Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/343



And hence if more leer bodies revolve about the great one, it may eaily be inferred that the orbits decribed will approach nearer to ellipes, and the decriptions of area's will be more nearly equable, if all the bodies mutually attract and agitate each other with accelerative forces that are as their abolute forces directly, and the quares of the ditances inverely; and if the focus of each orbit be placed in the common centre of gravity of all the interior bodies; (that is, if the focus of gravity and innermot orbit be placed in the centre of gravity of the greatet and innermot body; the focus of the econd orbit in the common centre of gravity of the two innermot bodies; the focus of the third orbit in the common centre of gravity of the three innermot; and o on) than if the innermot body were at ret, and was made the common focus of all the orbits.

In a ytem of everal bodies A, B, C, D, &c. if any one of tho bodies or A, attract all the ret, B, C, D, &c. with accelerative forces that are reciprocally as the quares of the ditances from the attracting body; the