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" If, from the vertices of a spherical triangle as poles, arcs of great circles are described, another spherical triangle is formed, called the polar triangle of the first. "
Plane and Spherical Trigonometry - Page 137
by George Albert Wentworth - 1902 - 232 pages
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1871 - 380 pages
...surface of a sphere is nearly if not quite as simple as the comparison of plane figures. 67. Definition. If from the vertices of a spherical triangle as poles, arcs of great circles are described, these arcs form by their intersection a second triangle which is called the polar triangle...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Mathematics - 1872 - 382 pages
...surface of a sphere is nearly if not quite as simple as the comparison of plane figures. 67. Definition. If from the vertices of a spherical triangle as poles, arcs of great circles are described, these arcs form by their intersection a second triangle which is called the polar triangle...
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An Elementary Geometry: Plane, Solid, and Spherical : with Numerous ...

William Frothingham Bradbury - Geometry - 1877 - 262 pages
...points on the surface of a sphere is the arc of a great circle joining the points. 181 Definition. If from the vertices of a spherical triangle as poles arcs of great circles are described, these arcs intersecting form a triangle which is called the polar triangle of the first...
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An Elementary Geometry: Plane, Solid and Spherical

William Frothingham Bradbury - Geometry - 1880 - 260 pages
...points on the surface of a sphere is the arc of a great circle joining the points. 18i Definition. If from the vertices of a spherical triangle as poles arcs of great circles are described, these arcs intersecting form a triangle which is called the polar triangle of the first...
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The Elements of Geometry

Webster Wells - Geometry - 1886 - 166 pages
...AA', BB', and CC' are diameters of the sphere, the triangle A'B'C' is symmetrical to ABC. 661. If with the vertices of a spherical triangle as poles arcs of great circles are described, a spherical triangle is formed which is called the polar triangle of the first. Thus if...
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The Elements of Solid Geometry

William C. Bartol - Geometry, Solid - 1893 - 106 pages
...the corresponding diedral angle between the planes of these circles are equal in value (188). 191. If, from the vertices of a spherical triangle as poles, arcs of great circles be described, a second spherical triangle will be formed which is called the polar triangle, of the...
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Plane and Solid Geometry: Suggestive Method

Charles Ambrose Van Velzer, George Clinton Shutts - Geometry - 1894 - 416 pages
...will F fall ? SUG. 6. Compare each part of DEF with a corresponding part of AB C. SOLID GEOMETRY. 543. If from the vertices of a spherical triangle as poles, arcs of great circles be drawn, a spherical triangle is formed which is called the polar of the first. If from A, B and C...
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The Elements of Geometry

Webster Wells - Geometry - 1894 - 400 pages
...called isosceles, equilateral, or right-angled in the same cases as a plane triangle. 611. If, with the vertices of a spherical triangle as poles, arcs of great circles be described, a spherical triangle is formed which is called the polar triangle of the first. Thus,...
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Elements of Geometry: Plane and Solid

John Macnie - Geometry - 1895 - 390 pages
...AB+ arc B C+ arc Cn+a,rcDA<.a, circumf . of a great O. QED (616) POLAR TRIANGLES. 629. DEFINITION. If from the vertices of a spherical triangle as poles, arcs of great circles be described, they will form by their intersection a second triangle, called the polar triangle of...
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Elements of Geometry

Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 554 pages
...Therefore the two given triangles are symmetrical. § 851 QED POLAR TRIANGLES 875. Def. — If, with the vertices of a spherical triangle as poles, arcs of great circles are described, these arcs will divide the spherical surface into eight triangles. One of these is called...
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