 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 - Geometry - 1871 - 380 pages
...same side of A'B'; therefore, ABC is the polar triangle of A'B'C'. PROPOSITION XVIII.— THEOREM. 69. 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... | |
 | William Chauvenet - Geometry - 1872 - 382 pages
...same side of A'B'; therefore, ABC is the polar triangle of A'B' C'. PROPOSITION XVIII.—THEOREM. 69. 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... | |
 | Harvard University - 1874 - 668 pages
...prism of the game base and altitude. 9. Every section of a sphere made by a plane is a circle. 10. In two polar triangles, each angle of one is measured by the supplement of the side lying opposite to it in the other. PLANE TRIGONOMETRY. 1. Define the complement, supplement, sine,... | |
 | William Chauvenet - Geometry - 1875 - 466 pages
...same side of A'B'; therefore, ABC is the polar triangle of A'B'C'. PROPOSITION XVIII.—THEOREM. 69. In two polar triangles, each angle of one is measured by the mpplement of the side lying opposite to it in the other. Let ABC and A'B' C' be two polar triangles.... | |
 | Harvard University - 1876 - 554 pages
...circle described from its vertex as a pole and included between its sides (produced if necessary). 7. In two polar triangles, each angle of one is measured by the supplement of the side lying opposite to it in the other. 8. Any side of a spherical triangle is less than the sum of the... | |
 | 1876 - 646 pages
...polar triangle. 1. If A'B'C' is the polar triangle of ABC, then ABC is the polar triangle of A'B'C'. 2. In two polar triangles each angle of one is measured by the supplement of the side opposite to it in the other. 6. The convex surface of a cone of revolution is equal to the product... | |
 | General Medical Council (Great Britain) - 1879 - 400 pages
...fused with a mixture of Na., = 02 = COZ + K-0-NO, ? " (6.) " In two polar triangles " [prove that] " each angle of one is measured by the supplement of the side lying opposite to it in the other." (/3) Answer from OHIO DENTAL COLLEGE. No. 286 Race Street, Cincinnati,... | |
 | Webster Wells - 1883 - 298 pages
...arcs a', b', and c', respectively, then, conversely, А B С is the polar triangle of A'B'C'. (h). In two polar triangles, each angle of one is measured by the supplement of the corresponding side of the other. That is, -4=180°-a', Б=180°-6', <7 =180°- c', ^'=180°- a, Б'=180°-6,... | |
 | Webster Wells - Trigonometry - 1887 - 200 pages
...the arcs a', b', and c', respectively, then conversely, ABC is the polar triangle of A'B'C'. A' (/) In two polar triangles, each angle of one is measured by the supplement of the side lying opposite to it in the other. 97 That is, A =180° -a', .4' = 180° — a, В =180°-Ь', В'... | |
 | William Chauvenet, William Elwood Byerly - Geometry - 1887 - 331 pages
...on the same side of A'B'; therefore ABC is the polar triangle of A'B'C'. PROPOSITION XL-THEOBEM. 51, 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... | |
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