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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. Given the spherical triangle ABC, with angle B equal to angle C. To prove that AC = AB. Proof. Let A A'B'C ' be the polar triangle... "
Plane and Solid Geometry - Σελίδα 450
των Fletcher Durell - 1911 - 546 σελίδες
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A Treatise on Plane and Spherical Trigonometry: Including the Construction ...

Enoch Lewis - 1844 - 234 σελίδες
...angles AEG, AFG, likewise equal (8.1) ; that is, the spherical angles ABC, ACB, are equal. QED ART. 50. If two angles of a spherical triangle are equal, the sides opposite to them are also equal. 83 Making the same construction as in the last article, we have, as before,...

An Elementary Treatise of Spherical Geometry and Trigonometry

Anthony Dumond Stanley - 1848 - 134 σελίδες
...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...

Elements of Geometry with Exercises for Students: An an Introduction to ...

Aaron Schuyler - 1876 - 384 σελίδες
...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, and denote the sides of...

Elements of Plane and Solid Geometry

George Albert Wentworth - 1877 - 416 σελίδες
...two symmetrical triangles. PROPOSITION XXVI. THEOREM. 747. If two angles of a spherical triangle be equal, the sides opposite these angles are equal, and the triangle is isosceles. In the spherical Л AB С, let ZB = Z С. We are to prove AC = AB. Let Л A' B' (7 be the polar Д...

An Elementary Geometry: Plane, Solid, and Spherical : with Numerous ...

William Frothingham Bradbury - 1877 - 262 σελίδες
...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...

An Elementary Geometry: Plane, Solid and Spherical

William Frothingham Bradbury - 1880 - 260 σελίδες
...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...

Elements of Plane and Solid Geometry

George Albert Wentworth - 1885 - 424 σελίδες
...two symmetrical triangles. PROPOSITION XXVI. THEOREM. 747. If two angles of a spherical triangle be equal, the sides opposite these angles are equal, and the triangle is In the spherical A ABC, let Z B = Z C. We are to prove AC = AB. Let ^A'B'C ' be the polar A of AA £...

Principles of Plane Geometry

James Wallace MacDonald - 1889 - 80 σελίδες
...the angles opposite the equal sides are equal. Proposition XXXV. A Theorem. 72. If two angles of a triangle are equal, the sides opposite these angles are equal, and the triangle is isosceles. COROLLARY. An equiangular triangle is also equilateral. Proposition XXXVI. A Theorem. 73. If two sides...

Principles of Plane Geometry

James Wallace MacDonald - 1894 - 76 σελίδες
...COROLLARY. An equilateral triangle is also equiangular. Proposition XXXV. A Theorem. 72. If two angles of a triangle are equal, the sides opposite these angles are equal, and the triangle is isosceles. COROLLARY. An equiangular triangle is also equilateral. Proposition XXXVI. A Theorem. 73. If two sides...

A Text-book of Geometry

George Albert Wentworth - 1888 - 464 σελίδες
...Ex. 579. To circumscribe a circle about a given spherical triangle. PROPOSITION XXIV. THEOREM. 755. If two angles of a spherical triangle are equal, the...these angles are equal, and the triangle is isosceles. In the spherical triangle ABC, let angle B equal angle C. To prove AC^= AB. Proof. Let the A A'B'C'...




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