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Bøker Bok 110 av 36If two angles of a spherical triangle are equal, the sides opposite these angles...
" 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 "
A Treatise on Plane and Spherical Trigonometry: Including the Construction ... - Side 82
av Enoch Lewis - 1844 - 228 sider
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An Elementary Treatise of Spherical Geometry and Trigonometry

Anthony Dumond Stanley - 1848 - 122 sider
...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...
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The elements of plane and spherical trigonometry

John Hind - 1855
...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,...
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Elements of plane geometry, book i, containing nearly the same propositions ...

1865
...less angle of every triangle is opposite to the less side. PROPOSITION XIX. THEOR. If two angles of a triangle are equal, the sides opposite to them are also equal. Let ABC be a triangle having the angle B equal to the angle C, the side AB is also equal to the side AC....
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Elements of Geometry with Exercises for Students: An an Introduction to ...

Aaron Schuyler - 1876 - 372 sider
...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,...
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An Elementary Geometry: Plane, Solid, and Spherical : with Numerous ...

William Frothingham Bradbury - 1877 - 240 sider
...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...
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An Elementary Geometry: Plane, Solid and Spherical

William Frothingham Bradbury - 1880 - 240 sider
...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...
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A Text-book of Geometry

George Albert Wentworth - 1892 - 437 sider
...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 £...
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THE ELEMENTS OF SOLID GEOMETRY

WILLIAM C. BATOL, A.M., - 1893
...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...
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Elements of Geometry

George Cunningham Edwards - 1895 - 293 sider
...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...
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Syllabus of Geometry

George Albert Wentworth - 1896 - 50 sider
...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...
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