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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 mathematical principles of natural philosophy - الصفحة 46
بواسطة Sir Isaac Newton, William Davis, William Emerson, John Machin - 1803
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## The Laws of Centripetal and Centrifugal Force...

William Emerson - 1769 - عدد الصفحات: 81
...if a body 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) : ^/zRs...
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## Cyclomathesis: Or, An Easy Introduction to the Several Branches of ..., المجلد 7

William Emerson - 1769
...if a body 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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## Tracts: Containing: I. Mechanics, Or the Doctrine of Motion: II.

William Emerson - 1793 - عدد الصفحات: 302
...if a body 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 (diameter) : \/zRs...
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## Encyclopædia Britannica: Or, A Dictionary of Arts ..., المجلد 13،الجزء 1

...inileaj of tlic radii. COR. 9. Frern the fame dcmonilration it likewife follows, that the arc whith a body uniformly revolving in a circle by means of...centripetal force defcribes in any time, is a mean propoitional between the diameter of the circle, and the fpace which the fame tody, f.Jling by the...
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## The Principles of Fluxions: Designed for the Use of Students in the University

Samuel Vince - 1812 - عدد الصفحات: 256
...constant central force, will be increased in the same ratio of 1 : a8 ; therefore the arc described in any time is a mean proportional between the diameter of the circle and the distance fallen through in the same timc5 by the constant action of the centripetal force. Now the...
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## Pantologia. A new (cabinet) cyclopædia, by J.M. Good, O. Gregory ..., المجلد 8

1819
...iu»te <d "f the radii. COR. 9. From the *ame demonstration it likewise follows, that 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...
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## A Practical Application of the Principles of Geometry to the Mensuration of ...

Jeremiah Day - 1815 - عدد الصفحات: 96
...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 ..., المجلد 16

1816
...tht bodies from the centres inftead of the radii. COR.. 9. From the fame demonftration it liktwife follows, that the arc which a body, uniformly revolving...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, المجلد 4

Thomas Leybourn - 1819
...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 ...

1821 - عدد الصفحات: 425
...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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