means ot che lame lenerhs
We can And the rest, Ilar, it supposine cheRadi-
us dirided into any Number oF equal PATES, We
can bur discorer hon many of tuch parts any sine
Tansent, or Secant ot auy Ark or Angle doth con-
cain. No chis is reads done r0 our Llands, in
che Table of Sines, Lansents, and Secants, wtich
ve have, wich prodisious Induster, in Books rea-
dy calculared For this purpole.
12. Wrhen cheretore any Friangle is siven t0 be
resolred, the Arst chins e hare to do, is to consi-
der, Thar there is in the Table oF Logarichms,
Sines, Tansents, and Secants, a Friangle exactiy
similar, and equal ro thac wtrich e are required
tololre, and Wrhose Sides are to one another inthe
very Came Proporrion ot chole of che Triangles
proposed.
2. Ie must understand wrhatever Ratio one
Side oF the Friansle siren, hach eo the orter Side
about che lame Angle, considered as Lenerhs esti-
mared or numbred br any knomn Meature, 25 sup-
Pole Inches, Tards, Miles, Leagues, (9c. the rerr
Tame hach checrro Sides abour che lame Ansle in
che Triangles in che Tables, or in the Tabular
Parrs: Which cro chines vell’ understood, do lead
us inro he wole Mytters ot Frigonometrical
Calculations.
13. Frixonometr, is cicher Plain ot sphericat:
and boch may be relolved by che means oF 4 Pro-
positions, which becaule ot their excellent Vle, are
Called Axioms.
24. The hrst or wohich relaces 10 Rectansle. Plain
Triansles; qere jo chid.
S. A Pine, as Y Se ronchine e Circte in che
Poine P, and Perpendieulax to che Radius CT, 16
chroush Otrom the Centre ot che Circle C) meet
9. LLaHIY Ark DC lels chan a OuadranE, 25 FC
che Disserence berirech he Radius andrhe Co. Sine
drant, as che Ark Ol dorh; chen che sum de
is che Verled Sine R T; buc il ic exceed a Oua
DC Y C R =DR che Versed hine oF che AC
20. The Radins with che sine and Co. Sine ot
any AEk (25 FO) do makre a Righr-angle Trian-
BIC, 25 OCR, erhich is similar roche Triansle
S L, mace OY che Radius, che Tangent, and
IHCSCCanE. AHO ie Radius, the Co- Tangent, anc
sence ris plain,
1. Thar as che Conine is co the Sine, (0 is che
Eiplio p0 ste Tauveru. Thalio. CP: A D