E 5°° ] 
In both cafes, if the point T be fuch, that the 
redangle under MOT be equal to that under 
Fig. 3,4. LOK, whereby MO fhall be to OT in 
the given ratio of the fquare of M O to the 
rectangle under L O IC, the given redangle under 
KML will be to the redangle under L T K (by 
Prop. 35. L. 7. Papp. [b] ) in this given ratio, and 
therefore given ; confequently the points T and O 
will be given. 
In like manner, if the redangle under MRV be 
equal to that under L R K, fo that M R be to R V 
in the given ratio of the fquare of R M to the rec- 
tangle under L R K, the given redangle under 
K M L (by Prop. 22. L. 7. Papp.) will be to the 
redangle under L V K in the fame given propor- 
tion, whence the points V and R will be given. 
Thus in both cafes the points T and V will be 
found by applying to the given line K L a rectangle 
exceeding by a fquare, to which the given redangle 
under KML fhall be in the given ratio of the 
fquare of M O to the rectangle under K O L, or 
of the fquare of M R to the rectangle under 
KRLj MO being to O T, and MR to RV, in 
that given ratio. 
But in the laft place, if this given ratio be that 
Fir ^ of equality, fo that the fquare of RM be equal 
to the rectangle under K R L, by adding to 
both the redangle under MRL, that under RML 
will be equal to that under KM, LR, and MR to RL 
as KM to M L, and the vertex R of the diameter 
greater or lefs than the ratio of the fquare of N O to the fquare 
of N M, which is the fame with that of the fquare of the differ- 
ence between A K, B L to the fquare of A B. 
[i] See pag. 51 1. 
R I 
