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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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New Elementary Geometry with Practical Applications

Benjamin Greenleaf - Geometry - 1874 - 206 pages
...whose bases are the two bases of the frustum, and a mean proportional between them. THEOREM VII. 353. Every section of a sphere made by a plane is a circle. Let ABE be a section made by a plane in the sphere whose center is C. From the center, C, draw CD perpendicular...
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Elements of Geometry and Trigonometry: From the Works of A.M. Legendre

Adrien Marie Legendre - Geometry - 1874 - 512 pages
...frustum, and a mean proportional between them ; which was to be proved. PROPOSITION VII. THEOREM. Any section of a sphere made by a plane, is a circle. Let C be the centre of a sphere, CA one of its radii, and AMB any section made by a plane : then will this...
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Catalogue - Harvard University

Harvard University - 1874
...third. 8. A triangular pyramid is one-third of a triangular 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...
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Elements of the Infinitesimal Calculus: With Numerous Examples and ...

James Gregory Clark - Calculus - 1875 - 441 pages
...positions are parallel to iach other, and whose center remains constantly upon he axis. JJow, since every section of a sphere made by a plane is a circle, we may take the equations of a sphere and a plane as the two equations of the circle which generates...
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Report, Volumes 11-20

1876
...are respectively equal to three faces similarly placed including a Jtriedral 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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Hand-book of the Terrestrial Globe, Or, Guide to Fitz's New Method of ...

Ellen Eliza Fitz - Globes - 1876 - 120 pages
...passing through the centre, and terminated on both sides by the surface. It is equal to two radii. 16. Every section of a sphere made by a plane is a circle. (For proof, consult some work on geometry, as Chauvenet's Geometry, p. 245.) MOUNTING AND OPERATING...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - Geometry - 1876 - 446 pages
...two great circles of a sphere, is measured by the arc of a great circle which joins their poles. 35. Every section of a sphere made by a plane is a circle : and if two parallel planes cut a sphere so that the sections are equal, they are equidistant from...
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Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - Geometry - 1877 - 458 pages
...describes a sphere, any circular sector, as ACD or DCE, describes a spherical sector. PROPOSITION I. THEOREM. Every section of a sphere made by a plane is a circle. Let ABD be a section made by a plane in a sphere whose centre is C. From the point C draw CE perpendicular...
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Elements of Plane and Solid Geometry

George Albert Wentworth - Geometry - 1877 - 416 pages
...the sphere is inscribed in the cylinder or cone. GEOMETRY. BOOK VIII. PROPOSITION I. THEOREM. 678. Every section of a sphere made by a plane is a circle. Let the section ABC be a plane section of a sphere whose centre is 0. We are to prove section ABC a circle....
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Elements of Geometry and the First Principles of Modern Geometry

Wm. H. H. Phillips - Geometry - 1878 - 236 pages
...greater or less than the radius. COB. 3. Spheres of equal radii or of equal diameters are congruent. VI. Theorem. Every section of a sphere made by a plane is a circle. HYPOTH. ABC is a plane section of the sphere, whose centre is M. To BE PROVED. ABC is a circle. PROOF....
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