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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... "
Euclid's Elements of Geometry: The Six First Books. To which are Added ... - Page 459
by Euclid, Rev. John Allen - 1822 - 494 pages
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The Mathematical Principles of Natural Philosophy, Volume 1

Isaac Newton - Celestial mechanics - 1729 - 320 pages
...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...
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A Demonstration of Some of the Principal Sections of Sir Isaac Newton's ...

John Clarke - Astronomy - 1730 - 313 pages
...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...
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The Philosophical Transactions ... Abridged ..., Volume 4

Royal Society (Great Britain) - Science - 1749
...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 Ellip▀s, tbe Pc▀tion...
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Collection of English Almanacs for the Years 1702-1835

1790
...&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 ú lat- re4t. f с...
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New Cambridge Guide; Or, A Description of the University, Town, and County ...

Cambridge (England) - 1804 - 130 pages
...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...
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The Principles of Fluxions

Samuel Vince - Calculus - 1812 - 256 pages
...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...
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The Mathematical Questions Proposed in the Ladies' Diary: And ..., Volume 3

Thomas Leybourn - Mathematics - 1817
...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,...
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Cambridge Problems: Being a Collection of the Printed Questions Proposed to ...

Mathematics - 1821 - 425 pages
...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...
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The First Three Sections of Newton's Principia: With Copious Notes and ...

Isaac Newton - Curves, Plane - 1826 - 183 pages
...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...
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First Principles of Mechanics: With Historical and Practical Illustrations

William Whewell - Mechanics - 1832 - 118 pages
...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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