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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... "
Cambridge Problems: Being a Collection of the Printed Questions Proposed to ... - Page 280
1821 - 425 pages
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A Course of Mathematics: Containing the Principles of Plane ..., Volumes 1-3

Jeremiah Day - Geometry - 1839 - 434 pages
...^. For V2 R2=l=sin2 45°+cos2 45=2sin2 45° Therefore, Sin 45°=Vi=— ,. 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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A Treatise of Plane Trigonometry, and the Mensuration of Heights and ...

Jeremiah Day - Logarithms - 1848 - 354 pages
...For V2 R*=1=sin" 45°+cos' 45=2 sin' 45° 1 Therefore, Sin 45°=Vi= — . V2 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, be an arc, of which AB is the chord, BF the sine, and AF the versed...
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An Elementary Course of Mathematics: Designed Principally for Students of ...

Harvey Goodwin - Mathematics - 1849 - 588 pages
...which a body moving uniformly in a circle under the action of a given central force describes in a given time, is a mean proportional between the diameter of the circle and the space through which the body would fall under the action of the same force and in the same time. [For, let...
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The Three First Sections and Part of the Seventh Section of Newton's ...

Isaac Newton - Curves, Plane - 1850 - 184 pages
...Corollorary of Newton's text can e better illustrated under Prop. VI. as is done by Svans. describes in any time, is a mean proportional between the diameter of the circle and the space, which the same body, descending by the same given force, would describe in the same given time. Let...
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New Elements of Geometry

Seba Smith - Geometry - 1850 - 214 pages
...square root of the diameter of the circle multiplied by the diameter of the segment ; or the chord is a mean proportional between the diameter of the circle and the diameter of the segment. AC, the diameter of the second circle, is 2. Therefore the chord IK cuts segments...
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A Treatise on the Steam Engine in Its Application to Mines, Mills, Steam ...

John Bourne - Steam engineering - 1851 - 346 pages
...circle by means of a given centripetal force, the portion of the circumference which it describes in any time is a mean proportional between the diameter of the circle and the space which the body would descend perpendicularly in the same time, and with the same given force continued...
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The Practical Model Calculator: For the Engineer, Mechanic, Machinist ...

Oliver Byrne - Engineering - 1851 - 310 pages
...circle by means of a given centripetal force, the portion of the circumference which it describes in any time is a mean proportional between the diameter of the circle and the space which the body would descend perpendicularly in the same time, and with the same given force continued...
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A Course of Mathematics: Containing the Principles of Plane Trigonometry ...

Jeremiah Day - Geometry - 1851 - 418 pages
...45°=-=. For V2 R2=l-=sm2 45°+cos2 45=-2sin2 45° Therefore, Sin 45°= V£ =~-^. 97. The chord of an^ 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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The Practical Model Calculator, for the Engineer, Mechanic, Machinist ...

Oliver Byrne - Engineering - 1863 - 600 pages
...circle by means of a given centripetal force, the portion of the circumference which it describes in any time is a mean proportional between the diameter of the circle and the space which the body would descend perpendicularly in the same time, and with the same given force continued...
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The Practical Examinator on Steam and the Steam Engine: with Instructive ...

William Templeton - 1865 - 178 pages
...by means of a given centripetal force, the portion of the circumference wfiich it describes in any time is a mean proportional between the diameter of the circle and the space which the body would descend perpendicularly in the same time, and with the same given force continued...
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