L 521 ] 
the orbit of the earth, and the point D the place of 
the earth, whence the planet would appear ftationary 
in longitude at B. 
Join AB, and draw a tangent to the earth’s orbit 
at the point D, which may meet CB in F, and 
the line AB in G 5 draw alfo AH making with 
DF the angle AHD equal to that under ABC. 
Then the point D being the place, whence the pla- 
net appears ftationary in longitude, as F B to F D fo 
will the velocity of the planet in longitude in B be 
to the velocity of the earth in D, this velocity ot 
the planet in B being al('o to the velocity of the eartn 
in D in the ratio compounded of the fubduplicate of 
the ratio of the l atm re Bum of the greater axis of 
the planet’s orbit, to the latus rcSiuni of the greater 
axis of the orbit of the earth, of the ratio of the 
co-line of the inclination of the planet’s orbit to the 
plane of the ecliptic to the radius, and of the ratio ot 
AH to AB : therefore the ratio of FB to FD will 
be compounded of the fame ratios ; and it I be taken, 
that the ratio of A B to I be compounded of the 
two firft of thefe, I wiil be given in magnitude, and 
the ratio of F B to F D will be compounded of the 
ratio of A B to I, and of All to AB. Whence 
FB will be to FD as AH to I; and the angles 
CB A, or FBG, and A H G being equal, where- 
by F G will be to FB as AG to A II, by equa- 
lity F G will be to F D as AG to I, and D H 
being drawn parallel to FB, BG will be .to BK as 
FG to FD, and therefore as AG to I. 
But now, as this problem may be diftributed into vari- 
ous cafes, in the firft place conlider the eartn as mov- 
ing in a circle concentric to the iun, and likewife C I*, 
the tangent to the planet’s orbit, perpendicular to AB. 
But 
