 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
 | William Chauvenet - Geometry - 1875 - 390 pages
...is equal to the volume of the ungula whose base is that lune. 23 PROPOSITION XXXI.— THEOREM. 95. A lune is to the surface of the sphere as the angle of the lune it to four right angles. Let ANBMA be a lune, and let MNP be the great circle whose poles are the extremities... | |
 | William Chauvenet - Geometry - 1875 - 466 pages
...equal to the volume of the ungula whose base is that lune. PROPOSITION XXXI.— THEOREM. 95. A lune if, to the surface of the sphere as the angle of the lune i* to four right angles. Let ANBMA be a lune, and let MNP be the great circle whose poles are the extremities... | |
 | William Guy Peck - Conic sections - 1876 - 376 pages
...tri-rectangular triangle which forms its base multiplied by J of the radius. PROPOSITION XIII. THEOREM. The area of a lune is to the surface of the sphere as the angle of the lune is to four right angles. Let PAQ be a semicircle whose centre is 0, and whose diameter is PQ; and let PA be a quadrant. If the... | |
 | Aaron Schuyler - Geometry - 1876 - 384 pages
...be concave? when will both be lines, and what will the sector be? 475. Proposition XXVI.— Theorem. 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 ABA'CA, whose angle is A ; S, the surface of the sphere ; BCD, a great circle... | |
 | William Guy Peck - Conic sections - 1876 - 412 pages
...generated whilst revolving through any angle is proportional to that angle ; hence, the surface of the lune, is to the surface of the sphere, as the angle of the lune, is to four right angles, which was to be proved. MANUAL OF GEOMETRY. Cor. 1. If we denote the area of the lune by L, its angle,... | |
 | William Frothingham Bradbury - Geometry - 1877 - 262 pages
...included between 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... | |
 | George Albert Wentworth - Geometry - 1877 - 416 pages
...radius is equal 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... | |
 | Elias Loomis - Conic sections - 1877 - 458 pages
...is .the remainder of the surface of the hemisphere. PROPOSITION XVIII. THEOREM. % The area of a lime is to the 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... | |
 | George Albert Wentworth - Geometry - 1877 - 436 pages
...equal to the diameter of the sphere. GEOMETRY. — BOOK VIII. PROPOSITION XXXI. THEOREM. 766. A lime is to the surface of the sphere as the angle of the lune is to four right angles. Let L denote the lune AB EC whose angle is A; S, the surface of the sphere; and BCDF, a great circle... | |
 | William Chauvenet - Geometry - 1879 - 380 pages
...to the volume of the ungula whose base is that lune. u PROPOSITION XXXI.— THEOREM. 95. AI in ic. is to the surface of the sphere as the angle of the lune u to Jour right angles. Let ANBMA be a lune, and let MNP be the great circle whose poles are the extremities... | |
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