 In two polar triangles, each angle of one is measured by the supplement of the side lying opposite to it in the other. Let ABC and A'B'C' be two polar triangles. Let the sides AB and AC, produced if necessary, meet the side B'C  Elements of Geometry: Geometry of space - Page 392by Andrew Wheeler Phillips, Irving Fisher - 1898Full view - About this book
 | William Chauvenet, William Elwood Byerly - Geometry - 1887 - 332 pages
...therefore ABC is the polar triangle of A'B'C'. ELEMENTS OF GEOMETRY. PROPOSITION XI.— THEOREM. 5LV» two polar triangles, each angle of one is measured by the supplement of the side lying opposite to it in the other. Let ABC and A'B'C' be two polar triangles. Let the sides AB and... | |
 | Edward Albert Bowser - Trigonometry - 1892 - 194 pages
...each other. Thus : , If A'B'C' is the polar triangle of ABC, then ABC is the polar triangle of A'B'C'. In two polar triangles, each angle of one is measured by the supplement of the corresponding side of the other. Thus : A = 180°-«', В = 180° -6', С = 180° -с', a =180° -A',... | |
 | Edward Albert Bowser - Trigonometry - 1892 - 392 pages
...each other. Thus : If A'B'C' is the polar triangle of ABC, then ABC is the polar triangle of A'B'C'. In two polar triangles, each angle of one is measured by the supplement of the corresponding side of the other. Thus: A = 180° - а', B = 180° -V, C = 180° - с', a =180° -A',... | |
 | William Chauvenet - 1893 - 340 pages
...triangle of the second, then, reciprocally, the second is the polar triangle of the first. PROPOSITION XI. In two polar triangles, each angle of one is measured by the supplement of the side lying opposite to it in the other. PROPOSITION XII. PROPOSITION XIII. Two triangles on the same sphere... | |
 | Charles Ambrose Van Velzer, George Clinton Shutts - Geometry - 1894 - 416 pages
...isosceles spherical triangles can be made to coincide, and are equal. PROPOSITION XIX. PROPOSITION XX. In two polar triangles each angle of one is measured by the supplement of the side opposite it in the other. PROPOSITION XXI. Two triangles, on the same sphere, or equal spheres, having... | |
 | Charles Ambrose Van Velzer, George Clinton Shutts - Geometry - 1894 - 522 pages
...of another spherical triangle ABC, then the triangle ABC is the polar oi ,"•/•"' PROPOSITION XX. In two polar triangles each angle of one is measured by the inp plement of the side opposite it in the other. PROPOSITION XXI. Two triangles, on the same sphere,... | |
 | Webster Wells - Trigonometry - 1896 - 236 pages
...sides B'C', C'A', and A'B', respectively, then, conversely, ABC is the polar triangle of A'B'C'. 6. In two polar triangles, each angle of one is measured by the supplement of the side lying opposite the homologous angle of the other; that is a' =180° -A. 6'=180°-Б. c' = 180° - C.... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 574 pages
...less than a quadrant, ABC is the polar triangle of A'B'C'. § 875 QED PROPOSITION XXIX. THEOREM #77. In two polar triangles, each angle of one is measured...opposite these angles, also measured in degrees. To PRO VE— A' + a = 1 80°, B' + b — \ 80°, C' + c = 1 80°, A + a'= 18c°, B-\-b'— 180°, C+c'... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1897 - 376 pages
...A'B'C. § 786 Q ED PROPOSITION XVII. THEOREM 788. In two polar triangles, each angle of one is measurca by the supplement of the side of which its vertex...these angles, also measured in degrees. To PROVE— A' = 1So°,B' + b= 180°, C'+<:= 180°, ^' = 180°, Crc'=i8o° Produce A 'B' and A'C'to meet BCat R and... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry, Modern - 1898 - 324 pages
...less than a quadrant, ABC is the polar triangle of A'B'C'. § 875 392 PROPOSITION XXIX. THEOREM 877. In two polar triangles, each angle of one is measured...polar triangles ABC and A'B'C'. Let A, B, C, and A', I", C' denote their angles, measured in degrees, and a, b, c, and a', b', c' the sides respectively... | |
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