of the Terms xc znd xh^ therefore Dividcndo ac^ at?- 
JTtfj xb^ which was to be done. 
PROBLEM. 
To Divide the given Lines ah Bq in x and j fo 
that Ay be to xc zs f to g and xb to as h to 
Conditiofis^ 
^^'^ f S 
and AT^ ; : A, 
Affalyps. 
Let therefore : ^ g. 
and alfo xb ye:: hy k. 
or bc^ cq. 
And as the fum of the Antecedents to the fum of the 
Confequents, fo one Antecedent to its Conftquent. 
Therefore xc^ yq:: % k\ 
©r g t. 
Therefore by Equality Ay, yq : t fy L . 
Conftruciion And 'DemonfirAtion, > .. 
Let h be to as be to ^j*, and fo g to7. Let Aqh^ 
be Divided in y in the Ratio of / to I, and let ay be 
to xc as f to g, I fay that xh^ yen hy k. for hnce 
by the Conftru^ion ay yq : : /, / * and ^7 to xe as f 
te ^ ; by Equality xc will be xoyq^ as g to I that is 
as ic to and becaufe the difference of the Antecedents 
is to the difference of the Confequents, as one Antecedent 
to its Confequent, xb will be to yc as be to cq^ that is, as 
^ to ^5 which was to be donco 
P R O B L E M. . 
A Square or Rhombus a b c i being given t© 
draw 
