 | Gerardus Beekman Docharty - Calculus - 1865 - 328 pages
...When x-0, C=0, and S=0. If we make a;=:A=the height of the cylinder, we have S=27tb.h. That is, the convex surface of a cylinder is equal to the circumference of its base multiplied by its altitude. Ex. 133. To find the surface of a sphere. Let y—^r^—y? be the equation of the generating circle.... | |
 | Benjamin Greenleaf - Geometry - 1873 - 202 pages
...always equal to the perimeter of its base multiplied by its altitude ; hence, the convex surface of the cylinder is equal to the circumference of its base multiplied by its altitude. BOOK VI. 340. Cor. 2. If H represent- the altitude of a cylinder, and R the radius of its base, then... | |
 | Adrien Marie Legendre - Geometry - 1874 - 500 pages
...the CONE, and the SPHERE, are sometimes called THE THREE ROUND BODIES. PROPOSITION I. THEOREM. The convex surface of a cylinder is equal to the circumference of its base multiplied by the altitude. Let ABD be the base of a cylinder whose altitude is H : then will its convex surface... | |
 | Benjamin Greenleaf - Geometry - 1874 - 206 pages
...always equal to the perimeter of its base multiplied by its altitude ; hence, the convex surface of the cylinder is equal to the circumference of its base multiplied by its altitude. BOOK VI. 340. Cor. 2. If H represent the altitude of a cylinder, and R the radius of its base, then... | |
 | Catherinus Putnam Buckingham - Calculus - 1875 - 374 pages
...(240) For the convex surface of a cylinder we have j=R=radius of the base hence S =2T that is, the convex surface of a cylinder is equal to the circumference of its base into its altitude (241) In the case of the sphere we have (Art. 68) a$ hence S= Estimating from the... | |
 | Catherinus Putnam Buckingham - Calculus - 1875 - 362 pages
...height. (240) For the convex surface of a cylinder we have _y=R=radius of the base hence that is, the convex surface of a cylinder is equal to the circumference of its base into its altitude (241) In the case of the sphere we have (Art. 68) hence S=2-Rx+C Estimating from... | |
 | William Guy Peck - Conic sections - 1876 - 412 pages
...sides. Hence, whatever is true of the prism is true of the cylinder, (Art. 66). Cor. 2. The lateral surface of a cylinder is equal to the circumference of its base multiplied by its altitude, (P. 3, B. 7). Cor. 3. The volume of a cylinder is equal to the product of its base and altitude, (P.... | |
 | Alfred Hix Welsh - Geometry - 1883 - 326 pages
...perpendicular to the planes of the bases, which are parallel. THEOREM I. The convex surface of a right cylinder is equal to the circumference of its base multiplied by its altitude. Let AB be a right cylinder; then will its convex surface be equal to the circumference of its base multiplied... | |
 | Evan Wilhelm Evans - Geometry - 1884 - 242 pages
...multiplied by their common altitude. That is, the volume of any prism is equal, etc. THEOREM XXII. The convex surface of a cylinder is equal to the circumference of its base multiplied by its altitude; and its volume is equal to the area of its base multiplied by its altitude. Let ABCD be a cylinder,... | |
 | Charles Davies, Adrien Marie Legendre - Geometry - 1885 - 538 pages
...For, the surface of the sphere is equal to four great circles (PX, C. 1), the convex surface of the cylinder is equal to the circumference of its base multiplied by its altitude (PI) ; that is, it is equal to the circumference of a great circle multiplied by its diameter, or to... | |
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THEOREM. 7?/6 convex surface of a cylinder is equal to the circumference of its base multiplied by its altitude. 
