 | Harvey Goodwin - Mathematics - 1846 - 500 pages
...the parabola, (Prop, v.) : hence the curve GAK is a parabola. THE ELLIPSE. B DKF. If a point P move in such a manner that the sum of its distances from two fixed points S, H is always the same, the curve traced out by P will be an ellipse. The points S, H are called the... | |
 | Auguste Comte - Mathematics - 1851 - 286 pages
...way, the elementary definition of the ellipse or of the hyperbola — as being the curve generated by a point which moves in such a manner that the sum or the difference of its distances from two fixed points remains constant — gives at once, for either... | |
 | Charles Davies, William Guy Peck - Electronic book - 1855 - 592 pages
...a line of measures ; in all other cases there is but one line of measures, and that ¡s found plane in such a manner that the sum of its distances from two fixed points of the plane is constant, the locus of the point is an by drawing a straight line through the centre... | |
 | Norman Macleod Ferrers - Conic sections - 1861 - 200 pages
...the straight line, which we shall make the basis of our investigation, is, that it is the locus of a point which moves in such a manner, that the sum of the areas of the triangles PA Q, PAR is constant. Let AQ = q, AR = r, then the areas of the triangles... | |
 | William Henry Drew - Conic sections - 1869 - 153 pages
...Minor Axis of the ellipse. In most geometrical treatises the ellipse is defined as the curve traced out by a point which moves in such a manner that the sum of its distances from two fixed points is always the same ; but it appears that the properties of the curve are more clearly exhibited by... | |
 | Elias Loomis - Conic sections - 1877 - 458 pages
...through the same point meets the axis. EI.I.IPSE. Definitions. 1. An ellipse is a plane curve traced out by a point which moves in such a manner that the sum of its distances from two fixed points is always the same. 2. The two fixed points are called the/oci of the ellipse. Thus, if F and F' are... | |
 | S. Holker Haslam, Joseph Edwards - Conic sections - 1881 - 168 pages
...points at which they cut the curve will be the extremities of conjugate diameters. 105. If a point move in such a manner that the sum of its distances from two fixed points is constant, prove that its distance from any one bears a constant ratio to its distance from some... | |
 | S. Holker Haslam, Joseph Edwards - Conic sections - 1881 - 168 pages
...points at which they cut the curve will be the extremities of conjugate diameters. 105. If a point move in such a manner that the sum of its distances from two fixed points is constant, prove that its distance from any one bears a constant ratio to its distance from some... | |
 | Henry Percy Smith - English language - 1883 - 542 pages
...inches. Ellandonan. District near Kintail, in Rossshire, in the Tudor period. Ellipse. [Gr. €AAdi(iis, a deficiency.} (Math.) The plane curve described by...implied, as, " He struck me, not I him." Ellipsoid [Gr. ?\Afii|<iî, an ellipse, cîîoi, form] ; E. of revolution. A solid (resembling an egg) a" whose plane... | |
 | Swan Moses Burnett - Astigmatism - 1887 - 274 pages
...some detail the optical properties of ellipses. Geometrically, an ellipse is " a plane curve traced by a point which moves in such a manner that the sum of the distances from the fixed points is always the same. The two fixed points are called the/b« of... | |
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The plane curve described by a point which moves in such a manner that the sum of its distances from two fixed points (the foci) remains the same in all its positions. 
