Chap. 2. PHILOSOPHY.

6 ?

weights, you might proceed to find the common center, if afourth weight were added, and by a gradual progress mightfind the common center of gravity belonging to any numberof weights whatever.

16. As all this is the obvious consequence of the proposi-tion laid down for assigning the common center of gravity ofany two weights, by the fame proposition the center of gra-vity of all figures is found. In a triangle, as A B C (infig. 18.) the center of gravity lies in the line drawn from themiddle point of any one of the fides to the opposite angle,as the line B D is drawn from D the middle of the line A C tothe opposite angle B a ; so that if from the middle of eitherof the other fides, as from the point E in the side A B, a linebe drawn, as E C, to the opposite angle; the point F, wherethis line crosses the other line B D, will be the center of gra-vity of the triangle b . Likewise D F is equal to half F B, andE F equal to half F C c . In a hemisphere, as A B C (fig. 19.)if from D the center of the base the line D B be erected per-pendicular to that base, and this line be so divided in E, thatD E be equal to three fifths of B E, the point E is the center ofgravity of the hemisphere d .

1.7. I t will be of use to observe concerning the center ofgravity of bodies ; that since a power applied to this centeralone can support a body against the power of gravity, and

prop. 1 .

d Idem L. II. prop. 2.

3 Archimed. de xquipond.prop. it.b Ibid. prop. t 2.

c Lucas Valerius De centr. gravit. solid. L. I.

K z

hold