 | Adrien Marie Legendre - 1819 - 574 pàgines
...the 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 - 1819 - 470 pàgines
...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.... | |
 | Adrien Marie Legendre - 1822 - 394 pàgines
...sector, ; 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... | |
 | Adrien Marie Legendre, John Farrar - 1825 - 294 pàgines
...the 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 - 1825 - 280 pàgines
...the 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 - 1825 - 342 pàgines
...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... | |
 | Charles Brooke - 1829 - 386 pàgines
...(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 - 1833 - 164 pàgines
...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 - 1836 - 394 pàgines
...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 - 1837 - 216 pàgines
...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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It will be demonstrated art. 452, that every section of a sphere made by a plane is a circle. 
