| Robert Woodhouse - Trigonometry - 1819 - 264 pages
...called rectangular, isosceles, equilateral, in the same cases that a plane triangle is. PROPOSITION I. **Every section of a sphere made by a plane is a circle. Let** An Em be the plane, draw CO * perpendicular to it, which consequently, (by Euclid, Book XI. Def. 3.)... | |
| Adrien Marie Legendre - Geometry - 1819 - 208 pages
...diameters also are equal, and each double of the radius. 439. It will be demonstrated art. 452, that **every section of a sphere made by a plane is a circle.** This being supposed, we call a great circle the section made by a plane which passes through the centre,... | |
| Charles Frederick Partington - Building - 1825 - 304 pages
...be circles, provided that the axis of the cylinder, or cone, tend to the centre of the sphere. For **every section of a sphere made by a plane is a circle,** and every section of a right cylinder, or cone, perpendicular to the axis, is also a circle. Let the... | |
| Adrien Marie Legendre, John Farrar - Geometry - 1825 - 224 pages
...circular sector as DCF, or FCH, describes a solid which is called a spherical sector. THEOREM. 452. **Every section of a sphere made by a plane is a circle.** Fig. 221. Demonstration. Let AMB (fig. 221) be a section, made by a plane, of the sphere of which C... | |
| Adrien Marie Legendre - Geometry - 1825 - 224 pages
...diameters also are equal, and each double of the radius. 439. It will be demonstrated art. 452, that **every section of a sphere made by a plane is a circle.** This being supposed, we call a great circle the section made by a plane which passes through the centre,... | |
| Henry Parr Hamilton - Geometry, Analytic - 1826 - 326 pages
...the resulting expression reduced, we have which is the equation to a circle. Whence it appears that **every section of a sphere, made by a plane, is a circle.** 327. PROF. 5. To find the equation to a tangent plane drawn through a given point (x', y , z) of the... | |
| Charles Brooke - Mathematics - 1829 - 358 pages
...(W. Ch. v; L. 72—84; Leg. 53—7; C. 559—615.) SPHEEICAL TRIGONOMETRY. (21.) General Principles. **Every section of a sphere made by a plane is a Circle.** The distance between the poles of two great circles is equal to the inclination of their planes. The... | |
| Henry Pearson - Mathematics - 1833 - 120 pages
...the centre, the equation of the sphere is the same for all positions of the rectangular axes. 208. **Every section of a sphere made by a plane is a circle. Let** the inclination of the cutting plane to the plane of xy be 0; and let us assume the common section... | |
| Adrien Marie Legendre - Geometry - 1836 - 359 pages
...the solidity of the frustum of the cone is measured by i«OP x (OA2+PD2+ AO x PD). PROPOSITION VII. **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 perpendicular... | |
| Benjamin Peirce - Geometry - 1837 - 159 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.** Demonstration. From the centre C (fig. 178) of the sphere draw the perpendicular CO to the section... | |
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