 | Elias Loomis - Conic sections - 1857 - 242 pages
...included side of the one, equal to two angles and the included side of the other PROPOSITION XVI. THEOREM. In an 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. Let ABC... | |
 | Elias Loomis - Conic sections - 1858 - 256 pages
...included side of the one, equal to two angles and the included side of the other PROPOSITION XVI. THEOREM. In an 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. Let ABC... | |
 | Horatio Nelson Robinson - Geometry - 1860 - 470 pages
...angles of the one will be equal to the sides and angles of the other, each to each. PROPOSITION X. In an isosceles spherical triangle, the angles opposite the equal sides are equal. Let ABC be an isosceles spherical triangle, in which AB and AC are the equal sides ; then will |_ B... | |
 | Horatio Nelson Robinson - 1869 - 276 pages
...angles of the one will be equal to the sides and angles of the other, each to each. PROPOSITION X. In an isosceles spherical triangle, the angles opposite the equal sides are equal. Let ABC be an isosceles spherical triangle, in which AB and AC are the equal sides; then will [_B =[_C.... | |
 | William Chauvenet - Geometry - 1871 - 380 pages
...triangles will then be similar, as in the case of plane triangles. PROPOSITION XXIII.— THEOREM. 78. In an isosceles spherical triangle, the angles opposite the equal sides are equal. In the spherical triangle ABC, let AB = AC; A then, B = C. For, draw the arc AD of a great circle, from the... | |
 | Elias Loomis - Geometry - 1871 - 302 pages
...included side of the one equal ID two angles and the included side of the other PROPOSITION XVI. THEOREM. In an 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. Let ABC... | |
 | William Chauvenet - Mathematics - 1872 - 382 pages
...triangles will then be similar, as in the case of plane triangles. PROPOSITION XXIII.— THEOREM. 78. In an isosceles spherical triangle, the angles opposite the equal sides are equal. In the spherical triangle ABC, let AB = AC; A then, B = C. For, draw the arc AD of a great circle, from the... | |
 | William Frothingham Bradbury - Geometry - 1872 - 262 pages
...Therefore the two triangles coincide, and are equal in all respects. THEOREM X. 42. In an isosceles triangle the angles opposite the equal sides are equal. In the isosceles triangle ABC let AB and BC be the equal sides ; then the angle A is equal to' the angle C. Bisect the... | |
 | William Frothingham Bradbury - Geometry - 1873 - 132 pages
...Therefore the two triangles coincide, and are equal in all respects. THEOREM X. 42. In an isosceles triangle the angles opposite the equal sides are equal. In the isosceles triangle ABC let AB and BC be the equal sides ; then the angle A is equal to the angle G. Bisect the... | |
 | William Frothingham Bradbury - Geometry - 1877 - 262 pages
...having two sides and the included angle, or two angles and the included side respectively equal, when their sides are similarly situated, are equal. For...the base C B. The triangles ADC, ABD are mutually eqiiilateral, and therefore mutually equiangular (21); hence the angle B = C. 30. Cor. 1. In an isosceles... | |
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In an isosceles spherical triangle, the angles opposite the equal sides are equal. In the spherical triangle ABC, let AB equal AC. 
