tRtougfi 4 let the line ;x , and through h the line 
be drawn , let yz. be join'd ^ I (ay that yz. is parallel 
to 4^. 
For fince the Redlangle vah has been made equal to cad^ 
and say is equal to the fame, the Redlangles vah xAy 
will be equal : Therefore the points y, h, will be in a 
Circle, and the Angles ayv, abx upon the fame Line 
will be equal , but beeaufe vy touches the Circle xyz, and 
xy cuts it , the Angle ajv is equal toj'^A:. Therefore the 
Angles yzv abx will be equal. Therefore the Lines 
y% 4^ will be parallel, which was to be done. 
. The fdUwing Problem is t^kenrnt of the [econd Book, 
ol P R O B L E M. 
The Line between^ and c being Divided in b and 
/ , to Divide it again in x fo that the Reiiangle 
€xb be to the Rejdlangle dxc as mf to^^p. 
f 1 J ; — — 
a b ^ / h 
Let therefore - , ^/ Ji^c: : mp, gp 
Therefore if you make. xd : ; mp, py 
And alfo "bx, xc; ; py gp 
The Eroblem will be folv'd ^ for the produds of the 
Analogous Terms will reftituxe the Prop.ortion. 
Let therefore ax , xd ; nip, py 
md' Compone^do ax, zd: : mp, my 
Let ^4 4^ be praportionai ak. mg 
^Ifo bX, jpe.i; -py- gp 
and Compose ftdo be, xc :; gy^ go 
Let bcjcf^ ^g^gp be proportional q£;^ i 3 
Therefore Compomndo. xf, xc^^ fiK^ 
and by equality ^4 Kc:.- ak, aS 
and C^^^^r/^/,^ ^^^^ l^v^^., ^j^^ 
T:be fmmtp^ Prohlm^ h m of iht'tbiri Book-^ ^ - ^ 
