BOOK III.] OF NATURAL PHILOSOPHY. 407 the ellipsis APBQ, about the axis AI3 is to the force of gravity in the same place A, towards the sphere described about the centre C with the radius AC, as 125 to 126. But the force of gravity in the place A to wards the earth is a mean proportional betwixt the forces of gravity to wards the spheroid and this sphere; because the sphere, by having its di ameter PQ, diminished in the proportion of 101 to 100, is transformed into the figure of the earth ; and this figure, by having a third diameter per pendicular to the two diameters AB and PQ, diminished in the same pro portion, is converted into the said spheroid ; and the force of gravity in A, in either case, is diminished nearly in the same proportion. Therefore the force of gravity in A towards the sphere described about the centre C with the radius AC, is to the force of gravity in A towards the earth as 126 to 1251. And the force of gravity in the place Q towards the sphere de scribed about the centre C with the radius QC, is to the force of gravity in the place A towards the sphere described about the centre C, with the radius AC, in the proportion of the diameters (by Prop. LXXII, Book I), that is, as 100 to 101. If, therefore, we compound those three proportions 126 to 125, 126 to 125