 | Adrien Marie Legendre - 1819 - 574 σελίδες
...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 σελίδες
...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 σελίδες
...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... | |
 | Charles Frederick Partington - 1825 - 342 σελίδες
...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 - 1825 - 280 σελίδες
...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 - 1825 - 276 σελίδες
...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 - 1826 - 354 σελίδες
...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... | |
 | Henry Pearson - 1833 - 164 σελίδες
...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 σελίδες
...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 σελίδες
...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... | |
| |
THEOREM. Every section of a sphere, made by a plane, is a circle. 
