26. AS all this is the obvious consequence of the proposition laid down for assigning the common center of gravity of any two weights, by the same proposition the center of gravity of all figures is found. In a triangle, as A B C (in fig. 18.) the center of gravity lies in the line drawn from the middle point of any one of the sides to the opposite angle, as the line B D is drawn from D the middle of the line A C to the opposite angle B[54]; so that if from the middle of either of the other sides, as from the point E in the side A B, a line be drawn, as E C, to the opposite angle; the point F, where this line crosses the other line B D, will be the center of gravity of the triangle[55]. Likewise D F is equal to half F B, and E F equal to half F C[56]. In a hemisphere, as A B C (fig. 19.) if from D the center of the base the line D B be erected perpendicular to that base, and this line be so divided in E, that D E be equal to three fifths of B E, the point E is the center of gravity of the hemisphere[57]. 27. IT will be of use to observe concerning the center of gravity of bodies; that since a power applied to this center alone can support a body against the power of gravity, and hold it fixed at rest; the effect of the power of gravity on a body is the same, as if that whole power were to exert itself on the center of gravity only. Whence it follows, that, when the power of gravity acts on a body suspended by any point, if the body is so suspended, that the center of gravity of the body can descend; the power of gravity will give motion to that body, otherwise not: or if a number of bodies are so connected together, that, when any one is put into motion, the rest shall, by the manner of their being joined, receive such motion, as shall keep their common center of gravity at rest; then the power of gravity shall not be able to produce any motion in these bodies, but in all other cases it will. Thus, if the body A B (in fig. 20, 21.) whose center of gravity is C, be hung on the point A, and the center C be perpendicularly under A (as in fig. 20.) the weight of the body will hold it still without motion, because the center C cannot descend any lower. But if the body be removed into any other situation, where the center C is not perpendicularly under A (as in fig. 21.) the body by its weight will be put into motion towards the perpendicular situation of its center of gravity. Also if two bodies A, B (in fig. 22.) be joined together by the rod C D lying in an horizontal situation, and be supported at the point E; if this point be the center of gravity common to the two bodies, their weight will not put them into motion; but if this point E is not their common center of gravity, the bodies will move; that part of the rod C D descending, in which the common center of gravity is found. So in like manner, if these two bodies were connected together by any more complex contrivance; yet if one of