 | Anthony Dumond Stanley - Geometry - 1848 - 134 pages
...are the same as the spherical angles DAB, DBA (Prop. 17) ; which are therefore also equal. PROP. XXV. If two angles of a spherical triangle a/re equal, the sides opposite them are also equal. Let ABC be a spherical triangle, of which the angles A and B are equal ; the sides... | |
 | John Hind - Trigonometry - 1855 - 540 pages
...opposite side, and the angles adjacent to it. 33. COR. 1. If A = B, we have cos a - cos ¿; that is, when two angles of a spherical triangle are equal, the sides opposite to them are also equal. 34. COR. 2. If С be a right angle, we have cos^f cos a = —. — = sm В which is positive or negative,... | |
 | Aaron Schuyler - Geometry - 1876 - 384 pages
...triangles. (?) 2. Symmetrical isosceles spherical triangles are equal. (?) 464. Proposition XX. — Theorem. If two angles of a spherical triangle are equal, the sides opposite these angles are equal, or the triangle is isosceles. For, let A'B'C' be the polar triangle of ABC,... | |
 | William Frothingham Bradbury - Geometry - 1877 - 262 pages
...perpendicular to the base. 31. Cor. 2. An equilateral spherical triangle is equiangular. THEOREM XII. 32. If two angles of a spherical triangle are equal, the sides opposite are also equal. SPHERICAL GEOMETRY. the polar triangle are also equal (29); and therefore the corresponding... | |
 | William Frothingham Bradbury - Geometry - 1880 - 260 pages
...perpendicular to the base. 31. Cor. 2. An equilateral spherical triangle is equiangular. THEOREM XII. 32. If two angles of a spherical triangle are equal, the sides opposite are also equal. the polar triangle are also equal (29); and therefore the corresponding sides of the... | |
 | George Albert Wentworth - Geometry - 1892 - 468 pages
...angle. Ex. 578. To inscribe a circle in a given spherical triangle. PROPOSITION XXIV. THEOREM. 755. If two angles of a spherical triangle are equal, the sides opposite, these angles arc equal, and tlu triangle is isosceles. In the spherical triangle ABC, let angle £... | |
 | William C. Bartol - Geometry, Solid - 1893 - 106 pages
...and its vertical angle, and it is also perpendicular to the base. PROPOSITION XXXIX. 224. THEOREM. If two angles of a spherical triangle are equal, the sides opposite are equal. A Let A'B'C' be a spherical triangle whose angles B' and C' are equal, then will A'C' and... | |
 | George Cunningham Edwards - Geometry - 1895 - 328 pages
...MB. A AMB = A CMB (3 sides equal). . ' . ZA = ZC, QED Z AMB = Z CMB = 90°, THEOREM 2. Conversely, if two angles of a spherical triangle are equal, the sides opposite them will be equal. If the sides are not equal, and AB > BC, a perpendicular erected at the middle... | |
 | George Albert Wentworth - Mathematics - 1896 - 68 pages
...angle, is perpendicular to the base, and divides the triangle into two symmetrical triangles. 755. If two angles of a spherical triangle are equal, the sides opposite these angles are equal, and the triangle is isosceles. 756. If two angles of a spherical triangle are... | |
 | George Washington Hull - Geometry - 1897 - 408 pages
...the radius of a small circle is less than the radius of the sphere. PROPOSITION XVII. THEOREM. 609. If two angles of a spherical triangle are equal, the sides opposite them are equal. Given—ABC a spherical triangle, with Z B — Z C. To Prove— AB = A C. Dem.—Construct... | |
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If two angles of a spherical triangle are equal, the sides opposite these angles are equal and the triangle is isosceles. In the spherical triangle ABC, let the angle B equal the angle C. To prove that AC = AB. Proof. Let the A A'B'C 
