 The area of a lune is to the area of the surface of the sphere as the angle of the lune is to four right angles.  Solid Geometry - Page 395by George Albert Wentworth - 1899 - 218 pagesFull view - About this book
 | George Albert Wentworth, David Eugene Smith - Geometry - 1913 - 491 pages
...180° is called the spherical excess of the triangle. PROPOSITION XXV. THEOREM 694. The area of a lune is to the area of the surface of the sphere as the angle of the lime is to four right angles. Given a lune PAQB, the great circle ABCD whose pole is P,... | |
 | George Albert Wentworth, David Eugene Smith - Geometry - 1913 - 496 pages
...180° is called the spherical excess of the triangle. PROPOSITION XXV. THEOREM 694. The area of a lune is to the area of the surface of the sphere as the angle of the lune is to four right angles. Given a lune PAQB, the great circle ABCD whose pole is P,... | |
 | George Albert Wentworth, David Eugene Smith - Geometry - 1913 - 496 pages
...100°, the spherical excess of the triangle is 90°. PROPOSITION XXV. THEOREM 694. The area of a lune is to the area of the surface of the sphere as the angle of the lune is to four right angles. Given a lune PAQB, the great circle ABCD whose pole is P,... | |
 | Walter Burton Ford, Charles Ammerman - Geometry, Solid - 1913 - 176 pages
...by its bounding arcs. Thus BAD is the angle of the lune ABCDA. 384. Theorem XVI. The area of a lune is to the area of the surface of the sphere as the angle of the lune is to four right angles. FIG. 258 Given the lune PAP'B, let L denote the area of... | |
 | William Charles Brenke - Trigonometry - 1917 - 194 pages
...difference between the sum of the angles of a spherical triangle and 180° is called its spherical excess. The area of a spherical triangle is to the area of the sphere as its spherical excess, in degrees, is to 720°. That is, if E be the spherical excess in degrees... | |
 | Fletcher Durell, Elmer Ellsworth Arnold - Geometry, Solid - 1917 - 220 pages
...to the lune FBF'D. 4. 5. § 686. Ax. 2. 6. Ax. 7. QED SPHERICAL AREAS PROPOSITION XX. THEOREM 709. The area of a spherical triangle is to the area of the sphere as the spherical excess of the triangle is to eight right angles. Given the spherical A ABC... | |
 | Herbert Edwin Hawkes, William Arthur Luby, Frank Charles Touton - Geometry, Solid - 1922 - 216 pages
...respectively. 4 7" .' "' HINT. The area of a spherical degree on a sphere of radius r is — — EXERCISES 86. The area of a spherical triangle is to the area of the sphere as its spherical excess is to 8 right angles. How many spherical degrees in the triangles whose... | |
 | Walter Burton Ford, Charles Ammermann - Geometry, Modern - 1923 - 406 pages
...by its bounding arcs. Thus BAD is the angle of the lune ABCDA. 384. Theorem XVI. The area of a lune is to the area of the surface of the sphere as the angle of the lune is to four right angles. Fio. 273 Given the lune PAP'B, let L denote the area of... | |
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