C 528 ] 
axis. Let this axis be ab meeting R P in c, rZ in 
d, P T in * and W V in f Then the angle a AM 
is given, being the didance between the heliocentric 
place ot the planet in the ecliptic from the earth’s 
aphelion. Alfo PT being parallel to C B, the angle 
AT e, and confequently the angle A e T, will in 
like manner be given, whence the points r, R, T, V 
being given, as in the folution above, the points d, 
c, e , and / will be given, the triangles A II c, A T e, 
being given in fpecies, and fimilar refpedtively to the 
triangles A r d , and A V f Alfo the redtangle under 
W D Z being equal to that under R r, V T, if D K 
be continued to the axis in^, and D/6 be drawn par- 
allel to PR, the redtangle under f g> hd is equal to 
that under j c, d c, and both being deducted from 
the rectangle under f h d the excefs of the re&angle 
under /’ h d above that under/ e, dc will be equal to 
that under g h d, fo that this difference will be a mean 
proportional between the fquare of h d and the fquare 
of bg, which is in a given ratio to the fquare of h D, 
and therefore in a given ratio to the recftangle under 
abb , D b being ordinately applied to the axis 
a b. 
Thus a biquadratic equation may be formed, where- 
by the point b fhall be found, and thence the point D, 
whofe diftance from A is to h e as the excentricity of 
the earth’s orbit to half its axis. 
Therefore I fhall only obferve farther, that here 
occurs an obvious queftion, what, in fo extended a 
fearch for principles leading to the folution of any 
problem, as the ancient analyfis admits of, can con- 
duct to the mod; genuine upon each feveral occafion. 
But 
