| Robert Woodhouse - Plane trigonometry - 1819 - 264 pages
...called rectangular, isosceles, equilateral, in the same cases that a plane triangle isPROPOSITION I. **Every section of a sphere made by a plane is a circle. Let** AnBm 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,... | |
| Robert Woodhouse - 1822
...called rectangular, isosceles, equilateralj 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 Bn be the plane, draw СO* perpendicular to it, which consequently, (by Euclid, Book XI. Def. 3.)... | |
| Adrien Marie Legendre - Geometry - 1822 - 367 pages
...sector, j 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 the section, made by a plane, in the sphere whose centre is C. From the point C, draw CO perpendicular... | |
| 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,... | |
| Adrien Marie Legendre, John Farrar - 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,... | |
| 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 - 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.** ?ig. 221. Demonstration. Let AMB (fig. 221) be a section, made by a plane, of the sphere of which C... | |
| Henry Parr Hamilton - Geometry, Analytic - 1826 - 326 pages
...This operation being executed, and the resulting expression reduced, we have Whence it appears that **every section of a sphere, made by a plane, is a circle.** 327' PROP. 5. To find the equation to a tangent plane drawn through a given point (x', y' , z') of... | |
| George Darley - 1827
...stand perpendicular to both, it shall also be perpendicular to the plane in which they lie, 97ART. 5. **Every section of a sphere, made by a plane, is a circle,** 101. ART. 6. All great circles of the-same sphere are equal to each other, 102. ART. 7- Two great circles... | |
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