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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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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1871 - 380 pages
...every diameter is double the radius, all the diameters are equal. 26. Definition. It will be shown that every section of a sphere made by a plane is a circle ; and as the greatest possible section is one made by a plane passing through the centre, such a section...
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An Elementary Geometry

William Frothingham Bradbury - Geometry - 1872 - 124 pages
...of a sphere are equal ; all the diameters are equal, and each is double the radius. THEOREM XIV. 58. 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...
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A Treatise on Special, Or Elementary Geometry

Edward Olney - Geometry - 1872 - 472 pages
...is equal to twice the radius. ELEMENTARY SOLID GEOMETRY. CIRCLES OF THE SPHERE. PROPOSITION L 533. Theorem. — Every section of a sphere, made by a plane, is a circle. P DEM. — Let AFEBD be a section of a sphere whose centre is O, made by a plane ; then is it a circle....
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1872 - 368 pages
...of the circle; and this diameter is called the axis of the circle. PROPOSITION VII.— THEOREM. 28. Every section of a sphere made by a plane is a circle. Let abc be a plane section of the sphere whose centre is O. All the straight lines Oa, Ob, etc., drawn...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1872 - 382 pages
...diameter is double the radius, all the diameters are equal. 26. .Definition. It will be shown that every section of a sphere made by a plane is a circle; and as the greatest possible section is one made by a plane passing through the centre, such a section...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - Geometry - 1872 - 464 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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Introduction to quaternions, by P. Kelland and P.G. Tait

Philip Kelland - 1873
...unit vector with it. The equation above gives in this case .: CO. CD = a' (19). EXAMPLES. 42. Ex. 1. Every section of a sphere made by a plane is a circle. Let p' — — a" be the equation of the sphere, a the vector perpendicular from the centre on the cutting...
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New Elementary Geometry: With Practical Applications; a Shorter Course, Upon ...

Benjamin Greenleaf - Geometry - 1873 - 202 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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Solid geometry and conic sections

James Maurice Wilson - 1873
...semicircle describes a circle whose plane 1s 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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Mensuration of lines, surfaces, and volumes

David Munn - 1873
...generated will evidently have all its points equally distant from the centre. It can be shewn that every section of a sphere made by a plane is a circle, and as the greatest possible section is one made by a plane passing through the centre, such a section...
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