[ 5°6 ] 
E G, E P or O G will be given ; and in the laft 
place the ratio of F G to GL being given, the 
ratio of the reCtangle under A G and G L to that 
under E G, O G will be given. And thus three 
points A, L, O, will be given with G E infilling 
on A B in a given angle, as in the preceding 
cafe. 
Moreover, AC and BD being parallel, AB and CD 
may be alio parallel. And then, when the ratio of 
^ the rectangle under AGB tothatunderGEF 
A J °’ 1 * is given, the determination of the locus is fo 
obvious as not to have required a diftinCt explanation. 
But when the reCtangle under AG, EF bears a given 
ratio to that under B G, G E ; let the diagonals 
A D, B C be drawn, and H E L K drawn parallel 
to A D. Then the rectangle under H E L will be 
to that under K E I in the fame given ratio ; 
and if C M be taken to M B in the fame ratio, the 
lines MNP, MOQ_ drawn, the firft parallel to 
A C, B D, and the other parallel to A B, C D, will 
be given in pofition, and the diagonal B M will 
bifeCt both IK, NO, and H L ; therefore the 
reCtangle under H E L being to that under K E I 
as M C to M B, that is, as NH to N K, here by 
divifion the reCtangle under H E L will be to that 
under I H K [ e~\ as NH to HK; therefore equal to 
that under N H and I H or K L. But the rect- 
angle under N E O is equal to the fum of the red- 
angles under H N L and under FI E L \ f\i there- 
fore the redangle under N E O is equal to that 
under N H, N K, equal to that under A P D, 
that is, equal to that under P A or that under 
P D Q, the diagonal B M bifeCtingboth P Q^and 
[c] By the prop, of Papp. before cited, [/] By the fame. 
A D. 
