Precejfion of the Equinoxes. 523; 
The velocity of d is equal to the difference of its two 
velocities round the refpedtive axes rb, ab, or the differ- 
ence of d’s velocity round rb, and p’s velocity round ab, 
fince all the points in pc move with the fame velocity 
round ab. Draw dt parallel to cr, and this difference 
will be proportional to pt, becaufe the velocities of p 
round rb, ab, are fuppofed equal to each other, and pt 
is proportional to dv, and every point in the plane moves 
round pb with a velocity proportional to its diftance; and 
the lame thing may be lliewn when any point is taken 
without the plane abcpr. 
§ 17. Becaufe any point c in the axis rb moves with 
the fame velocity round pb as it does round ab, the angu- 
lar velocities round the two axes ab, pb, will be to each 
other in verfely as their refpedtive diftances cn, cm-, and ; 
becaufe cn:cw:: pb:pc and pr : pqj: pc : cb, it fol- 
lows, that pb the diagonal of the parallelogram pgbc will 
reprefent the angular velocity of the revolving plane , whew 
bg, bc, are taken to each other as the angular velocities 
of the fame plane round thofe refpe&ive axes . 
§ 18. From this it clearly follows, that the reafom 
given by simpson fc) , in his mifcellaneous tradfs, of the 
difference between his own folution and that of newton 
in the Principia, cannot poffibly be the true one. “ It 
(c) Pages 44. and 45. 
it 
appears 
