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" ... poles. 751. COR. 2. All great circles of a sphere are equal. 752. COR. 3. Every great circle bisects the sphere. For the two parts into which the sphere is divided can be .so placed that they .will coincide; otherwise there would be points on the... "
A System of Plane and Spherical Trigonometry: To which is Added a Treatise ... - Page 181
by Richard Wilson - 1831 - 330 pages
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A Treatise on Trigonometry

George Biddell Airy - Trigonometry - 1855 - 121 pages
...but not generally more than three. A small circle may be drawn through any three given points. (82.) Two great circles bisect each other. For the intersection...sphere, and is therefore a diameter of both circles ; and the circles are therefore bisected. (83.) The inclination of two great circles, is the angle...
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A Second Book in Geometry

Thomas Hill - Geometry - 1863 - 136 pages
...a spherical triangle arc the same as the diedral angles made by the planes of their sides. 442. Any two great circles bisect each other ; for the intersection of their planes must pass through the centre of the sphere, and be a diameter in each circle. 444. The shortest path...
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The Elements of Solid Geometry: With Numerous Exercises

Arthur Latham Baker - Geometry, Solid - 1893 - 154 pages
...bisects the sphere and its surface. For the two parts can be made to coincide, § 213. 230. COR. 5. Any two great circles bisect each other. For the intersection of their planes passes through the centre of the sphere, and is therefore a diameter of each circle. 231. COR. C. An...
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The Elements of Geometry

Webster Wells - Geometry - 1894 - 400 pages
...coincide throughout; for all points of either are equally distant from the centre. 586. COR. IV. Any two great circles bisect each other. For the intersection of their planes passes through the centre of the sphere, and hence is a diameter of each circle. 587. COR. V. An arc...
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The Essentials of Geometry

Webster Wells - Geometry - 1899 - 424 pages
...throughout ; for all points of either surface are equally distant from the centre. 571. Cor. IV. Any two great circles bisect each other. For the intersection of their planes is a diameter of the sphere, and therefore a diameter of each O. (§ 152) 572. Cor. V. Between any...
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Plane and Solid Geometry

George Albert Wentworth - Geometry - 1899 - 496 pages
...coincide ; otherwise there would be points on the surface unequally distant from the centre. 753. COR. 4. Two great circles bisect each other. For the intersection of their .planes passes through the centre, and is, therefore, a diameter of each circle. 754. COR. o. If the planes...
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Solid Geometry, Volumes 6-9

George Albert Wentworth - Geometry, Solid - 1899 - 248 pages
...coincide ; otherwise there would be points on the surface unequally distant from the centre. 753. COR. 4. Two great circles bisect each other. For the intersection of their planes passes through the centre, and is, therefore, a diameter of each circle. 754. Con. 5. If the planes...
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Solid Geometry, Volumes 6-9

George Albert Wentworth - Geometry, Solid - 1902 - 248 pages
...coincide; otherwise there would be points on the surface unequally distant from the centre. 753. COR. 4. Two great circles bisect each other. For the intersection of their planes passes through the centre, and is, therefore, a diameter of each circle. 754. COR. 5. If the planes...
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Plane and Solid Geometry

George Albert Wentworth - Geometry - 1904 - 496 pages
...coincide ; otherwise there would be points on the surface unequally distant from the centre. 753. COR. 4. Two great circles bisect each other. For the intersection of their planes passes through the centre, and is, therefore, a diameter of each circle. 754. COR. 5. If the planes...
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New Plane and Solid Geometry

Webster Wells - Geometry - 1908 - 336 pages
...coincide throughout; for all points of either surface are equally distant from the centre. 522. Any two great circles bisect each other. For the intersection of their planes is a diameter of the sphere, and therefore a diameter of each O. (§ 153) 523. Between any two points...
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