| Thomas Grainger Hall - 1848 - 192 pągines
...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. But the following is a direct proof of this proposition. 4. Every section of a sphere made by a plane... | |
| Elias Loomis - 1849 - 252 pągines
...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... | |
| Anna Cabot Lowell - 1850 - 412 pągines
...All the radii of a sphere are equal ; all the diameters are also equal, and double the radius. § 2. Every section of a sphere made by a plane is a circle. If a sphere is cut by a plane which passes through the centre, the section is called a great circle... | |
| Charles Davies - 1850 - 238 pągines
...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,... | |
| Charles Davies - 1850 - 218 pągines
...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,... | |
| John Radford Young - 1850 - 294 pągines
...the sphere; and a line through the centre meeting the surface in two opposite points is a diameter. Every section of a sphere, made by a plane is a circle ; a section through the centre is called a great circle of the sphere, any other a small circle. A... | |
| George Roberts Perkins - 1850 - 332 pągines
...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 centre is C. From the point C, draw CO... | |
| Adrien Marie Legendre - 1852 - 436 pągines
...are equal ; all the diameters are equal, and each is double the radius. 12. It will be shown (p. 7,) that every section of a sphere, made by a plane, is a circle : this granted, a great circle is a section which passes through the centre ; a small circle, is one... | |
| Royal Military Academy, Woolwich - 1853 - 400 pągines
...Archimedes himself in an edition of his works.] CHAPTER VII. THE CONE, CYLINDER, AND SPHERE. PROPOSITION I. Every section of a sphere made by a plane is a circle. 1 . Let the plane pass through the centre 0 of the sphere : then all lines drawn from the centre in... | |
| Charles Davies - 1854 - 436 pągines
...are equal ; all the diameters are equal, and each is double the radius. 12. It will be shown (p. 7,) that every section of a sphere, made by a plane, is a circle: this granted, a great circle •is a section which passes through the centre ; a small circle, is one... | |
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