 | Adrien Marie Legendre - 1819 - 574 σελίδες
...at the same time the diameter of the circumscribed circle. THEOREM. 535. The surface of a sphere is equal to the product of its diameter by the circumference of a great circle. Demonstration. 1. We say that the diameter of a sphere multiplied by the circumference of a great circle... | |
 | Adrien Marie Legendre - 1825 - 276 σελίδες
...the same time the diameter of the circumscribed circle, • THEOREM. 535. The surface of a sphere is equal to the product of its diameter by the circumference of a great circle. Demonstration. 1. We say that the diameter of a sphere multiplied by the circumference of a great circle... | |
 | Adrien Marie Legendre, John Farrar - 1825 - 280 σελίδες
...at the same time the diameter of the circumscribed circle. THEOREM. 535. The surface of a sphere is equal to the product of its diameter by the circumference of a great circle. measure of^the surface of a greater sphere. For, if it be possiFig. 263. ble, let AB x circ. AC (Jig.... | |
 | Jared Sparks, Edward Everett, James Russell Lowell, Henry Cabot Lodge - 1828 - 598 σελίδες
...parallel sides, or half the sum of the two circumferences. QED Theorem 535. ' The surface of a sphere is equal to the product of its diameter by the circumference of a great circle.' This is incuded in the preceding corollary. ' The entire surface described by the revolution of a semipolygon... | |
 | Jared Sparks, Edward Everett, James Russell Lowell, Henry Cabot Lodge - 1828 - 598 σελίδες
...parallel sides, or half the sum of thetwo circumferences. QED Theorem 535. ' The surface of a sphere is equal to the product of its diameter by the circumference of a great circle.' This is incuded in the preceding corollary. ' The entire surface described by the revolution of a semipolygon... | |
 | Adrien Marie Legendre - 1828 - 346 σελίδες
...the same time be the diameter of the circumscribed circle. THEOREM. 535. The surface of a sphere is equal to the product of its diameter by the circumference of a great circle. We shall first shew, that the diameter of a sphere multiplied by the circumference of its great circle... | |
 | Adrien Marie Legendre - 1836 - 394 σελίδες
...(HI + IP) xcirc. ON, or equal to HP x circ. ON. PROPOSITION X. THEOREM. The surface of a sphere is equal to the product of its diameter by the circumference-...perpendicular to one of the sides. Let the semicircle and the ' semi-polygon be revolved about the axis AE : the semicircumference ABCDE will describe the surface... | |
 | Adrien Marie Legendre - 1837 - 376 σελίδες
...(HI + IP) x circ. ON, or equal to IIP x circ. ON. PROPOSITION X. THEOREM. The surface of a sphere is equal to the product of its diameter by the circumference of a great circle. D E O A Let ABCDE be a semicircle. Inscribe in it any regular semi-polygon, and from the centre O draw... | |
 | Benjamin Peirce - 1837 - 216 σελίδες
...surface generated by the circular segment ABCD is a zone. Hence the area of the surface of a sphere is the product of its diameter by the circumference of a great circle. And, the area of a zone is the product of its altitude by the circumference of a great circle. 473.... | |
 | Adrien Marie Legendre - 1838 - 372 σελίδες
...(HI + IP) x circ. ON, or equal to HP x circ. ON. PROPOSITION X. THEOREM. The surface of a sphere is equal to the product of its diameter by the circumference...Inscribe in it any regular semi-polygon, and from the I centre O draw OF perpendicular to one of the sides. Let the semicircle and the semi-polygon be revolved... | |
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The surface of a sphere is equal to the product of its diameter by the circumference of a great circle. 
