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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 First Three Sections of Newton's Principia: With Copious Notes and ... - עמוד 26
מאת Isaac Newton - 1826 - 183 דפים
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The Mathematical Principles of Natural Philosophy, כרך 1

Isaac Newton - 1729 - 444 דפים
...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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The Laws of Centripetal and Centrifugal Force...

William Emerson - 1769 - 104 דפים
...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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Cyclomathesis: Or, An Easy Introduction to the Several Branches of ..., כרך 7

William Emerson - 1769 - 370 דפים
...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 - 386 דפים
...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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The Principles of Fluxions: Designed for the Use of Students in the University

Samuel Vince - 1812 - 274 דפים
...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 ..., כרך 8

John Mason Good - 1819 - 788 דפים
...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 ti .ie. By means ot the...
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A Practical Application of the Principles of Geometry to the Mensuration of ...

Jeremiah Day - 1815 - 388 דפים
...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 ..., כרך 16

1816 - 778 דפים
...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, כרך 4

Thomas Leybourn - 1819 - 430 דפים
...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 continued...
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Cambridge Problems: Being a Collection of the Printed Questions Proposed to ...

University of Cambridge - 1821 - 254 דפים
...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 continued...
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