r 69 ] 
{tribe a circle round the earth, as EOL , the adtion 
of the fun would have changed this orbit into an 
oval, as OADBC-, whofe greateft diameter, palling 
thro’ the quadratures CD, is to the lead; as 70-\ to 
69—. The reafon and determination of which we 
have in Princip. lib. iii. prop. 26, 28. 
1 1 . That this action of the fun, and the figure re- 
fulting from it, muft lelTen the mean motion of the 
apogee, is eafily fhewn. 
For let P be the moon’s place in her orbit, when 
the apfis is llationary, and EOL the circle of her 
mean motion, cutting the orbit very near the odtant 
O, and P'T in 0 : then, the accelerating forces of the 
earth at P and 0, being inverfely as the fquares of 
PT and oT , and the fun’s difturbing force at the 
points P, 0 , being in the limple diredt ratio of the 
fame lines ; 0 T being given, the ratio of the fun’s 
difturbing force at the point P, to the earth’s accele- 
rating force at the fame point, that is, the quantity c 
in the theorem, will be as the cube of the diftance 
PT : and, a fortiori , in every point of the orbit, 
from the quadrature C to P, will exceed the mean 
force at O, and its effect in producing a retrograde 
motion of the apfis will be greater. 
For the remaining part of the quadrant, where 
the motion of the apjis is diredt, the force c is indeed 
greater than its mean quantity from P to O; but, 
thro’ the whole odtant OA , it is continually de- 
creaftng as the cube of the diftance from T: whence, 
upon the whole, that force, and its effedt, from P 
to A, fall fhort of their mean quantities at O. Seeing 
therefore the diredt motion is diminifhed, and the re- 
trograde increafedj their difference, that is, the di- 
redt 
