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" The area of a lune is to the surface of the sphere as the angle of the lune is to four right angles, or as the arc which measures that angle is to the circumference. "
Elements of Geometry with Exercises for Students: An an Introduction to ... - Page 331
by Aaron Schuyler - 1876 - 372 pages
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Elements of Geometry and Trigonometry: With Notes

Adrien Marie Legendre - Geometry - 1828 - 346 pages
...same name, and is the difference between a hemisphere and the former triangle. THEOREM. The surface of a lune is to the surface of the sphere, as the angle of this lune, is to four right angles, or as the arc which measures that angle, is to the circumference....
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Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - Geometry - 1830 - 584 pages
...the proportion which its surface bears to the surface of the sphere. For, since the surface of any lune is to the surface of the sphere, as the angle of the lune to four right angles (V. 21.), or as twice its angle to eight right angles ; if the surface of the...
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Library of Useful Knowledge: Geometry plane, solid, and spherical [by Pierce ...

Mathematics - 1835 - 684 pages
...the proportion which its surface bears to the surface of the sphere. For, since the surface of any lune is to the surface of the sphere, as the angle of the lune to four right angles (V. 21.), or as twice its angle to eight right angles ; if the surface of the...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1836 - 394 pages
...difference between a hemisphere and the former triangle. PROPOSITION XVII. THEOREM. The surface of a lune is to the surface of the sphere, as the angle of this lune, is to four right angles, or as the arc which measures that angle, is to the cwcumferenee....
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Higher Geometry and Trigonometry: Being the Third Part of a Series on ...

Nathan Scholfield - Geometry - 1845 - 506 pages
...the difference between a hemisphere and the former triangle. PROPOSITION XIX. THEOREM. The surface of a lune is to the surface of the sphere, as the angle of this lune, is to four right angles, or as the arc which measures that angle, is 'to the circumference....
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Elementary Course of Geometry ...

Charles William Hackley - Geometry - 1847 - 248 pages
...surface of the sphere would be expressed by the number 8. PROP. xv. The surface of a lune is to the whole surface of the sphere as the angle of the lune is to four right angles, or as the arc which measures the angle of the lune is to a circumference. It is evident, from a mere...
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Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1849 - 252 pages
...be expressed in whole numbers, it may be proved, as in Prop. XIV., B. III., that the lune is still to the surface of the sphere, as the angle of the lune to four right angles. Cor. 2. We have seen that the entire surface of the sphere is equal to eight...
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Elements of Geometry: With, Practical Applications

George Roberts Perkins - Geometry - 1850 - 332 pages
...hemisphere and the former triangle. PROPOSITION XXXII. THEOREM. The surface of a lune is to the entire surface of the sphere, as the angle of the lune is to four rightangles, or as the arc which measures the angle of the lune is to the circumference. Suppose, in...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1852 - 436 pages
...make a hemisphere, and eight the entire surface of a sphere. PROPOSITION XV. THEOEEM. The surface of a lune is to the surface of the sphere, as the angle of the lune, to four right angles ; or, as the arc which measures that angle, to the circumference. Let AMBN be...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - Geometry - 1854 - 436 pages
...make a hemisphere, and eight the entire surface of a sphere. PROPOSITION XV. THEOREM. The surface of a lune is to the surface of the sphere, as the angle of the lune, to four right angles ; or, as the arc which measures that angle, to the circumference. Let AMBN be...
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