 | Isaac Newton - 1729 - 444 σελίδες
...fubduplicate ratio of the diftance. la the hyperbola the perpendicular is lefs variable, in the ellipfis more. COR. 7. In a parabola, the velocity of a body at any diflance from the focus, is to the velocity of a body revolving in a circle at the fame djinnce from... | |
 | John Clarke - 1730 - 382 σελίδες
...Hence I fay it follows (by Compaction) i/ D that the Velocity of a Body revolving in a Conick Section, is to the Velocity of a Body revolving in a Circle at the fame Diftance, as a mean Proportional betwixt that common Diftance and half the principal Lotus retfum... | |
 | Royal Society (Great Britain) - 1749 - 878 σελίδες
...to 1/ С D. Therefore ex ¿quo the Velocity of a Body revolving in an Ellipfis at the Diftance SP, is to the Velocity of a Body revolving in a Circle at the fame Diftance, as ^ PF ta V С D. C( rol. 2.] Having given the Velocity in an Ellipßs, tbe Pcßtion... | |
 | 1790 - 408 σελίδες
...&f т and т tn being limilar, Tf.^nV.sp ; т s (i). But the velocity of the comet at the point т is to the velocity of a body revolving in a circle at that diitance from' tltfi fun fPrincipia, lib. i. prop. 16, cor. 9) as v's т X £ lat- re4t. f с... | |
 | 1804 - 476 σελίδες
...to the perihelion distance. 17- Compare the velocity in an ellipse, at the greatest distance, with the velocity of a body revolving in a circle at the same distance. Evening Problems. — Mr. Turton. 1. Explain the nature of the stereographic projection of the sphere... | |
 | Samuel Vince - 1812 - 298 σελίδες
...mft is negative. PRoP. CXXX. The velocity of a body revolving in any curve about a centre of force : velocity of a body revolving in a circle at the same distance, in the subduplicate ratio of the chord of curvature : twice the distance, or in the sub, yt HI duplicate... | |
 | Thomas Leybourn - 1817 - 456 σελίδες
...similar, it : т/г : : Sp (CT- \/(2a — 1)) : TS (1). But the velocity of the comet at the point т is to the velocity of a body revolving in a circle at that distance from the $un (Principia, lib/ 1. prop. 16, cor. 9) as v4ST x т latus rectum) is to sp,... | |
 | 1821 - 464 σελίδες
...to the perihelion distance. 17. Compare the velocity in an ellipse, at the greatest distance, with the velocity of a body revolving in a circle at the same distance. Evening Problems. — Mr. TURTON. 1 . Explain the nature of the stercographic projection of the sphere... | |
 | Isaac Newton - 1826 - 208 σελίδες
...is less ; in an hyperbola greater. Cor. 8. The velocity of a body, revolving in any conic section, is to the velocity of a body revolving in a circle, at the distance of half the principal latus rectum of the section, as that distance, to the perpendicular... | |
 | William Whewell - 1832 - 572 σελίδες
...the distance, (as SA,) and oa COR. 3. To compare the velocity at any point of a conic section, with the velocity of a body revolving in a circle at the same distance, and acted on by the same force. The velocity in any curve is equal to that acquired by falling down... | |
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In a parabola, the velocity of a body at any distance from the focus is to the velocity of a body revolving in a circle, at the same distance... 
