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# Title: Lexicon Technicum: Or, An Universal English Dictionary Of Arts And Sciences (shelfmarks Leibn. Marg. 71; ZEN Leibn. Marg. 71)
# Folio - , page id 806933011:0840
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PROPOSTTTONL
 every Triansse, ihe sum of all ihe three
eguat 1olo Riehrones; and the external ansl
made by any Side produced, is equal to the sum c
the incernal and its opposite.
ICay, 1. a -  b -
 a
= 2 b
e
on che ocher hand, it the sides are equal.
the Angles must; for being equal, ther Hust necds
be equally enclined to che Ba(C a D, t C LOIEC,
ohere cher meet.
PR OP. UI.
in ruo Trianeles A B C, and 2B C, is all ehe ctree
Sides, or tvo Sides and onc Angle, or euo angles
and one Side, be respectively equal one to another,
the whole Friancles are equal
Os ibe Properies o Plame Friameles.
F
beins laid one on anocher, ) vill coneur:
N.
(3. e. Y. FVCl.) Wherctore b  a  0 = 2l
D. F. D.
Fucl.) ilc beraken trom boru, thete mult remain
5 = b Y a. 8. F. D.
COROLLARY. 1.
Htence no S can have 2 obrule or2 L.
COROL. II. 
In a Riehr-argled A, the 2 oblique Angles mul
make a rieh one berween chem.
C OR OL. HII.
H2 Aneles in one A Be = 102 in anorter, 1
remainins Angles mult allobe equal.
PR OP. I.
In the same Triancle, equal Sides subtend; and are
subtended hy equat Ansles.
T(ay, it a = b, then a c = cb.
Llas, che Triangles a b0 and ebc, havine chc
b0, arel deceen che lame parallel Lires
Drav che prickd Line chrouxh che Vertex
criancles on the same Base, and havine the same
Deiehr, (ehat is, beins betreon che same pacalibt
Lines) are equal.
.
c
Came Ba
parallel torhe Base: Then will che Angles d and e
be sererally equal ro che alternate ones b and c.
(29 e. L FuCL) BUL d 1 = a  c = b (bY C OF. 2
dL aned, dec equal.
Dra de and es Parallet e0 ab.
1. The Priangles d ce and cc f are equal, be-
caule cach equal ro hale the Parallelogram d f..
2. The Triangles a b e and eb fare allo equali
eins cach equal ro half rhe Parallelosram af.
3. Bur A ab 0-F Aces = halF he L af.
4. And L eb c-] A ocs = hals che a5.
Theretore, is ihe A Ces be taten avay trom
borh Sides, ihe Ae bc must remain = e0 rhe
Triongles a b6. 8. F. .
And since c-] fare al(o equa 10 2L (15. e r.
Becaule che Angles a ane b are equal, che Lines
ac and c b must be equally inclined co. rhe Bale
ab; and consequentY, be (0 ac the POinE C; WherC
cher meet, and theretore c must be equidictant
From a and B3 FOr iF C DC neaTeK EO, OF FartHer
from b than a; ic must be because the Angle a is
hettec o srealet Manb, rhicn is contraty 10 Mhe
Dubpotaron.