 | George Albert Wentworth - Geometry - 1877 - 416 pages
...to the diameter of the sphere. GEOMETRY. — HOOK VIII. PROPOSITION XXXI. THEOREM. 766. A lune is to the surface of the sphere as the angle of the lune is to four right angles. Let L denote the lune AB £С whose angle is A; S, the suriace of the sphere; and BСDF, a great circle... | |
 | William Frothingham Bradbury - Geometry - 1877 - 262 pages
...two semi-circumferences of great circles, as ABDEA in (41). BOOK VIII. THEOREM XVI. 41 1 A lune is to the surface of the sphere as the angle of the lune is to four right angles. Let ABDEA be a lune on the sphere whose centre is C, and let A and D be the poles of the great circle... | |
 | Edward Olney - Geometry - 1877 - 272 pages
...measure of the diedral m-AB-ra, is the angle of the lune i PROPOSITION XXVffl. 607. Theorem.—The area of a lune is to the area of the surface of the sphere on which it is situated, as the angle of the lune is to four right angles. is the same thing, the plane... | |
 | Horatio Nelson Robinson - Trigonometry - 1880 - 228 pages
...equivalent the lunc DCHAD, whose angle is ADC. PROPOSITION 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 that angle is to the circumference of a great circle. "LetABFCA be a... | |
 | Edward Olney - Geometry - 1883 - 352 pages
...148° ? One whose augles are 152J, 136°, and 168J? (See 714, o.) PROPOSITION XXXII. 728. Theorem. — The area of a lune is to the area of the surface of the sphere on which it is situated as the angle of the lune is to four right angles. FIRST DEMONSTRATIONS Let... | |
 | Edward Olney - Geometry - 1883 - 344 pages
...applying one to the other. Let the student make the application.] PROPOSITION XXXII. 728. Theorem.—The area of a lune is to the area of the surface of the sphere on which it is situated as the angle of the lune is to four right angles. FIRST DEMONSTRATION. Let... | |
 | Alfred Hix Welsh - Geometry - 1883 - 326 pages
...generated by a circular sector of the semicircle which generates the sphere. THEOREM XIX. A lune is to the surface of the sphere as the angle of the lune is to four rig/it angles. Let AB A' C be a lune (L), whose angle is A, or BOC; S, the surface of the sphere; and... | |
 | George Albert Wentworth - Geometry - 1885 - 424 pages
...whose radius is equal to the diameter of the sphere. PROPOSITION XXXI. THEOREM. 766. A lune is to ihe surface of the sphere as the angle of the lune is to four right angles. Let L denote the lune ABEC whose angle is A; S, the surface of the sphere; and DCDF, a great circle... | |
 | William Chauvenet - Geometry - 1887 - 346 pages
...triangle whose third angle is an angle of one degree. PROPOSITION XXI.— THEOREM. 70. A lune is to the surface of the sphere as the angle of the lune is to four right angles. A Let ANBMA be a lune, and let MNP bo the great circle whose poles are the extremities of the diameter... | |
 | William Chauvenet, William Elwood Byerly - Geometry - 1887 - 331 pages
...equivalent to a lune whose angle is the angle between the arcs in question. PROPOSITION XXI. A lune is to the surface of the sphere as the angle of the lune is to four right angles. PROPOSITION XXII. The area of a spherical triangle is equal to the excess of the sum of its angles... | |
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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. 
