 | Edward Albert Bowser - Geometry - 1890 - 414 pages
...is the lune CAC'B. EXERCISE. SOLID GEOMETRY. Proposition 1 8. Theorem. 731. The area of a lune is to the surface of the sphere as the angle of the lune is to four right angles. Hyp. Let ACBD be a lune, and ECDH the great O whose poles are A and B; let L denote the area of the... | |
 | Edward Albert Bowser - Geometry - 1890 - 418 pages
...triangle are respectively 105°, 70°, and 50°. Proposition 1 8. Theorem. 731. Tlie area of a lune is to the surface of the sphere as the angle of the lune is to four riy-ht angles. Hyp. Let ACBD be a lune, and ECDH the great O whose poles are A and B; let L denote... | |
 | Edward Albert Bowser - Geometry - 1890 - 420 pages
...area of the tri-rectangidar triangle. 734. COR. 3. The volume of a spherical wedge is to the volume of the sphere as the angle of the lune is to four right angles. For, the lunes being equal, the spherical wedges are also equal (727) ; hence two spherical wedges... | |
 | Seth Thayer Stewart - Geometry, Modern - 1891 - 422 pages
...BOOK vi., PROP, i., and PROP, vi. and PROP. xi., it may be 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 ; T, the trirectangular triangle ;... | |
 | William Chauvenet - 1893 - 340 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... | |
 | 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... | |
 | Charles Ambrose Van Velzer, George Clinton Shutts - Geometry - 1894 - 522 pages
...spherical degrees. PROPOSITION XXIX. THEOREM. 561. The area of a Iwne is to the area of the surface of a sphere as the angle of the lune is to four right angles. A "Let AS DC represent a lune whose angle is BA C. To prove that the area of AB DC is to the area of... | |
 | 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 - 386 pages
...of the acute angles is greater than a right angle. 326 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,... | |
 | 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... | |
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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. 
