 | James Bates Thomson - Geometry - 1844 - 268 pages
...proportional between tnose areas, multiplied by a third of its altitude. PROPOSITION VII. 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... | |
 | Nathan Scholfield - Conic sections - 1845 - 244 pages
...this volume, is used to denote because; when applied in algebraic notation. PROPOSITION I. THEOREM. 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 point C, draw CO... | |
 | Nathan Scholfield - Geometry - 1845 - 506 pages
...between the two parallel planes, which form the bases of the zone or segment PROPOSITION I. THEOREM. 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 point C, draw CO... | |
 | Nathan Scholfield - 1845 - 894 pages
...sector, as DCF or FCH, describes a solid, which is named a spherical sector. PROPOSITION I. THEOREM. 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 point C, draw CO... | |
 | Nathan Scholfield - Conic sections - 1845 - 542 pages
...sector, as DCF or FCH, describes a solid, which is named a spherical sector. 4 PROPOSITION I. THEOREM. Every section of a sphere, made by a plane, is a circle. Let j\MB be a section, made by a plane, in'the sphere, whose centre is C. From the point G, draw CO... | |
 | Harvey Goodwin - Mathematics - 1846 - 500 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... | |
 | George Roberts Perkins - Geometry - 1847 - 326 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 B / centre is C. From the point C, draw... | |
 | 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. 4. Every section of a sphere made by a plane is a circle. Let AMB be the section made by the plane.... | |
 | 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... | |
 | Harvey Goodwin - Mathematics - 1849 - 588 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 EOF be any such section of a sphere, of which the centre is 0. Draw OC from O perpendicular to... | |
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that every section of a sphere, made by a plane, is a circle. 
