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" THEOREM. Two triangles on the same sphere, or on equal spheres, are equal in all their parts, when they have each an equal angle included between equal sides. Suppose the side... "
Elements of Geometry: With, Practical Applications - Page 276
by George Roberts Perkins - 1850 - 320 pages
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Elements of Geometry, After Legendre, with a Selection of Geometrical ...

Charles Scott Venable - 1881 - 380 pages
...triangle may be placed on the symmetrical of the second so as to coincide with it. PROPOSITION XV. THEOREM. Two triangles on the same sphere or on equal spheres are equal in ail their parts : 1 . When they have their sides equal, each to each. 2. When they have their angles...
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Essentials of Geometry

Alfred Hix Welsh - Geometry - 1883 - 326 pages
...one are equal to two sides and the included angle of the other; in the second, the Hypothesis is that two angles and the included side of the one are equal...to two angles and the included side of the other. In the first, there are given two sides and the included angle; in the second, two angles and the included...
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The Journal of speculative philosophy: Ed. by Wm. T. Harris ..., Volume 19

Philosophy - 1885 - 460 pages
...we cannot know by a single intuition. For instance ; two triangles lie before me, and I am told that two angles and the included side of the one are equal to the two angles and the included side of the other ; and I am further told that, such being the case,...
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A Manual for Teachers, Including Definitions, Principles, and Rules and ...

John Henry Walsh - 1895 - 296 pages
...and the included angle of the other, each to each ; and (Z>) when two angles and the included side of one are equal to two angles and the included side of the other, each to each. From 59, they should learn that when two triangles have the three sides of the one equal...
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Mathematics for Common Schools: A Manual for Teachers, Including Definitions ...

John Henry Walsh - 1896 - 282 pages
...and the included angle of the other, each to each ; and (6) when two angles and the included side of one are equal to two angles and the included side of the other, each to each. From 69, they should learn that when two triangles have the three sides of the one equal...
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New Plane and Solid Geometry

Wooster Woodruff Beman, David Eugene Smith - Geometry - 1899 - 416 pages
...A'O'B', BOC ^ B'O'C', CO A ^ C'O'A'. Prop. XVII (a') 8. .'.A ABC = A A'B'C'. Ax. 2 PROPOSITION XIX. 482. Theorem. Two triangles on the same sphere, or on equal spheres, are either congruent or symmetric and equal if (a) two sides and the in- (b) two angles and the included...
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Solid Geometry

Wooster Woodruff Beman, David Eugene Smith - Geometry, Solid - 1900 - 160 pages
...the opposite dihe- other, the opposite angles are dral angles are equal. equal. PROPOSITION XXI. 484. Theorem. Two triangles on the same sphere, or on equal spheres, are either congruent or symmetric and equal if (a) the three sides (b) the three angles of the one figure...
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Solid Geometry

Wooster Woodruff Beman, David Eugene Smith - 1903 - 158 pages
...spherical A AOB ^ A'O'B', BOC , B'O'C', CO A C'O'A'. 468, 480 (a ' ) PROPOSITION XIX. 482. Theorem. Two triangles on the same sphere, or on equal spheres, are either congruent or symmetric and equal if (a) two sides and the in- (b) two angles and the included...
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Solid Geometry

Fletcher Durell - Geometry, Solid - 1904 - 232 pages
...equal to two sides and the included angle of the other; or II. If two angles and the included side of one are equal to two angles and the included side of the other, the corresponding equal parts being arranged in the same order in each case. I. Given the spherical...
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Plane and Solid Geometry

Fletcher Durell - Geometry - 1911 - 553 pages
...equal to tivo sides and the included angle of the other; or II. If two angles and the included side of one are equal to two angles and the included side of the other, the corresponding equal parfs l)eing arranged in reverse order. A I. Given the spherical A ABC and...
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