66

Sir I s a a c Newton’s Book I.

fame reason, is two weights A and B (in fig. 16.) were con-nected together by an inflexible rod C D, drawn from C thecenter of gravity of A to D the center of gravity of B ; andif the rod C D were to be so divided in E, that the part D Ebear the fame proportion to the other part C E, as the weightA bears to the weight B : then this rod being supported at Ewill uphold the weights, and keep them at rest without mo-tion. This point E, by which the two bodies A and B will besupported, is called their common center of gravity. And ifa greater number of bodies were joined together, the point, bywhich they could all be supported, is called the common centerof gravity of them all. Suppose (in fig. 17.) there were threebodies A, B, C, whose respective centers of gravity were joinedby the three lines D E, D F, E F: the line D E being so dividedin G, that D G bear the fame proportion to G E, as B bears toA ; G is the center of gravity common to the two bodies Aand B ; that is, a power equal to the weight of both the bo-dies applied to G would support them, and the point G ispressed as much by the two weights A and B, as it would be,if they were both hung together at that point. Therefore,if a line be drawn from G to F, and divided in H, so that G Hbear the fame proportion to H F, as the weight C bears toboth the weights A and B, the point H will be the commoncenter of gravity of all the three weights; for H would betheir common center of gravity, if both the weights A and Bwere hung together at G, and the point G is pressed as muchby them in their present fituation, as it would be in that cafe.In the fame manner from the common center of these three

weights,