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" The surface of a sphere is equal to the product of its diameter by the circumference of a great circle. "
ELEMENTS OF GEOMETRY AND TRIGONOMETRY - الصفحة 215
بواسطة A. M. LEGENDRE - 1852
عرض كامل - لمحة عن هذا الكتاب

A Practical Application of the Principles of Geometry to the Mensuration of ...

Jeremiah Day - 1815 - عدد الصفحات: 96
...surface of a. hemisphere is equal to the product of its radius into the circumference of its base ; and the surface of a sphere is equal to the product of its diameter into its circumference. Cor. T . From this demonstration it follows, that the surface of any segment...

Elements of Geometry

Adrien Marie Legendre - 1819 - عدد الصفحات: 208
...circle. This axis FG will be 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...

Elements of Geometry

Adrien Marie Legendre - 1825 - عدد الصفحات: 224
...circle. This axis FG will be 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...

Elements of Geometry...: Translated from the French for the Use of the ...

Adrien Marie Legendre, John Farrar - 1825 - عدد الصفحات: 224
...circle. This axis FG will be 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....

The North American Review, المجلد 27

Jared Sparks, Edward Everett, James Russell Lowell, Henry Cabot Lodge - 1828
...half the sum of all the parallel sides, or half the sum of the two circumferences. QED Theorem 535. ' The surface of a sphere is equal to the product of...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...

The North American Review, المجلد 27

Jared Sparks, Edward Everett, James Russell Lowell, Henry Cabot Lodge - 1828
...half the sum of all the parallel sides, or half the sum of thetwo circumferences. QED Theorem 535. ' The surface of a sphere is equal to the product of...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...

Elements of Geometry and Trigonometry: With Notes

Adrien Marie Legendre - 1828 - عدد الصفحات: 316
...circle. This axis FG xvill at 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...

The Principles of Plane Trigonometry, Mensuration, Navigation and Surveying

Jeremiah Day - 1831 - عدد الصفحات: 370
...surface of a hemisphere is equal to the product of its radius into the circumference of its base ; and the surface of a sphere is equal to the product of its diameter into its circumference. Cor. 1. From this demonstration it follows, that the surface of any segment...

A Treatise of Plane Trigonometry: To which is Prefixed a Summary View of the ...

Jeremiah Day - 1831 - عدد الصفحات: 155
...surface of a hemisphere is equal to the product of its radius into the circumference of its base; and the surface. of a sphere is equal to the product of its diameter into its circumference. Cor. 1. From this demonstration it follows, that the surface of any segment...

Elements of Geometry and Trigonometry

Adrien Marie Legendre - 1836 - عدد الصفحات: 359
...described by ED + DC, is equal to (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...circle. Let ABCDE be -a semicircle. Inscribe in it any regular semi-polygon, and from the centre O draw OF perpendicular to one of the sides. Let the...




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