...multiplied by half the side cannot be the measure of the surface of a smaller cone. Hence finally, the convex surface of a cone is equal to the circumference of its base multiplied by half its side. Scholium. Let L be the side of a cone, B, the radius of its base...

...equal pyramid, and the base of the cone to that of an equal cone, the surface of the two pyramids will enclose that of the two cones, and consequently will...conclude then, that the convex surface of a cone is equal Jo the circumference of the base multiplied by half of its side. 529. Scholium. Let L be the side of...

...the frustum of a cone has for its measure iOPx (7iX-dO + 7ixDP+nxAOxDP) (422), or \n : THEOREM. 528. The convex surface of a cone is equal to the circumference of its base multiplied by half its side. Kg. 259. Demonstration. Let AO (Jig. 259), be the radius of .the...

...an infinite number of faces. Therefore it must have the same measure of solidity. QED Theorem 528. ' The convex surface of a cone is equal to the circumference of its base multiplied by half its side.' This results necessarily from the definition of a cone just...

...an infinite number of faces. Therefore it must have the same measure of solidity. QED Theorem 528. ' The convex surface of a cone is equal to the circumference of its base multiplied by half its side.'* This results necessarily from the definition of a cone just...

...Prop. XII. Cor. 2.) ; and the solidity of the cylinder will be «R2 x H, PROPOSITION III. THEOREM. The convex surface of a cone is equal to the circumference of its base, multiplied by half its side. Let the circle ABCD be the base of a cone, S the vertex, SO...

...S—CDB, the cone S—FKH be taken away, the remaining part is called the frustum of a cone. M? 8. The convex surface of a cone is equal to the circumference of the base multiplied by half the slant height. Thus, the convex surface of the cone C — AED is equal to circumference AEDx \CA....

...measure i OP X (* X AO + * X DP + *xAOx DP) (422), or i * X OP X (AO + PD + AO X DP). THEOREM. 528. The convex surface of a cone is equal to the circumference of its base multiplied by half its side. Demonstration. Let AO (fig. 259), be the radius of the base of...

...contained arcs divided by their radii. 29. The capacity of solids are as the cubes of their properties. 30. The convex surface of a cone is equal to the circumference of its base, multiplied by half its slant height. 31. The convex surface of the frustum of a cone, is...

...figure, are to each other as the sums of the rectangles of the sides adjacent to their extremities. 34. The convex surface of a cone is equal to the circumference of its base, multiplied by half its slant height 35. The convex surface of a frustum of a cone is equal...