 | Eli Todd Tappan - Geometry - 1873 - 288 pages
...motion of a straight line, every possible section of it is a curve. SECANT PLANES. 744. Theorem— Every section of a sphere made by a plane is a circle. But if the section do not pass through the center, as DGF, then from the center C let CI fall perpendicularly... | |
 | Edward Olney - Geometry - 1872 - 472 pages
...twice the radius. ELEMENTARY SOLID GEOMETRY. CIRCLES OF THE SPHERE. PROPOSITION L 533. Theorem. — Every section of a sphere, made by a plane, is a circle. P DEM. — Let AFEBD be a section of a sphere whose centre is O, made by a plane ; then is it a circle.... | |
 | William Chauvenet - Geometry - 1872 - 382 pages
...diameter is double the radius, all the diameters are equal. 26. .Definition. It will be shown that every section of a sphere made by a plane is a circle; and as the greatest possible section is one made by a plane passing through the centre, such a section... | |
 | James Maurice Wilson - 1873 - 178 pages
...semicircle describes a circle whose plane 1s at right angles to AB, and centre lies in AB. THEOREM 35. Every section of a sphere made by a plane is a circle. Let a plane RQR' cut the sphere whose centre is O ; then shall the section be a circle. Draw ON perpendicular... | |
 | Philip Kelland - 1873 - 248 pages
...unit vector with it. The equation above gives in this case .: CO. CD = a' (19). EXAMPLES. 42. Ex. 1. Every section of a sphere made by a plane is a circle. Let p' — — a" be the equation of the sphere, a the vector perpendicular from the centre on the cutting... | |
 | Benjamin Greenleaf - Geometry - 1873 - 202 pages
...whose bases are the two bases of the frustum, and a mean proportional between them. THEOREM VII. 353. Every section of a sphere made by a plane is a circle. Let ABE be a section made by a plane in the sphere whose center is C. From the center, C, draw CD perpendicular... | |
 | David Munn - 1873 - 160 pages
...generated will evidently have all its points equally distant from the centre. It can be shewn that every section of a sphere made by a plane is a circle, and as the greatest possible section is one made by a plane passing through the centre, such a section... | |
 | Benjamin Greenleaf - Geometry - 1874 - 206 pages
...whose bases are the two bases of the frustum, and a mean proportional between them. THEOREM VII. 353. Every section of a sphere made by a plane is a circle. Let ABE be a section made by a plane in the sphere whose center is C. From the center, C, draw CD perpendicular... | |
 | Harvard University - 1874 - 668 pages
...third. 8. A triangular pyramid is one-third of a triangular prism of the game base and altitude. 9. Every section of a sphere made by a plane is a circle. 10. In two polar triangles, each angle of one is measured by the supplement of the side lying opposite... | |
 | Adrien Marie Legendre - Geometry - 1874 - 500 pages
...frustum, and a mean proportional between them ; which was to be proved. PROPOSITION VII. THEOREM. Any section of a sphere made by a plane, is a circle. Let C be the centre of a sphere, CA one of its radii, and AMB any section made by a plane : then will this... | |
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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. 
