[ 36 ] 
Then in the right angled plane triangle C/S, it will 
be as rad. (i) : CS (d) : : fine SC / (V) : S/ (</V), 
and confequently Ck (= K S — S / ) ~ r — d V ; 
but by prop. III. Ck = V^-^xzv+zvT > whence we 
fhall have r — d V = W— ^xzv+zv) : Now by 
proportion I. we fhall find £ == b' x p -f p'z* 
P —p* 
Z = / and Z = / t by prop. II. 
/ 2 X I 
0 2 4?'— H 
** ^ r__7 ~ p > and = "T* T J i a %byprop.IV. 
V = - — and V = 
yA — q v 
P 
q r ~~ 3 which values bein^ 
qA—q'v 0 
fubfiituted in the above equation will exhibit the 
nature of the required curve rtRN, in terms of z 
and v. 
SCHOLIUM. 
If the fphere LIKQI reprefents the fun, and the 
fpheroid BPOD one of the primary planets, it will 
appear, from the preceding reafoning, that the figure 
of the fe&ion of its fhadow received upon a plane, 
which is perpendicular to its axis, will not be a circle 
(except when the axis of the planet produced pafle.s 
through the fun’s center) but a curve of the oval kind, 
whofe fpecies will be known from the foregoing 
equation. 
If the fphere LIKQI had been regarded as a 
fpheroid in the above folution, it is eafy to lee that 
tlie foregoing procefs would have determined the 
nature 
