[ 5°2 ] 
under AK, BL to the fquare of half AB, or of the 
redangle under AC, B D to the fquare of AB. 
But if one of the oppofite fedions pafs through 
A and B, and the other through C and D, the ra- 
tio of the redangle under F E G to that under 
A G B will be lefs than that of the redangle under 
Fig 7 AC, BD to the fquare of A B. For CL 
y ' being drawn parallel to A B, and A D joined 
and continued to M, the line D M falls wholly 
within the fedion palling through C and D : there- 
fore K M is lefs than K L, and the ratio of K D 
to K L lefs than that of K D to KM, that is, 
of B D to A B i whence B K being equal to A C, 
and C K to A B, the ratio of the redangle under 
B K D to that under C K L, being the ratio of the 
redangle under E G H, or F E G, to that under 
A G B, will be lefs than the ratio of the redangle 
under AC, B D to the fquare of A B. 
And here the point L is given ; for the given 
redangle under B K D is to that under CKL in 
the given ratio of the redangle under H G E, or 
that under F E G, to the redangle under AGB; 
hence C K, equal to A B, being given, K L is 
given, and confequently the point L. 
Again, B L being joined, and N E O P drawn 
parallel to A B, alfo G EF continued to Q, as A G, 
equal to C Q, to F Q_ fo will C K be to D K, and 
O P to E G, equal to O B, as K L to B K, con- 
fequently the redangle under O P, A G will be to 
that under E G, F Q_ as that under K L, C K to 
that under K B, D K, that is, as the redangle un- 
der A G B to thrtt under FEG; and by combining 
the antecedents and confequents the redangle 
under PEN will be to that under Q^E G in the 
fame given ratio. More- 
