 | James Hayward - Geometry - 1829 - 228 pages
...position and magnitude of the circle which is the intersection of a given sphere and a given plane. By drawing a perpendicular from the centre of the sphere to the cutting plane, and determining the meeting of this line and the proposed plane, we have the centre... | |
 | George Salmon - Geometry, Analytic - 1862 - 494 pages
...the values already found (Arts. 330, 332). -~~ is obviously the length of the perpendicular distance from the centre of the sphere to the plane of the circle of curvature. 340. To find the co-ordinates of the centre of the osculating sphere. Let the equation... | |
 | George Salmon - Geometry, Analytic - 1862 - 490 pages
...values already found (Arts. 330, 332). •j- is obviously the length of the perpendicular distance from the centre of the sphere to the plane of the circle of curvature. 340. To find the co-ordinates of the centre of the osculating sphere. Let the equation... | |
 | Adrien Marie Legendre - Geometry - 1863 - 464 pages
...circle is equal to the square of the radius of the sphere diminished by the square of the distance from the centre of the sphere to the plane of the circle (B. IV., P. XL, C. l) : hence, circles which are equally distant from the centre, are equal ; and of... | |
 | Charles Davies - Geometry - 1872 - 464 pages
...circle is equal to the square of the radius of the sphere diminished by the square of the distance from the centre of the sphere to the plane of the circle (B. IV., P. XI., C. 1) : hence, circles which are equally distant from the centre, are equal; and of... | |
 | Adrien Marie Legendre - Geometry - 1874 - 500 pages
...circle is equal to the square of the radius of the sphere diminished by the square of the distance from the centre of the sphere to the plane of the circle (B. IV., P. XI., C. 1) : hence, circles which are equally distant from the centre, are equal ; and... | |
 | National cyclopaedia - 1879 - 668 pages
...Great Circle, and one which does not pass through the centre a Small Circle. The centre of a circular section is found by drawing a perpendicular from the centre of the sphere to the plane of the section. All sections whose planes are parallel have their centres on one straight line, namely, the... | |
 | Charles Davies, Adrien Marie Legendre - Geometry - 1885 - 538 pages
...circle is equal to the square of the radius of the sphere diminished by the square of the distance from the centre of the sphere to the plane of the circle (B. IV., P. XI., C. 1): hence, circles which are equally distant from the centre, are equal ; and of... | |
 | Thomas Franklin Holgate - Geometry - 1901 - 462 pages
...sphere. 586. COROLLARY II. The centre of any rirde of a sphere is the foot of the perpendicular drawn from the centre of the sphere to the plane of the circle. 587. COROLLARY III. The centres of all great circles coincide with the centre of the sphere, and all... | |
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... impossible. Cor. 3. The centre of a sphere, and the centre of any small circle of that sphere, are in a straight line perpendicular to the plane of the circle. Cor. 4. The square of the radius of any small circle is equal to the square of the radius... 