[ 5 2 3 ] 
therefore is given, and the angles A P D, P D A be- 
ing given, the angle P A D is given. 
Coroll. Here, where the orbit of the earth is fup- 
pofed a circle, the ratio of 1 to A B, that is, of the 
rectangle under A B, I to the fquare of A B, will be 
compounded of the lubduplicate ratio of AM, the 
femidiameter of the earth’s orbit, to half the latus rec- 
tum to the greater axis of the planet’s orbit, and of the 
ratio of radius to the co-line of the inclination of the 
planet’s orbit to the plane of the ecliptic ; and adding 
on both fides the ratio of the fquare of A B to the 
fquare of A M, the ratio of the redangle under A B, 
I to the fquare of AM will be compounded of the 
ratio of the fquare of A B to the rectangle under A M^ 
and the mean proportional between A M and the half 
of this latus reffium of the planet’s orbit, and of the ratio 
of the radius to the co-line of the inclination of the 
net’s orbit. 
In the next place, though the earth’s orbit is not a 
circle concentric to the fun ; yet if the projection of 
the planet falls on the line perpendicular to the axis 
of the earth’s orbit, the point A will Hill bifed L M. 
In this cafe draw to the points L and M tangents 
to the elliplis meeting in P, from whence through 
D drawP D meeting the elliplis again in Q^and in- 
terfering L M in O. Here if a tangent be drawn to 
the elliplis in it will meet the tangent at Fig< 
D on the line L M in the point G. 
Now L G will be to G JV1 as L O to O M, and 
the point A bifeding L M, the redangle under GAO 
will be equal to the fquare of A M. But B G is to 
B K as A G to I. Therefore B N being taken 
equal to I, A B will be to K N as A G to I, and 
the redangle under AB, I equal to that undei AG, 
