 | Alfred Hix Welsh - Geometry - 1883 - 326 pages
...is perpendicular to the base, and divides the triangle into two symmetrical triangles. THEOREM XII. If two angles of a spherical triangle are equal, the triangle is isosceles. A In the spherical triangle ABC, let B = C; Again, but then AB — A C. For, draw the polar A' B' C'.... | |
 | Edward Olney - Geometry - 1883 - 344 pages
...an isosceles spherical triangle, the angles opposite the equal sides are equal; and, conversely, // two angles of a spherical triangle are equal, the triangle is isosceles. DEMONSTRATION. Let ABC be an isosceles spherical triangle, in which AB =_- AC. Then angle ABC = ACB.... | |
 | Charles Davies, Adrien Marie Legendre - Geometry - 1885 - 538 pages
...triangle. 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. BOOK IX. For, draw the arc- of a great circle from the vertex A, to the middle point D, of the base... | |
 | William Chauvenet, William Elwood Byerly - Geometry - 1887 - 336 pages
...middle point of the base is perpendicular to the base, and bisects the vertical angle. 3. Theorem.—If two angles of a spherical triangle are equal, the triangle is isosceles. PROPOSITION XVI.—THEOREM. 61. Any side of a spherical triangle is less than the sum of the other... | |
 | William Chauvenet, William Elwood Byerly - Geometry - 1887 - 331 pages
...middle point of the base is perpendicular to the base, and bisects the vertical angle. 3. Theorem.—If two angles of a spherical triangle are equal, the triangle is isosceles. PROPOSITION XVI.—THEOREM. 61. Any side of a spherical triangle is less than the sum of the other... | |
 | William Chauvenet - Geometry - 1888 - 826 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, For, let^i'.B'C" be the polar triangle of ABC. Then, the sides... | |
 | Edward Albert Bowser - Geometry - 1890 - 418 pages
...their spheres (433) ; the triangles are then similar, as in the case of plane triangles. 722. CoR. 1. If two angles of a spherical triangle are equal, the triangle is isosceles. For, since the polar A is isosceles (716), the Zs opp. the two equal sides are equal (712); .-. the... | |
 | Arthur Latham Baker - Geometry, Solid - 1893 - 154 pages
...sides of A = sides of 7?. QED By §§ 275, 276 they are (.Tiber equal or eqwwaKjnfT QED 284. COR. 1. If two angles of a spherical triangle are equal, the triangle is isosceles. 285. COR. 2. If three mutually perpendicular planes meet at the centre of a sphere, they divide the... | |
 | William Chauvenet - 1893 - 340 pages
...middle point of the base is perpendicular to the base, and bisects the vertical angle. 3. Theorem.—If two angles of a spherical triangle are equal, the triangle is isosceles. PROPOSITION XVI.—THEOREM. 61. Any side of a spherical triangle is less than the sum of the other... | |
 | Charles Ambrose Van Velzer, George Clinton Shutts - Geometry - 1894 - 522 pages
...Ex. 346. The angles opposite the equal sides of an isosceles spherical triangle are equal. Ex. 847. If two angles of a spherical triangle are equal the triangle is isosceles. SuG. Take the polar of the given A. PROPOSITION XXVI. THEOREM. 553. The sum of the angles of a, spherical... | |
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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... 
