 | William Chauvenet - Geometry - 1871 - 380 pages
...every 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... | |
 | Eli Todd Tappan - Geometry - 1873 - 288 pages
...generated by the 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... | |
 | William Frothingham Bradbury - Geometry - 1872 - 124 pages
...of a sphere are equal ; all the diameters are equal, and each is double the radius. THEOREM XIV. 58. Every section of a sphere made by a plane is a circle. Let ABD be a section made by a plane cutting the sphere whose centre is C ', then is ABD a circle. Draw... | |
 | Edward Olney - Geometry - 1872 - 472 pages
...is equal to 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 - Mathematics - 1872 - 382 pages
...of the circle; and this diameter is called the axis of the circle. PROPOSITION VII.— THEOREM. 28. Every section of a sphere made by a plane is a circle. Let abc be a plane section of the sphere whose centre is O. All the straight lines Oa, Ob, etc., drawn... | |
 | 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... | |
 | Charles Davies - Geometry - 1872 - 464 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... | |
 | 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... | |
 | 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... | |
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THEOREM. Every section of a sphere, made by a plane, is a circle. 
