| Benjamin Peirce - Geometry - 1847 - 204 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... | |
| 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.** But the following is a direct proof of this proposition. 4. Every section of a sphere made by a plane... | |
| James M'Intire - Astronomy - 1850 - 352 pages
...AND SMALL CIRCLES. The circles of the terrestrial and celestial spheres are either great or small. **A great circle is a section made by a plane, which passes through the** centre of the sphere, and divides it into two equal parts. A small circle is a section made by a plane,... | |
| John Radford Young - Measurement - 1850 - 294 pages
...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 sphere... | |
| George Roberts Perkins - Geometry - 1850 - 332 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 centre is C. From the point C, draw CO... | |
| Anna Cabot Lowell - Astronomy - 1850 - 412 pages
...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 - 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,... | |
| 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,... | |
| Adrien Marie Legendre - Geometry - 1852 - 436 pages
...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 - Mathematics - 1853 - 400 pages
...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... | |
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