Books Books 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... Cambridge Problems: Being a Collection of the Printed Questions Proposed to ... - Page 280
1821 - 425 pages ## The Mathematical Principles of Natural Philosophy, Volume 1

Isaac Newton - Celestial mechanics - 1729 - 436 pages
...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.... ## The Laws of Centripetal and Centrifugal Force...

William Emerson - Centrifugal force - 1769 - 81 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)... ## 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)... ## Tracts: Containing: I. Mechanics, Or the Doctrine of Motion: II.

William Emerson - Centrifugal force - 1793 - 386 pages
...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... ## The Principles of Fluxions

Samuel Vince - Calculus - 1812 - 256 pages
...constant central force, will be increased in the same ratio of 1 : a2 ; 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 time, by the constant action of the centripetal force. Now the... ## Pantologia. A new (cabinet) cyclopædia, by J.M. Good, O. Gregory ..., Volume 8

John Mason Good - 1819 - 790 pages
...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... ## 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... ## New Series of The Mathematical Repository, Volume 4

Thomas Leybourn - Mathematics - 1819 - 430 pages
...and the fluxion a1 — л* '--9 (* + *)* - 7, The аг-c of a> circle which. a body, acted u-ponby, a centripetal force, uniformly describes in any given...mean proportional between the diameter of the circle, andi the «pace described by a heavy body from rest in the same time when urged by the force in the... ## Euclid's Elements of Geometry: The Six First Books. To which are Added ...

Rev. John Allen - Astronomy - 1822 - 516 pages
...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... 