[ 52 6 ] 
In the laft place when the line LM drawn through 
t’ne fun in A, and the proje&ed place of the planet 
in B, is neither the axis of the earth’s orbit, nor bi- 
feded in A, the tangents to the points L,M 
2 9* being drawn to meet in P, let LM be bifed- 
ed in Q, and the point R taken, that the redangle under 
A Q R be equal to the fquare of Q M, whereby 
P D O being drawn, the redangle under A QR (hall 
be equal to that under O QG, and QG to A Q as 
QJl to QjO, or by compofition A G to A Qjis O R 
to QO. Therefore if N B be here alfo taken equal 
to I, and N S to A B as I to A Q, A B being as 
before, to N K as A G to I j by equality N S will be 
to NK as A Gto AQ^thatis, as OR to CfO. Whence 
by converfion N S will be to K S as O R to (VR ; 
and if P T be drawn parallel to C B and S V be here 
taken to N S as QJL to T R, by equality S V will 
be to K S as O R to T R and alfo by converfion S V 
to K V as O R to O T. Moreover S V will be given 
in magnitude, and the point V given; therefore VW 
drawn parallel to C B, or K D, will here be 
given in polition. But WDXY being alfo drawn 
parallel to R V, S V will be to K V, or D W, as 
Y D toXD, and Y Z being taken equal to the given 
line S V, Y Z will be to D W as Z D to X W, equal 
to T V, and the given redangle under Y Z, T V 
equal that under W D Z. Therefore r Z being 
drawn parallel to R P, R T, and its equal Y Z, be- 
ing given, the line r Zis given in pofition, and the 
point D in an hyperbola having for afymptotes V W, 
F Z, and palling through P. 
4 
Thus 
