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" A point on the surface of a sphere, which is at the distance of a quadrant from each of two other points, not the extremities of. a diameter, is the pole of the great circle passing through these points. "
Mathematics: Course of Study for Senior and Junior High Schools - Page 116
by Baltimore (Md.). Department of Education - 1924 - 169 pages
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Elements of Plane and Solid Geometry

George Albert Wentworth - Geometry - 1877 - 426 pages
...the points B and С. .-. A' is a pole of the arc BС, § 726 (a point upon the surface of a sphere which is at a quadrant's distance from each of two other points is one of the poles of the great eirele which passes through those points). In like manner, it may...
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A Text-book of Geometry

George Albert Wentworth - Geometry - 1892 - 468 pages
...PROPOSITION IV. THEOREM. 705. A point on the surface of a sphere, which is at the distance of a quadrant from each of two other points, not the extremities of a diameter, is a pole of the great circle passing through these points. Let the distances PA and PB be quadrants....
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The Elements of Solid Geometry: With Numerous Exercises

Arthur Latham Baker - Geometry, Solid - 1893 - 150 pages
...PROPOSITION V. THEOREM. 248. A point on the surface of a sphere, which is at the distance of a quadrant from each of two other points, not the extremities of a diameter, is a pole of the great circle passing through these points. Notation, Let P be a point at a quadrant's...
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Syllabus of Geometry

George Albert Wentworth - Mathematics - 1896 - 68 pages
...is a quadrant-arc. 705. A point on the surface of a sphere, which is at the distance of a quadrant from each of two other points, not the extremities of a diameter, is a pole of the great circle passing through these points. 707. Given a material sphere to find its radius....
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Solid Geometry, Volumes 6-9

George Albert Wentworth - Geometry, Solid - 1899 - 248 pages
...PROPOSITION III. THEOREM. 762. A point on the surface of a sphere, which is at the distance of a quadrant from each of two other points, not the extremities of a diameter, is a pole of the great circle passing through these points. Let the distances PA and PB be quadrants,...
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Plane and Solid Geometry

George Albert Wentworth - Geometry - 1899 - 496 pages
...PROPOSITION III. THEOREM. 762. A point on the surface of a sphere, which is at the distance of a quadrant from each of two other points, not the extremities of a diameter, is a pole of the great circle passing through these points. Let the distances PA and PB be quadrants,...
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Plane and Solid Geometry

William James Milne - Geometry - 1899 - 404 pages
...equal spheres. How do their polar distances compare ? 4. Select a point on the surface of a sphere which is at a quadrant's distance from each of two other points. Where is this point situated with reference to a pole of a great circle that passes through the other...
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Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 396 pages
...circle. PROPOSITTOX III. THEOREM 691. On the surface of a sphere, a point at a quadrant's distance from two other points, not the extremities of a diameter, is the pole of a great circle passing through these tivo points. Hyp. P, A, and B are three points on the surface...
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Plane and Solid Geometry

Arthur Schultze - 1901 - 392 pages
...Find PROPOSITION III. THEOREM 691. On the surface of a sphere, a point at a quadrant's distance from two other points, not the extremities of a diameter, is the pole of a great circle passing through these two points. Hyp. P, A, and B are three points on the surface of...
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Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1902 - 394 pages
...330 PROPOSITION III. THEOREM 691. On the surface of a sphere, a point at a quadrant's distance from two other points, not the extremities of a diameter, is the pole of a great circle passing through these two points. Hyp. P, A, and B are three points on the surface of...
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