Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/72

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28
Mathematical Principles
Book I.

two and that of a third body will be either at reſt or moving uniformly in a right line becauſe at that centre the diſtance between the common centre of the two bodies, and the centre of this laſt, is divided in a given ratio. In like manner the common centre of theſe three, and of a fourth body, is either at reſt, or moves uniformly in a right line; becauſe the diſtance between the common centre of the three bodies, and the centre of the fourth is there alſo divided in a given ratio, and ſo on in infinitum. Therefore, in a ſyſtem of bodies where there is neither any mutual action among themſelves, nor any foreign force impreſſed upon them from without, and which conſequently move uniformly in right lines, the common centre of gravity of them all is either at reſt or moves uniformly forward in a right line.

Moreover, in a ſyſtem of two bodies mutually acting upon each other, the diſtances between their centres and the common centre of gravity of both are reciprocally as the bodies; the relative motions of thoſe bodies, whether of approaching to or of receding from that centre, will be equal among themſelves. Therefore ſince the changes which happen to motions are equal and directed to contrary parts, the common centre of thoſe bodies, by their mutual action between themſelves, is neither promoted nor retarded, nor ſuffers any change as to its ſtate of motion or reſt. But in a ſyſtem of ſeveral bodies, becauſe the common centre of gravity of any two acting mutually upon each other ſuffers no change in its ſtate by that action; and much leſs the common centre of gravity of the others with which that action does not intervene; but the diſtance between thoſe two centres is divided by the common centre of gravity of all the bodies into parts reciprocally proportional to the total ſums of thoſe bodies

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