 | Albert Ensign Church - Geometry, Analytic - 1851 - 318 pages
...hence, r' = a + ™ (2). a Adding equations (1) and (2), member by member, we have r + r' = 2a; hence, the sum of the distances from any point of the curve to the two foci is equal to the transverse axis. This remarkable property enables us to define an ellipse... | |
 | Albert Ensign Church - Geometry, Analytic - 1854 - 322 pages
...hence, r' = a + ™ (2). Adding equations (1) and (2), member by member, we have r + r' = 2a; hence, the sum of the distances from any point of the curve to the two foci is equal to the transverse 'axis. This remarkable property enables us to define an ellipse... | |
 | Charles Davies, William Guy Peck - Electronic book - 1855 - 592 pages
...remarkable properties. 1. One of the most common definitions of the ellipse is the following : An ellipse is a plane curve, such that the sum of the distances from any point to two fixed points is equal to a given distance. The fixed points are called foci, and the given distance... | |
 | Mathematics - 1860 - 294 pages
...becomes manifest. To illustrate, suppose we had the equation ar-{-br,.— a constant, r and r. being the distances from any point of the curve to two fixed points, and a and 6 any multipliers, and let » and f i be the angles made by the tangent to the curve at any... | |
 | Charles Davies, William Guy Peck - Mathematics - 1865 - 592 pages
...remarkable properties. 1. One of the most common definitions of the ellipse is the following : An ellipse is a plane curve, such that the sum of the distances from any poult to two fixed points is equal to a given distance. The fixed points are called foci, and the given... | |
 | Selim Hobart Peabody - Astronomy - 1869 - 388 pages
...Definitions. — Observing that the length of the string is constantly the same, we say: An ellipse is a curve such that the sum of the distances from any point of the curve to two fixed points within, is invariable. The space included is called an ellipse as well as the line which includes it.... | |
 | Samuel Edward Warren - Geometry, Descriptive - 1877 - 310 pages
...THEOREM IV. — In the ellipse, section of a cone made by a plane actually cutting all its elements, the sum of the distances from any point of the curve to two fixed points within it is constant and equal to the transverse axis 56 PROBLEM XXIV. — To represent a cone by... | |
 | Samuel Edward Warren - Geometry, Descriptive - 1877 - 312 pages
...THEOREM IV. — In the ellipse, section of a cone made by a plane actually cutting all its elements, the sum of the distances from any point of the curve to two fixed points within it is constant and equal to the transverse axis 56 PROBLEM XXIV. — To represent a cone by... | |
 | Samuel Edward Warren - Geometry, Descriptive - 1888 - 328 pages
...FS ;) and 0&, respectively A and B, OF = db = V W—cd? = V A2— B2. THEOREM XIY. In the ellipse, the sum of the distances from any point of the curve to the foci is constant, and equal to the transverse axis of the curve. PL HI. These ellipses are cut... | |
 | Frederick Newton Willson - Geometry, Descriptive - 1898 - 322 pages
...125. According to the foregoing construction the ellipse may be defined as a curve in which the «um of the distances from any point of the curve to two fixed points i* constant. That constant is evidently the longer or fra,wow (major) axis, A C. The shorter or conjugate... | |
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A plane curve, such that the sum of the distances from any point of the curve to two fixed points is a constant. 
