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" THEOREM. Every section of a sphere, made by a plane, is a circle. "
Elements of Geometry: On the Basis of Dr. Brewster's Legendre : to which is ... - Page 196
by James Bates Thomson - 1844 - 237 pages
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The Elements of Coordinate Geometry: In Three Parts: 1. Cartesian Geometry ...

De Volson Wood - Geometry, Analytic - 1882 - 360 pages
...sphere, and equations (1), (2), (3), of Article 386 will be the equation of a tangent plane. EXAMPLES. 1. Every section of a sphere made by a plane is a circle. Let 5 be a vector perpendicular to the plane, d the scalar of 5, r the radius of the sphere, p the vector...
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The Elements of Plane and Solid Geometry: With Chapters on Mensuration and ...

Isaac Sharpless - Geometry - 1879 - 282 pages
...the arcs of the same great circles on opposite sides of the sphere. Proposition 1. Theorem.—Every section of a sphere made by a plane is a circle. Let ABC be any section of a sphere made by a plane; it is a circle. Take D, the centre of the sphere, and...
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An Elementary Geometry: Plane, Solid and Spherical

William Frothingham Bradbury - Geometry - 1880 - 260 pages
...of a sphere are equal; all the diameters are equal, and each is double the radius. THEOREM XXVI. 92. Every section of a sphere made by a plane is a circle. Let ABD be a section made by a plane cutting the sphere whose centre is C; then is ABD a circle. Draw CE...
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A Geometry for Beginners

George Anthony Hill - Geometry - 1880 - 346 pages
...are circles differing in size, the largest being that which passes through the centre of the orange. Every section of a sphere made by a plane is a circle. If the section passes through the centre of the sphere, it is called a great circle ; in all other...
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Report on the Training Systems for the Navy and Mercantile Marine of England ...

French Ensor Chadwick - Merchant marine - 1880 - 207 pages
...SENIOR PUPIL TEACHERS — SIXTH YEAH. SPHERICAL TRIGONOMETRY. (Time allowed, 3 hours.) 1. Prove that every section of a sphere made by a plane is a circle. 2. In spherical triangle ABC, given a — 87 10' 15", ft = 62 36' 45", and c=100 10' 15"; find...
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Elements of Geometry, After Legendre, with a Selection of Geometrical ...

Charles Scott Venable - 1881 - 382 pages
...points. The demonstration is exactly the same as that of Proposition III., Book II. PROPOSITION II. THEOREM. Every section of a sphere, made by a plane, is a circle. Let AMD be a section made by a plane in the sphere whose centre is C. From the point C, draw CO, perpendicular...
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The Cambridge Examiner, Volume 1

Education, Higher - 1881
...zenith, the zenith distance and altitude of a star, arimuth, solstice, oblate spheroid. 6. Prove : Every section of a sphere made by a plane is a circle. Any two great circles bisect the one the other. 7. Explain the causes of solar and lunar eclipses....
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Elementary Geometry: Including Plane, Solid, and Spherical Geometry, with ...

Edward Olney - Geometry - 1883 - 354 pages
...is a Diameter. The diameter is equal to twice the radius. CIRCLES OF THE SPHERE. PROPOSITION I. 649. Theorem. — Every section of a sphere made by a plane is a circle. DEMONSTRATION. Let AFEBD be a section of a sphere, whose centre is O, made by a plane; then is the...
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Yale Examination Papers

F. B. Stevens - Examinations - 1884 - 175 pages
...are respectively equal to three faces similarly placed including a triedral angle of the other. 9. Every section of a sphere made by a plane is a circle. 10. Between what two limits does the sum of the angles of a spherical triangle lie? Write expressions...
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Solid Geometry and Conic Sections: With Appendices on Transversals, and ...

James Maurice Wilson - Conic sections - 1885 - 180 pages
...semicircle describes a circle whose plane is at right angles to AB, and centre lies in AB. THEOREM 35. Every section of a sphere made by a plane is a circle. Let a plane RQR' cut the sphere -whose centre is O ; then shall the section *' be a circle. Draw ON perpendicular...
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