 | 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,... | |
 | 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,... | |
 | 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,... | |
 | 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.... | |
 | Edward Albert Bowser - Geometry - 1890 - 414 pages
...surface of the whole sphere is 720°. Hence The area of a spherical triangle is to that of the surface of the sphere as its spherical excess, in degrees, is to 720°. Proposition 2O. Theorem. 739. The area of a spherical polygon is equal to its spherical excess. Hyp.... | |
 | Edward Albert Bowser - Trigonometry - 1892 - 392 pages
...shown in Gcometry (Art. 738) that the absolute area of a spherical triangle is to that of the surface of the sphere as its spherical excess, in degrees, is to 720°. Cor. The areas of the colunar triangles are (2A-E) • (2B-E) . (2C-E) . "180° "' 180^' 180» ** •... | |
 | Edward Albert Bowser - Trigonometry - 1892 - 194 pages
...shown in Geometry (Art. 738) that the absolute area of a spherical triangle is to that of the surface of the sphere as its spherical excess, in degrees, is to 720". .-. К : 4^ = E : 720°. .-. * = ~^ . . . (1) 118. Problem. — To find the area of a triangle, having... | |
 | George Albert Wentworth - Mathematics - 1896 - 68 pages
...expressed in spherical degrees, is numerically equal to the spherical excess of the triangle. 775. Cor. 1. The area of a spherical triangle is to the area of the surface of the sphere as the number which expresses its spherical excess is to 720. 776. Cor. 2. The... | |
 | 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, the angles made with them... | |
 | Yale University - 1898 - 212 pages
...of the other. 4. What is the spherical excess of a spherical triangle? Prove the area of a sphericaj triangle is to the area of the sphere as its spherical excess is to eight right angles. JUNK 1894. PLANE. 1. If two lines are parallel, the angles made with them... | |
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The area of a spherical triangle is to the area of the surface of the sphere as the number which expresses its spherical excess is to 720. 
