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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 806933011:0843
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LLaY, then d c = = R, set ele rvo Triangles
V: =RR; 1. c. coche v: kL, Or20 1: 3 kk
WrheretorezRR =F, Ot 16; Or a b4 == 3Rl.
D. F.. D.
ratins a Letrahedrum, and in lCriBIIS IE I a BIVen
Sphere. Sec Prop. 13. e 13.
sea ande a d, are equal, a5 havins rvo Angles
and one Side Equal in borh. Wheretore che
Square ot e d = = R R; ertich beins subtracted ina Triansle, a Parallet 1o che Base, is 10 che Basc
trom. R R, lcares P P = + RR. Wheretore
P= V. 3 RR; and consequeny ies double a b
N. B. Flereir  coundeuuastraset
OP. X
The Sides of a Friangle are cut Proporcionablys 
Line drann Parallet to the Base.
Thac 15, it makes, a b : b c : : a d : des
Wraw ihe, LineS b c ala 6 do
 t t tolco Atac  l cottcit. Abt   Et tot C HB etl
Le55.
hac i6, d0: cb: : a d: a0. : 4c: a b.
Dear d5 parallet 10 e b.
Then will f b = d c: ThCLCTOLC CWII DE
f: fc:: d a: d c: And b7
inversion, fc: bf: : d c: d a. And chen b
Composition, fc -  - b f (1. C. b c): bf (1. C. d e
5: dc = d a (1. C. a c): d 4; Or do cb: de:: 40
: d a.
E. D.
irien trverced, ejves dc: cb:: a d: ac
R O P. XII
in a Rixhr angled Friangle (a B C) a L ine (2 d)
dranon fromthe Riche-ansle at the Top, Perpendi-
cular to the FIyporhenuse (DC) divides the Friangle
(ab C) into eivo other Ristc angled Triangles.
robich are similar tothe first Friancte, an 10 one
arehie
B seue
Demonstration.
P. The Triansles bde, and bde, are equal, because
on rhe Came Bale, and berreen che lame Parallels.
Pherclore he Triangle a b a, Wwill hare che lame
Proporrion rochem bott, 2. c. a b d: b dc:: a b d:
b aC. Bur che Prianele a b d, having che Camie
heighe Wvith che o equal Triancles b dc and
bde, ill beco chem as ies to Sides a b and a d,
are corheir Bales b0 and d c.
Theretore a b: cb:: a d: d e.
Trhich Proporrionals, may be consdered and
varied accordins 10 che sereral Species ot Propor.
tion.
ASby inversion, c b: a b: : d c: d a FhC PATES OF
che Lexs belo che Parallel, are Proporrional t0
chole above ir.
ol one Les abore itic P’arallel, isto che l’arrot the
oiher Leg abore che Parallel, a5 the ParES Below
Thelane chine mas be done by composicion d
Division, _C.
aat . dd det st  dtt tet
ebo c tato
AIIO alternately, a b: a d:: c b: d c. The ParE
arCFO One anOThet.
r. For all chree Triar e ut  L alBlC
And che Trians  aleu d, have ihe Anele
common lo boch) and consequens ine Lhirc
2. The Case is che lame, a5 ro che Friangles
a bc and a dc: Bucche Friangles a   a
beins similar ro the grear one a b c, must bc al-
(0 similar tO OnC anOtHCF. 2. F.. D.
From the Similarier ot wrhich chrec Trianeles,
ic ill Follor, thar che Sides abour else Lsctal An-
glesare proporrional (by 4. e 6. FuCL.) and chence
arises he PrOOF oF che nexE Famous LLopbirion, b)
chis means prorelt 2 tourchi War.