will be Similar J Th^efore the Angle dxz will be equal 
to the Angle xlz, that is, to the Angle (for the 
Angles and are equal , becaufe ^^^in a Square 
or Rhombus is equal to the hngk abd^ or its equal j^^^ 
hence adding the common Angle xbyy the Angles dby 
xlz will be equal.) Therefore finct ihe Triangles d&x^ dby 
have the Angles ^^-^ and eq ni, and the hn^^bdx 
common, they will be fimilar, and therefore db will 
be to by as dx to xz that is to g 5 but becaufe ad^ bx 
are parallel, will be to ^7 as to x;. Therefoie by 
Equality ab is to db as ^ to xy. But by the ConftruClioa 
nb is to db 2lS g to m , Theretx re xy is equal to 
Which was to be done. 
F R O B L E M. 
A Circle xyz being given by Pofition ^ and two 
Points in it a and ^ being given, to draw the Lines 
ax^xb fothat j» (hall be Parallel to 4^. 
ANALYSIS. 
Let therefore yz be parallel to Ab 
Therefore the Angle abx t= yzx 
Let the Angle ayv be made abx 
Therefore the Angle ayv — yzx 
Therefore Xy y^ are in a Circle 
Therefore the Redan gle vay xaj 
But the Reftangle xay any Redangle through a 
Theref. the Redangle "oab = any Reftangle through a^ 
ConjlruBion and Vemonflration^ 
Let the Re6iangle vab be made eqiial to any Redangle 
through fuch as , let the Tangent vy be drawn 
K k through 
