 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.  Solid Geometry - Page 456by George C. Shutts - 1913Full view - About this book
 | Seth Thayer Stewart - Geometry - 1891 - 426 pages
...to that in BOOK vi., PROP, i., and PROP. vi. and PROP. XL, it maybe proved that the surface of any lune is to the surface of the sphere as the angle of the lune is to four right angles ; that is, L : 8 T : : A : 4, in which L may represent any lune ; 7", the trirectangular triangle ;... | |
 | William Chauvenet - 1893 - 340 pages
...bi-rectangular spherical 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. Let ANBMA be a lune, and let MNP be the great circle whose poles are the extremities of the diameter... | |
 | William C. Bartol - Geometry, Solid - 1893 - 112 pages
...two equal sides. A'B'CB is a lune. See (226). PROPOSITION XLI. 228. THEOREM. A lune is to the entire surface of the sphere as the angle of the lune is to four right angles. whole surface of the sphere by S, and the angle of the lune by A: then L : S :: A : 4 rt. angles. Let... | |
 | William Chauvenet - Geometry - 1894 - 380 pages
...lune, is equal to the volume of the ungula whose base is that lune, PROPOSITION XXXI.— THEOREM. 95. A lune is to the surface of the sphere as the angle of the lime it to four right angles. Let ANBMA be a lune, and let MNP be the great circle whose poles are... | |
 | Webster Wells - Geometry - 1894 - 400 pages
...these limits are equal. (§ 188.) ACBD Z CAD 648. COR. I. The surface of a lune is to the surface ofthe sphere as the angle of the lune is to four right angles. For the surface of a sphere may be regarded as a lune whose angle is equal to four right angles. 649.... | |
 | John Macnie - Geometry - 1895 - 390 pages
...angle, the sum of the acute angles is greater than a right angle. PROPOSITION XXIII. THEOREM. 657. A lune is to the surface of the sphere as the angle of the lune is to four right angles. Given: A lune L upon a sphere whose surface is S, and AOB, the angle of the lune, whose poles are P, P' ; To... | |
 | Elias Loomis - Geometry - 1895 - 450 pages
...angles of the triangle of the same name, f PROPOSITION XVIII. THEOREM. The area of a lune is to tJie surface of the sphere as the angle of the lune is to four right angles. Let ADBE be a lune, upon a sphere whose centre is C, and the diameter AB; then will the area of the... | |
 | Henry Dallas Thompson - Geometry, Solid - 1896 - 226 pages
...finally, V= fr rz, QED i8o MENSURATION OF FIGURES ON A SPHERE 305. THEOREM. A lune is to the whole surface of the sphere as the angle of the lune is to four right angles. I. If the angle of the lune be commensurable with four right angles : Let A be a vertex of the lune... | |
 | George Washington Hull - Geometry - 1897 - 408 pages
...*Jr • - = — - . o. ED FBEDF Z FEE 614. COR. 1.— The surface of a lune is to the surface of a sphere as the angle of the lune is to four right angles. 615. COR. 2. — The area of a lune is L — 2A X T, in which L denotes the area of the lune, A its... | |
 | James Howard Gore - Geometry - 1898 - 232 pages
...the Edge of the ungula, and the lune ACBD is called its Base. PROPOSITION VI. THEOREM. 523. The area of a lune is to the surface of the sphere as the, angle of the lune is to four right angles. Let ACBD be a lune, and ECDH the great circle whose poles are A and ZJ; let L be the area of the lune,... | |
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