| William Chauvenet - Geometry - 1879 - 380 pages
...whose radius is the chord of the generating are of the zone. PROPOSITION XI.— THEOREM. -•o 41. **The area of the surface of a sphere is equal to the product of its diameter by the** tircumference of a great tirde. This follows directly from the preceding proposition, since the surface... | |
| William Frothingham Bradbury - Arithmetic - 1879 - 446 pages
...a sphere is a line passing through the centre, and limited in both directions by the surface. 498. **The surface of a sphere is equal to the product of its** circumference and its diameter. Surface of a Sphere = Circumference X Diameter. 58. What is the surface... | |
| Benjamin Gratz Brown - Geometry - 1879 - 68 pages
...the product of a perimeter of a right section by an element of the surfa6e ; that of the sphere is **the product of its diameter by the circumference of a great circle.** The volume on the other hand of the cone is equal to one-third of base into the altitude ; of the cylinder,... | |
| Education - 1883 - 684 pages
...be produced, they will meet in a straight line, belongs to the former division. The proposition that **the area of the surface of a sphere is equal to the...its diameter by the circumference of a great circle,** belongs to the latter division. Now, descriptive geometry deals immediately with relations of form... | |
| Elias Loomis - Conic sections - 1880 - 452 pages
...base of the frustum, its upper base, and a mean proportional between them. PROPOSITION VII. THEOREM. **The surface of a sphere is equal to the product of...diameter by the circumference of a great circle. Let** ABDF be the semicircle by the revolution of which the sphere is described. Inscribe in the semicircle... | |
| William Frothingham Bradbury - Geometry - 1880 - 260 pages
...passes through the centre of the sphere, its radius will be the radius of the sphere. THEOREM XXVII. 95. **The surface of a sphere is equal to the product of...diameter by the circumference of a great circle. Let** ABCDEF be the semicircle by whose revolution about the diameter AF, the sphere may be described; then... | |
| Simon Newcomb - Geometry - 1881 - 418 pages
...whence Surface = ±nr*. Now we have found the area of a circle of radius r to be ^(§480). Hence: 863. **The area of the surface of a sphere is equal to the** area of four great circles. The area of a hemisphere is equal to twice that of a great circle. CHAPTER... | |
| Alfred Hix Welsh - Geometry - 1883 - 326 pages
...to its projection on the axis multiplied by the circumference of the inscribed circle. THEOREM III. **The surface of a sphere is equal to the product of...its diameter by the circumference of a great circle.** A Let ACF be a semi-circumference, and AF its diameter; then will the surface generated by its revolution... | |
| Evan Wilhelm Evans - Geometry - 1884 - 242 pages
...of the square. Similarly, rotate an octagon, and examine the surface of the figure. THEOREM XXVIII. **The surface of a sphere is equal to the product of its diameter by** its circumference. Let ABCDEF be a semicircle, having the half of a regular polygon inscribed in it.... | |
| Alfred Hix Welsh - English language - 1885 - 364 pages
...earth's surface is equal to the product of its diameter by its circumference': or general; as, 'man,' **'The surface of a sphere is equal to the product of...diameter by the circumference of a great circle.'** To gather up into one view all the objects that possess organism, life, sensation, voluntary motion,... | |
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