 | Elias Loomis - Geometry - 1871 - 302 pages
...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 be a spherical triangle, having the side AB equal to AC ; then will the angle ABC be equal... | |
 | William Chauvenet - Geometry - 1871 - 380 pages
...by applying the isosceles triangle to its symmetrical triangle (65). PROPOSITION XXIV.-THEOREM. 81. If two angles of a spherical triangle are equal, the triangle is isosceles. In the triangle ABC let B = C; then, AB = AC. For, letA'B'C' be the polar triangle of ABC. Then, the... | |
 | Charles Davies - Geometry - 1872 - 464 pages
...proved. PROPOSITION XI. THEOREM. In any 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. 1°. Let ABC be a spherical triangle, having the side AB equal to AC: then will the angle C be equal... | |
 | William Chauvenet - Geometry - 1872 - 382 pages
...applying the isosceles triangle to its symmetrical triangle (65). PROPOSITION XXIV.—THEOREM. 81. If two angles of a spherical triangle are equal, the triangle is isosceles. In the triangle ABC let B = C; then, AB = AC. For, let A'B'C' be the polar triangle of ABG. Then, the... | |
 | William Chauvenet - Mathematics - 1872 - 382 pages
...applying the isosceles triangle to its symmetrical triangle (65). PROPOSITION XXIV.— THEOREM. 81. If two angles of a spherical triangle are equal, the triangle is In the triangle ABC let B — C; then, = AC. For, let A'B'C' be the polar triangle of ABC. Then, the... | |
 | Harvard University - 1873 - 732 pages
...cylinder, (3) parabolic cylinder. Prove that the bases of any cylinder are equal. 3. Prove that when two angles of a spherical triangle are equal, the triangle is isosceles. ANALYTIC GEOMETRY. 1. Sketch rapidly the locus of the equation — + •— = 1. Let the ".' y unit... | |
 | Adrien Marie Legendre - Geometry - 1874 - 500 pages
...proved. PROPOSITION XI. THEOREM. In any 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. 1°. Let ABC be a spherical triangle, having the side AB equal to AC : then will the angle G be equal... | |
 | Aaron Schuyler - Geometry - 1876 - 384 pages
...the isosceles spherical triangle ABC, letAB = AC; then, B — C. For, the arc AD of a great circle drawn from the vertex A to the middle point D of the base BC, divides the triangle ABC into two triangles, ABD, ACT), which are mutually equilateral, and hence,... | |
 | Charles Scott Venable - 1881 - 380 pages
...PROPOSITION XVI. 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. This theorem is a consequence of the analogous property of iso-edral and iso-angular triedrals (Book... | |
 | Edward Olney - Geometry - 1882 - 262 pages
...PROPOSITION XV. 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. DEM.— Let ABC be an isosceles spherical triangle in which AB = AC ; then angle ABC = ACB. For, draw... | |
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For, if the arc AD be drawn from the vertex A to the middle point D of the base, the two triangles ABD, ACD, will have all the sides of the one respectively equal to the corresponding sides of the other... 
