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confequents, the redangle under r P Q^will be to 
that under S P t, that is, to the redangle under 
A Q B, in the quadrilateral ABC d, whofe two 
lides AC, B d, are parallel, in the given ratio. 
In like manner, if three of the given lines palfed 
through one point, as the lines C A, C B, C D, and 
the redangle under QJP R be to that under S P T 
Fi<r. 2 * n a S* ven rat io> this cafe is with the fame fa- 
cility reduced to the like quadrilateral thus. 
Draw B E parallel to A C, that (hall cut S T 
produced in t, and let the point F be taken, that 
the redangle under C A , E F be to the fquare of 
A B in the ratio given ; then CrF being drawn, 
B t, or Q P, will be to T t as A C to A B, and 
R r to A Q, or S P, as E F to AB; whence the 
rectangle under QJP, R r will be to that under 
T t, S P, as that under AC, E F to the fquare of 
A B, that is, in the given ratio of the redangle 
under QJ 3 R to that under S P T, and the rec- 
tangle under QJP r will be to that under S V t or 
A QJB in the quadrilateral A B C F, whofe two 
fides A C, B F are parallel, in the fame given 
ratio. 
Now let A B C D be a quadrilateral having the 
two fides A C, B D parallel, with any conic fec- 
tion palling through the four points A, B, C, D ; 
. alfo, the point E being taken in the fedion, 
and E F G being drawn parallel to A C 
or B D, let the ratio of the redangle under AG B 
to the redangle under F E G be given : then the 
conic fedion will he given. 
Let the fides A B, C D meet in M, and draw 
M I bifeding A C and B D in K and L. Then the 
4 ' diameter 
