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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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An Elementary Course of Mathematics: Designed Principally for Students of ...

Harvey Goodwin - Mathematics - 1846 - 468 pages
...any line passing through the centre and bounded by the surface is called a diameter of the sphere. 3. Every section of a sphere made by a plane is a circle. Let EDF be any such section of a sphere, of which the centre is O. Draw OC from O perpendicular to the...
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Elements of Geometry: With Practical Applications ...

George Roberts Perkins - Geometry - 1847 - 308 pages
...This axis FG will, at the same time, be the diameter of the circumscribed circle. PROPOSITION VIII. THEOREM. Every section of a sphere, made by a plane,...be the section, made by a plane in the sphere whose B/ centre is C. From the point C, draw CO perpendicularly to the plane AMB ; and draw lines CM, CM...
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An Elementary Treatise on Plane and Solid Geometry

Benjamin Peirce - Geometry - 1847 - 150 pages
...radii of a sphere are equal ; and all its diameters are also equal, and double of the radius. 419. Theorem. Every section of a sphere made by a plane is a circle. Proof. From the centre C (fig. 178) of the sphere draw the perpendicular CO to the section AMB and...
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Elementary Course of Geometry ...

Charles William Hackley - Geometry - 1847 - 248 pages
...all the diameters are equal, and each double of the radius. 3. It will be demonstrated (Prop. 1) that every section of a sphere made by a plane is a circle ; this being assumed, A great circle of a sphere is the section made by a plane passing through the...
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A treatise on plane and spherical trigonometry

Thomas Grainger Hall - Trigonometry - 1848 - 194 pages
...110 XIII. Examples Ill SPHERICAL TRIGONOMETRY. CHAPTER I. Р1ОЖ I. Definition of a sphere . 115 II. Every section of a sphere made by a plane is a circle 116 III. In a spherical triangle, any side is less than the sumí of the other two ) IV. The sum of...
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Elements of Geometry and Trigonometry Translated from the French of A.M ...

Charles Davies - Trigonometry - 1849 - 384 pages
...PD.i; since AO x PD." is a mean proportional between OA"." and PD*.n PROPOSITION VII. THEOREM. xeciion of a sphere, made by a plane, is a circle. Let AMB be a section, made by a plane, in the sphere whose centre is C. From the point C, draw CU perpendicular...
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Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1849 - 252 pages
...passing through the center, and terminated each way by the surface. 3. It will be shown (Prop. I.), that every section of a sphere made by a plane is a circle. A great circle is a section made by a plane which passes through the center of the sphere. Any other...
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Elements of Geometry: With, Practical Applications

George Roberts Perkins - Geometry - 1850 - 332 pages
...This axis FG will, at the same time, be the diameter of the circumscribed circle. PROPOSITION VIII. THEOREM. Every section of a sphere, made by a plane,...sphere whose centre is C. From the point C, draw CO perpendicularly to the plane AMB ; and draw lines CM, CM to different points of the curve AMB, which...
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Elementary Geometry: With Applications in Mensuration

Charles Davies - Geometry - 1850 - 236 pages
...follows that similar cylinders are to each other as the cubes of the linear dimensions. THEOREM XX. Every section of a sphere, made by a plane, is a circle. Let AMB be a section, made by a plane, in the sphere whose centre is C. From the centre C draw CO, perpendicular...
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Elementary Geometry: With Applications in Mensuration

Charles Davies - Geometry - 1850 - 216 pages
...follows that similar cylinders are to each other as the cubes of the linear dimensions. THEOREM XX. Every section of a sphere, made by a plane, is a circle. Let AMB be a section, made by a plane, in the sphere whose centre is C. From the centre C draw CO, perpendicular...
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