| 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 the... | |
| George Roberts Perkins - Geometry - 1847 - 326 pages
...This axis 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,...be the section, made by a plane in the sphere whose** B/ centre is C. From the point C, draw CO perpendicularly to the plane AMB ; and draw lines CM, CM... | |
| Benjamin Peirce - Geometry - 1847 - 204 pages
...radii 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... | |
| Charles William Hackley - Geometry - 1847 - 248 pages
...all the diameters are equal, and each double of the radius. 3. It will be demonstrated (Prop. 1) that **every section of a sphere made by a plane is a circle** ; this being assumed, A great circle of a sphere is the section made by a plane passing through the... | |
| Thomas Grainger Hall - Trigonometry - 1848 - 192 pages
...110 XIII. Examples Ill SPHERICAL TRIGONOMETRY. CHAPTER I. Р1ОЖ I. Definition of a sphere . 115 II. **Every section of a sphere made by a plane is a circle** 116 III. In a spherical triangle, any side is less than the sumí of the other two ) IV. The sum of... | |
| Charles Davies - Trigonometry - 1849 - 372 pages
...PD.i; since AO x PD." is a mean proportional between OA"." and PD*.n PROPOSITION VII. THEOREM. xeciion **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 CU perpendicular... | |
| 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... | |
| George Roberts Perkins - Geometry - 1850 - 332 pages
...This axis 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,...sphere whose centre is C. From the point C, draw CO** perpendicularly to the plane AMB ; and draw lines CM, CM to different points of the curve AMB, which... | |
| 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, perpendicular... | |
| 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, perpendicular... | |
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