 | 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... | |
 | Benjamin Peirce - 1872 - 192 pages
...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 J1MB and... | |
 | William Chauvenet - Mathematics - 1872 - 382 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... | |
 | Philip Kelland, Peter Guthrie Tait - Quaternions - 1873 - 254 pages
...same 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, o the vector perpendicular from the centre on the cutting... | |
 | Philip Kelland - 1873 - 248 pages
...same 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 2 = — a 2 be the equation of the sphere, a the vector perpendicular from the centre on the cutting... | |
 | William Frothingham Bradbury - Geometry - 1873 - 132 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... | |
 | James Maurice Wilson - 1873 - 178 pages
...semicircle describes a circle whose plane is at right angles to AB, and centre lies \nA£. 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. Then since OQ is... | |
 | 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... | |
 | David Munn - 1873 - 160 pages
...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... | |
 | Benjamin Peirce - Geometry - 1873 - 202 pages
...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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(1). Every section of a sphere made by a plane is a circle. Let 
