 | Charles Davies - Geometry - 1870 - 392 pages
...follows that similar cylinders are to each other as the cubes of the linear dimentdons. THEOREM JfK. 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,... | |
 | Elias Loomis - Geometry - 1871 - 302 pages
...equal; all the diameters aie also equal, and each double of the radius. 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... | |
 | Benjamin Peirce - Geometry - 1871 - 192 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... | |
 | William Chauvenet - Geometry - 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... | |
 | 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... | |
 | 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... | |
 | William Frothingham Bradbury - Geometry - 1872 - 146 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 A BI) a circle.... | |
 | 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... | |
 | Eli Todd Tappan - Geometry - 1873 - 288 pages
...the motion of a straight line, every possible section of it is a curve. SECANT PLANES. 744. Theorem.- Every section of a sphere made by a plane is a circle. But if the section do not pass through the center, as DGF, then from the center C let CI fall perpendicularly... | |
 | David Munn - 1873 - 160 pages
...thus 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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that every section of a sphere, made by a plane, is a circle. 
