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" 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 395
by George Albert Wentworth - 1899 - 218 pages
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A Treatise on Special Or Elementary Geometry

Edward Olney - 1872 - 270 pages
...angle FIo 350 AFB = AEB =. DEC, side AF = side ED, each being PROPOSITION XXX. 612. Theorem.—The area of a spherical triangle is to the area of the surface of the hemisphere in which it is situated, as its spherical excess is to four right angles, or 360°. DEM.—Let...
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A Treatise on Special Or Elementary Geometry

Edward Olney - Geometry - 1872 - 472 pages
...upper base having become tangent to the sphere. PROPOSITION xxra. 603. Theorem. — The area of a zone is to the area of the surface of the sphere as the altitude of the zone is to the diameter of the sphere ; which gives for the area of a zone 2тrаЕ,...
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A Treatise on Special Or Elementary Geometry

Edward Olney - Geometry - 1877 - 272 pages
...sum of the triangles CED and AEB is equivalent to the lune FBEA, PROPOSITION XXX. 612. Theorem.—The area of a spherical triangle is to the area of the surface of the hemisphere in which it is situated, as its spherical excess is to four right angles, or 360°. DEM.—Let...
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A Treatise on Special Or Elementary Geometry: Including an Elementary, and ...

Edward Olney - Geometry - 1879 - 502 pages
...the triangles CED and AEB is equivalent to the lune FBEA. o.. ED PROPOSITION XXX. 612. Theorem. — The area of a spherical triangle is to the area of the surface of the hemisphere in which it is situated, as its spherical excess is to four right angles, or 360°. 1 'KM...
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A Treatise on Special Or Elementary Geometry

Edward Olney - Geometry - 1882 - 262 pages
...triangles CED and AEB is equivalent to the lune FBEA. li- BO FIG. 330. PROPOSITION XXX. 612. Theorem. — The area of a spherical triangle is to the area of the surface of the hemisphere in which it is situated, as its spherical excess is to four right angles, or 360°. DEM....
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Elementary Geometry: Including Plane, Solid, and Spherical Geometry, with ...

Edward Olney - Geometry - 1883 - 352 pages
...the triangles CED and AEB is equivalent to the lune FBEA. QE »PROPOSITION XXXIV. 733. Theorem. — The area of a spherical triangle is to the area of the surface of the hemisphere on which it is situated, as its spherical excess is to four right angles, or 360°. DEMONSTRATION....
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Elementary Geometry: Including Plane, Solid, and Spherical Geometry, with ...

Edward Olney - Geometry - 1883 - 352 pages
...supplement of AE; and BF = CE, each being the supplement of EB. PROPOSITION XXXIV. 733. Theorem.—The area of a spherical triangle is to the area of the surface of the hemisphere on which it is situated, as its spherical excess is to four right angles, or 360°. DEMONSTRATION....
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A Treatise on Trigonometry

James Edward Oliver - Trigonometry - 1889 - 178 pages
...from the vertex of an isosceles triangle to the base bisects both the vertical angle and the base. The area of a spherical triangle is to the area of the hemisphere as the excess of the sum of the three angles over two right angles is to four right angles....
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Syllabus of Geometry

George Albert Wentworth - Mathematics - 1896 - 68 pages
...is equivalent to a circle whose radius is the chord of the generating arc. 769. The area of a lime is to the area of the surface of the sphere as the number of degrees in its angle is to 360. 770. Cor. 1. The numerical value of a lune expressed in spherical...
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Yale University Entrance Examinations in Mathematics: 1884 to 1898

Mathematics - 1898 - 228 pages
...including a trihedral angle of the other. 4. What is the spherical excess of a spherical triangle ? Prove the area of a spherical triangle is to the area of the sphere as its spherical excess is to eight right angles. JCNK 1894. PLANE. 1. If two lines are parallel,...
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