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" If two sides of a spherical triangle are unequal, the angles opposite them are unequal, and the greater angle lies opposite the greater side ; and conversely. "
The Essentials of Plane and Spherical Trigonometry - Page 96
by Webster Wells - 1887 - 151 pages
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A Practical Text-book on Plane and Spherical Trigonometry

Webster Wells - Trigonometry - 1883 - 234 pages
...sides of a spherical triangle are equal, the angles opposite them are equal ; and conversely. (c) . If two sides of a spherical triangle are unequal,...angle lies opposite the greater side ; and conversely. (cZ) . The perpendicular from the vertex to the base of an isosceles spherical' triangle bisects the...
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Plane and Solid Geometry: Suggestive Method

George Clinton Shutts - Geometry - 1894 - 412 pages
...prove that CD is perpendicular to the hypotenuse AB, PROPOSITION XXXIV. 128. Theorem. // two sides of a triangle are unequal the angles opposite them are unequal, and the greater angle is opposite the greater side. A Let ABC represent a triangle in which the side AB is greater than the...
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Plane and Spherical Trigonometry

George Albert Wentworth - Trigonometry - 1897 - 234 pages
...is called a quadrantal triangle. It is shown in Solid Geometry, that in every spherical triangle I. If two sides of a spherical triangle are unequal,...angles opposite them are unequal, and the greater angle is opposite the greater side ; and conversely. II. The sum of the sides is less than 360. III. The...
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Plane and Spherical Trigonometry, Surveying and Tables

George Albert Wentworth - Logarithms - 1897 - 384 pages
...is called a quadrantal triangle. It is shown in Solid Geometry, that in every spherical triangle I. If two sides of a spherical triangle are unequal,...angles opposite them are unequal, and the greater angle is opposite the greater side; and conversely. II. The sum of the sides is less than 360. III. The...
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The Essentials of Geometry

Webster Wells - Geometry - 1899 - 180 pages
...of a great O meeting AC at D, and making Z CBD equal to Z C.) 614. Cor. (Converse of Prop. XXVII.) If two sides of a spherical triangle are unequal, the angles opposite are unequal, and the greater angle lies opposite the greater side. (Prove by Reductio ad Absurdum.')...
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The Essentials of Geometry

Webster Wells - Geometry - 1899 - 450 pages
...of a great O meeting AC at D, and making Z CBD equal to Z C.) 614. Cor. (Converse of Prop. XXVII.) If two sides of a spherical triangle are unequal, the angles opposite are unequal, and the greater angle lies opposite the greater side. PROP. XXVIII. THEOREM. 615. The...
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Elements of Plane and Solid Geometry

Alan Sanders - Geometry - 1903 - 392 pages
...angle. Let ABC be a triangle having ZC greater than ZA . To Prove AB > BC. SOLID GEOMETRY CONVERSE. If two sides of a spherical triangle are unequal, the angles opposite them are unequal, the greater angle lying opposite the greater side. [Prove indirectly.] 1150. EXERCISE. Prove the converse...
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Plane Geometry Suggestive Method

George Clinton Shutts - 1905 - 260 pages
...that CD is perpendicular to the hypotenuse A B. PROPOSITION XXXIV. 128. Theorem. // two sides of a triangle are unequal the angles opposite them are unequal, and the greater angle is opposite the greater side. A Let ABC represent a triangle in which the side AB is greater than the...
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Plane Geometry

Edward Rutledge Robbins - Geometry, Plane - 1906 - 268 pages
...= BC (?). QED 121. THEOREM. An equiangular triangle is equilateral. 122. THEOREM. If two sides of a triangle are unequal, the angles opposite them are unequal, and the greater side subtends the greater angle. A Given: A ^BC; AB>AC. To Prove : Z 4CB > Z B. Proof : On AB take...
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Plane and Solid Geometry

Isaac Newton Failor - Geometry - 1906 - 431 pages
...unequal, the sides opposite are unequal, and the greater side is opposite the greater angle ; conversely, if two sides of a spherical triangle are unequal, the angles opposite are unequal, and the greater angle is opposite the greater side. HYPOTHESIS. In the spherical A ABC,...
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