yt> THE ELEMENTS OF

part, the greatest is that G F whichpasses through the center ; and thosenearer to OF are greater than those thatare further off.—But of those that go tothe convex part the least, is that G H,which continued would pass through thecenter C; and those nearer to that, asG A, are less than those that are furtheroff.-—(PI. 3. fig. 1 a.)

Draw C A, C D, G B, C E ; (P. I. B. I.)

then in the triangle GCE, GC + CE, orG F is greater than G E. (T. IX. B. I.) Andin the triangles G C B, G C E; G C, E C, areequal G C, C B, and angle G C E greater thanGCB; consequently G E is greater than G B.(T. XXVI. B. I.)

Also in the triangle G C A, C A + A G isgreater than C G, or CH + HG. (T. IX.B. I.) Take away /C A = II C, and A G isgreater than HG. And in the triangles GAG,C D G ; C G, CA, are equal to C G, C D,and angle G C A less than GCD; thereforeGA is less than GD. (T. XXVI. B. I.;

COR. I. There can only two. arches bedrawn of equal length from the point G to