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" If two spherical triangles on the same sphere, or equal spheres, have two sides and the included angle of one equal, respectively, to two sides and the included angle of the other, I. "
Solid Geometry - Page 396
by John H. Williams, Kenneth P. Williams - 1916 - 162 pages
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Elements of Geometry and the First Principles of Modern Geometry

Wm. H. H. Phillips - Geometry - 1878 - 236 pages
...other, each to each, the two triangles will be congruent or symmetrical, and hence equal (15). xxui. If two spherical triangles on the same sphere, or equal spheres, have two angles of the one equal to two angles of the other, each to each, and the included sides equtd, the...
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The Elements of Plane and Solid Geometry: With Chapters on Mensuration and ...

Isaac Sharpless - Geometry - 1879 - 282 pages
...equal in either case in all its parts to DEF. Proposition 10. Theorem.—If two triangles, on the same or equal spheres, have two sides and the included angle of one respectively equal to the two sides and the included of another, they are equal in all their parts....
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The Elements of Geometry

George Bruce Halsted - Geometry - 1885 - 389 pages
...symmetrical is henceforth devoted entirely to such. THEOREM V. 688. Two spherical triangles having two sides and the included angle of one equal respectively to two sides and the included angle of the other, are either congruent or symmetrical. (1) If the parts given equal are arranged in the...
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The Elements of Geometry

George Bruce Halsted - Geometry - 1886 - 394 pages
...symmetrical is henceforth devoted entirely to such. THEOREM V. 688. Two spherical triangles having two sides and the included angle of one equal respectively to two sides and the included angle of the other, are either congruent or symmetrical. (1) If the parts given equal are arranged in the...
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The Elements of Plane and Solid Geometry ...

Edward Albert Bowser - Geometry - 1890 - 418 pages
...of its sides. Proposition 9. Theorem.* 709. Two triangles on the same, or on equal spheres, having two sides and the included angle of one equal respectively to two sides and the included angle of the other, are either equal or equivalent. Hyp. Let ABC, DEF be two A s having the side AB = DE,...
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The Elements of Solid Geometry: With Numerous Exercises

Arthur Latham Baker - Geometry, Solid - 1893 - 148 pages
...line joining the two points. QED PROPOSITION IX. THEOREM. 275. Two triangles on equal spheres, having two sides and the included angle of one equal respectively to two sides and the included angle of the other, are either equal or equivalent. Proof. By superposing one Sph. A upon the other, or upon...
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The Elements of Geometry

Webster Wells - Geometry - 1894 - 400 pages
...mutually equilateral, their polar triangles are mutually equiangular. PROPOSITION XVII. THEOREM. 629. If two spherical triangles on the same sphere, or equal...equal respectively to two sides and the included angle of the other, I. They are equal if the equal parts occur in the same order. II. They are symmetrical...
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The Elements of Geometry

Webster Wells - Geometry - 1894 - 394 pages
...equiangular. (The proof is left to the student ; compare 627.) PROPOSITION XVII. THEOREM. 629. If two spherical triangles on the same sphere, or equal...one equal respectively to two sides and the included anjle of the other, I. They are equal if tlte equal parts occur in the same order. II. They are symmetrical...
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The Elements of Geometry

Webster Wells - Geometry - 1894 - 398 pages
...mutually equiangular. PROPOSITION XVII. THEOREM. 629. If two spherical triangles on the same sphere, Br equal spheres, have two sides and the included angle...equal respectively to two sides and the included angle of the other, I. They are equal if the equal parts occur in the same order. II. They are symmetrical...
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Elements of Geometry

Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 564 pages
...hypothesis that angle >angle c. Therefore AB<BC. QED PROPOSITION XXII. THEOREM 70. If two triangles have two sides and the included angle of one, equal respectively to two sides and the included angle of the other, the triangles are equal. C' GIVEN — AB, AC, and a, of the triangle ABC respectively...
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