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" From the same demonstration it likewise follows that the arc which a body, uniformly revolving in a circle by means of a given centripetal force, describes in any time is a mean proportional between the diameter of the circle and the space which the same... "
The Principles of Fluxions: Designed for the Use of Students in the University - Page 256
by Samuel Vince - 1812 - 256 pages
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The Mathematical Principles of Natural Philosophy, Volume 1

Isaac Newton - Celestial mechanics - 1729 - 444 pages
...arc which a body, uniformly revolving in a circle by means of a given centripetal force, defcribes in any time, is a mean proportional between the diameter of the circle, and the fpace which the fame body falling by the fame given force would defcend thro' in the .fame given time....
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Cyclomathesis: Or, An Easy Introduction to the Several Branches of ..., Volume 7

William Emerson - Mathematics - 1769 - 370 pages
...revolves uniformly in a circle, by means of a given centripetal force; the arch which it defcribes in any time, is a mean proportional between the diameter of the circle, and the fpacf which the body would defcend thro' in the fame time, and with the fame given force. For 2R (diameter)...
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The Laws of Centripetal and Centrifugal Force...

William Emerson - Centrifugal force - 1769 - 104 pages
...revolves uniformly in a circle, by means of a given centripetal force ; the arch which it defcribes in any time, is a mean proportional between the diameter of the circle, and the fpace which the bod}' would defcend thro' in the fame time, and with the fame given force. For 2R (diameter)...
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Tracts: Containing: I. Mechanics, Or the Doctrine of Motion: II.

William Emerson - Centrifugal force - 1793 - 386 pages
...revolves uniformly in a circle, by means of a given centripetal force ; the arch -which it defcribes in any time, is a mean proportional between the diameter of the circle, and the fpace -which the body would defcend through in the fame time, and -with the fame given force. For 2R...
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Pantologia. A new (cabinet) cyclopędia, by J.M. Good, O. Gregory ..., Volume 8

John Mason Good - 1819 - 788 pages
...the arc wh.ih a body uniformly revolving in a circle by means of a given centripetal force describes in any time, is a mean proportional between the diameter of the circle, and the space which the same body, lulling by the same gi .'en fo ce, would desceud thiou^h in the same given...
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A Practical Application of the Principles of Geometry to the Mensuration of ...

Jeremiah Day - Measurement - 1815 - 388 pages
...equal to half radius. For the cosine of 60° is the sine of 30°. (Art. 89.) 97. The chord of any arc is a mean proportional, between the diameter of the circle, and the versed sine of the arc. Let ADB (Fig. 6.) be an arc, of which AB is the chord, BF the sine, and AF...
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Encyclopaedia Perthensis; Or Universal Dictionary of the Arts ..., Volume 16

Encyclopedias and dictionaries - 1816 - 778 pages
...arc which a body, uniformly revolving in a circle by means of a given centripetal force, defcribes in any time, is a mean proportional between the diameter of the circle anj the fpace which the fame body, falling by the fame given force, would defcend through in the fame...
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New Series of The Mathematical Repository, Volume 4

Thomas Leybourn - Mathematics - 1819 - 430 pages
...The arc of a circle which a body, acted upon by a centripetal force, uniformly describes in any given time is a mean proportional between the diameter of the circle, and the space described by a heavy body from rest in the same time when urged by the force in the circumference...
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Cambridge Problems: Being a Collection of the Printed Questions Proposed to ...

University of Cambridge - Mathematics - 1821 - 254 pages
...The arc of a circle which a body, acted upon by a centripetal force, uniformly describes in any given time is a mean proportional between the diameter of the circle, and the space described by a heavy body from rest in the same time when urged by the force in the circumference...
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Euclid's Elements of Geometry: The Six First Books. To which are Added ...

Rev. John Allen - Astronomy - 1822 - 516 pages
...the arch, which a body, by revolving uniformly in a circle with a given centripetal force, describes in any time, is a mean proportional between the diameter of the circle, and the descent of the body performed in the same time by falling with the same given force. Scholium. The...
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