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" I.), that every section of a sphere made by a plane is a circle. "
Elements of Geometry and Conic Sections - Page 148
by Elias Loomis - 1849 - 226 pages
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An Elementary Treatise on Plane and Solid Geometry

Benjamin Peirce - Geometry - 1847 - 204 pages
...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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A Treatise on Plane and Spherical Trigonometry ...

Thomas Grainger Hall - Trigonometry - 1848 - 192 pages
...circle ; and since we may assume the generating circle to be in any part of the sphere, we may conclude that every section of a sphere made by a plane is a circle. But the following is a direct proof of this proposition. 4. Every section of a sphere made by a plane...
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A New Treatise on Astronomy, and the Use of the Globes, in Two Parts ...

James M'Intire - Astronomy - 1850 - 352 pages
...AND SMALL CIRCLES. The circles of the terrestrial and celestial spheres are either great or small. A great circle is a section made by a plane, which passes through the centre of the sphere, and divides it into two equal parts. A small circle is a section made by a plane,...
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An Introductory Treatise on Mensuration in Theory and Practice ...

John Radford Young - Measurement - 1850 - 294 pages
...the sphere; and a line through the centre meeting the surface in two opposite points is a diameter. Every section of a sphere, made by a plane is a circle ; a section through the centre is called a great circle of the sphere, any other a small circle. A sphere...
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Elements of Geometry: With, Practical Applications

George Roberts Perkins - Geometry - 1850 - 332 pages
...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, is a circle. Let AMB be the section, made by a plane in the sphere whose centre is C. From the point C, draw CO...
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The Elements of Astronomy: Or, The World as it Is, and as it Appears

Anna Cabot Lowell - Astronomy - 1850 - 412 pages
...All the radii of a sphere are equal ; all the diameters are also equal, and double the radius. 2. Every section of a sphere made by a plane is a circle. If a sphere is cut by a plane which passes through the centre, the section is called a great circle...
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Elementary Geometry: With Applications in Mensuration

Charles Davies - Geometry - 1850 - 218 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,...
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Elementary Geometry: With Applications in Mensuration

Charles Davies - Geometry - 1850 - 238 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,...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1852 - 436 pages
...are equal ; all the diameters are equal, and each is double the radius. 12. It will be shown (p. 7,) that every section of a sphere, made by a plane, is a circle : this granted, a great circle is a section which passes through the centre ; a small circle, is one...
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The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...Archimedes himself in an edition of his works.] CHAPTER VII. THE CONE, CYLINDER, AND SPHERE. PROPOSITION I. Every section of a sphere made by a plane is a circle. 1 . Let the plane pass through the centre 0 of the sphere : then all lines drawn from the centre in...
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