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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 806933011:0842
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Ihe Third may.
L(a7, 4c9; = ab 93  b09
2. ANet 00 = PB. E. a
3. Bucbb-- 00 = bb-  a a - ] P P.
L. L.. D.
Wherctore BB ehcccllo ie late diet d 2du
P R O P. VIII.
In an Acute aneled Friangle, est Square os the
Side (H) subtendins an ACure- disC, is less thanthe
Sum of the Squares os the other d sous, by dou
blethe Rectansle under the nhole Base, (B-) 2
the dcure ansle
and the Serment of the Base (2) which is next te
all ehre
culaF pP.
Make B k = 10 e b, aliet compleat alt cheSquare:
Ttien will,
1ac = D -  X 7 27 l.
Dab = X ] R. p. O.
060 = Z -] II.
Wheretore cakins aay what is common, l
mains D. I Y = R ] II. ]- O. Bur chen,
R = T, Bec, a0 = d e, a5 = ab, and L5 = b.
Remains co be prorec, chat
t. bb- pp - 2 a aF 2 a b, 15 ehc dum Ot
D = HI.-]- O. Which ic is, becaule D = R che Squares OF che LeBS.
(aS havins 2 = Sides and one L) and R WaS prO.
ed = T, and T = O-) FI, becaule a c == 6c
che Angle at b = k, and the Ansle a c b = eck
(becaule cach writh bce makes a l.)
Wheretore, che Square oF a c = ab 9; -] - b09;
P. L. D.
PROP. VII.
in an Obrule aneled Frianple, ihe Square s che Side
subtendins tbe Obtase Ansle, excceds the Sum of
Rectanete, (2 b a) under ihe Basen alca cide paio
added t0 it.
Tet Fall che Perpendieular p, and produce b, ril
le mec vernaie.
the Squares of the ether evo Sides by the double
Demonseration.
Demonstration.
2. 11+F
2. b = p p. 1 e a.
3.  b. F a  2  .
WHeretore Bh is less chan thal B) 2 a a -F 2 ab,
Wrhich is plainly equal ro che Double Rect. angle
underche whole Base, and he PaHE a.
L R OP. LX.
. Lb = bb + 2b a + aa + 2Y.
The Side ab os an Equilareral Frianele, ab C, in
Scribed in a Circle, is in Pover Triple of the Ra-
aldo; or its square is equal 1o chriee che Square os
the andius, 2 d.
.0. -..
Tec he Racius be called R, nud conlequemis
o dguaee K R.
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