[ 5 2 4 ] 
KN: whence AO being to K N as the redangle 
under GAO to that under AG and KN, AO will 
be to K N as the given fquare of A M to the red- 
angle under AB and I, alfo given. 
Draw R P parallel to C B, and take PS to A P, 
alio N T to A R in this given ratio inverted. Then 
will the points T and S be both given, alfo A O will 
be to K N, and R O to K T, as A R to N T, that 
is, as A P to P S. Therefore if T V be drawn par- 
allel to C B, that is, to K D, and V S parallel to 
LM, thefe lines will be both given in pofition ; and 
WDXY being alfo drawn parallel to LM, WD will 
be equal to KT, and RO being to KT, as 
AP to PS, DY will be to WD as XP to PS, and by 
compofition YW to WD as XS to PS, and the given 
redangle under YW, or SV, and PS equal to that un- 
der W D, and XS. Whence SV being parallel to LM, 
the point D will be in an hyperbola paffing thro’ P, and 
having for afymptotes the lines VS, VTgiven in pofition. 
But if the projedion of the planet fall on the axis 
of the earth’s orbit, or the fame continued, A B ex- 
tended to the earth’s orbit in L and M will be the 
axis of that orbit. 
If alfoC B fhould be perpendicular to AB, K D 
Fj _ would be ordinately applied toLM; and 
lg ‘ 2 "‘ the point R being taken, that Q^being the 
center of the orbit, the redangle under A QJl be 
equal to the fquare of Q_ M, the fame will be equal 
alfo to the redangle under G Q^K ; whence as G Q 
to A QJo R Q^to Q^K, and A G to A as K R 
to QJC. But, as above, B G being to B K as A G to I, 
and B N taken equal to I, B G will be to B K as 
A G to B N, and A B to K N alfo as A G to B N or I. 
1 herefore if N S be taken to A B as 1 to A Q, by 
equality 
