 ... equal as to the magnitude of those parts. Hence, those two triangles, having all their sides respectively equal in both, must either be absolutely equal, or at least symmetrically so; in both of which cases their corresponding angles must be equal,...  An Elementary Treatise on Plane and Solid Geometry - Page 137by Benjamin Peirce - 1865 - 150 pagesFull view - About this book
 | Adrien Marie Legendre - Geometry - 1822 - 394 pages
...which cases, their corresponding angles must be equal, and lie opposite to equal sides. PROPOSITION XV. THEOREM. In every isosceles spherical triangle, the angles opposite the equal sides are equal ; and conversely, if two angles of a spherical triangle are equal, the triangle will be isosceles.... | |
 | Adrien Marie Legendre - Geometry - 1830 - 344 pages
...which cases, their corresponding angles must be equal, and lie opposite to equal sides. THEOREM. 483. In every isosceles spherical triangle, the angles opposite the equal sides are equal ; and conversely, if two angles of a spherical triangle are equal, the triangle is isosceles. O, First-... | |
 | Adrien Marie Legendre - Geometry - 1836 - 394 pages
...cases, their corresponding angles must be equal, and lie opposite to equal sides. PROPOSITION XIII. THEOREM. In every isosceles spherical triangle, the angles opposite the equal sides are equal ; and conversely, if two angles of a spherical triangle are equal, the triangle is isosceles. First.... | |
 | Benjamin Peirce - Geometry - 1837 - 216 pages
...angle of the other, they are equal, or else they are symmetrical. Isosceles Triangle. "Demonstration. For one of the triangles may be applied to the other,...triangle the angles opposite the equal sides are equal. Demonstration. Let AB (fig. 184) be equal to AC. From A draw AD to the middle of BC. ' In the triangles... | |
 | Nathan Scholfield - Geometry - 1845 - 506 pages
...which cases their corresponding angles must be equal, and lie opposite to equal sides. PROPOSITION XV. THEOREM. In every isosceles spherical triangle, the angles opposite the equal sides are equal ; and conversely, if two angles of a spherical triangle are equal, the triangle is isosceles. First.... | |
 | Nathan Scholfield - Conic sections - 1845 - 542 pages
...which cases their corresponding angles must be equal, and lie opposite to equal sides. PROPOSITION XV. THEOREM. In every isosceles spherical triangle, the angles opposite the equal sides are equal ; and conversely, if two angles of a spherical triangle are equal, the triangle is isosceles. First.... | |
 | Nathan Scholfield - 1845 - 894 pages
...which cases their corresponding angles must be equal, and lie opposite to equal sides. PROPOSITION XV. THEOREM. In every isosceles spherical triangle, the angles opposite the equal sides are equal ; and conversely, if two angles of a spherical triangle are equal, the triangle is isosceles. First.... | |
 | George Roberts Perkins - Geometry - 1847 - 326 pages
...cases, their corresponding angles must be equal, and lie opposite to equal sides. PROPOSITION XXVIII. THEOREM. In every isosceles spherical triangle, the angles opposite the equal sides are equal ; and, conversely, if two angles of a spherical triangle are equal, the triangle will be isosceles.... | |
 | Charles Davies - Trigonometry - 1849 - 372 pages
...cases, their corres80 ponding angles must be equal, and lie opposite to equal sides. PROPOSITION XIU. THEOREM. In every isosceles spherical triangle, the angles opposite the equal sides are equal; and conversely, if two angles of a spherical triangle are equal, the triangle is isosceles. First.... | |
 | George Roberts Perkins - Geometry - 1850 - 332 pages
...cases, their corresponding angles must be equal, and lie opposite to equal sides. PROPOSITION XXVIII. THEOREM. In every isosceles spherical triangle, the angles opposite the equal sides are equal; and, conversely, if two angles of a spherical triangle are equal, the triangle will be isosceles. First.... | |
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