...of all. Therefore the convex surface AE is less thaii any which encloses it. •11 ' THEOREM. 516. The solidity of a cylinder is equal to the product of its but by its altitude. Fig. 258. Demonstration. Let CA {Jig. 258) he the radius of the basr of the given...

...cylinder, multiplied by its altitude, cannot be the measure of 'a greater cylinder. Hence finally, the solidity of a cylinder is equal to the product of its base by its altitude. Cor. 1. Cylinders of the same altitude are to each other as their bases ; and cylinders of...

...of a cylin~ der by its altitude should be the measure of a greater cylinder. We conclude then, that the solidity of a cylinder is equal to the product of its base by its altitude. 517. Corollary i. Cylinders of the same altitude are to each other as their bases, and cylinders...

...base of a cylinder by its altitude should be the measure of a greater cylinder. We conclude then, that the solidity of a cylinder is equal to the product of its base by its altitude. 517. Corollary i. Cylinders of the same altitude are to each other as their bases, and cylinders...

...smallest of alL Therefore the convex surface AB is less than any which encloses it. THEOREM. 51 6. We' solidity of a cylinder is equal to the product of its base by its altitude. Fig. 258. Demonstration. Let CA (fig. 258) be the radius of the base of the given cylinder,...

...THEOREM. 516. The solidity of ttcylinder is equal to the product of its base by its altitude. 31Let CA be a radius of the given cylinder's base ; H the...to show that the solidity of the cylinder is surf. CAxH. For, if surf. CAxH is no.t the measure of the given cylinder, it must be the measure of a greater...

...all those which envelope it. THEOREM. 516. The solidity of a cylinder is equal to the product. of Us base by its altitude. Let CA be a radius of the given...of the cylinder is surf. CA X H. • For, if surf. CAxH is not the measure of the given cylinder, it must be the measure of a greater cylinder, or of...

...their convex surfaces perpendicular to the common base : hence the two solids will be equal ; therefore the solidity of a cylinder is equal to the product of its base by its altitude. Cor. 1. Cylinders of the same altitude are to each other as tKeir bases ; and cylinders of...

...cylinder is equal to the circumference of its base multiplied by its altitude. PROPOSITION II. THEOREM. The solidity of a cylinder is equal to the. product of its base by ill altitude. Let CA be the radius of the base of the cylinder, and II the altitude. Let the circ-le...

...of a cylinder by its altitude should be the measure of a greater cylinder. We conclude, then, that the solidity of a cylinder is equal to the product of its base by its altitude. 517. Corollary i. Cylinders of the same altitude are to each other as their bases, and cylinders...