## Of Motion; an elementary treatise1859 |

### From inside the book

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Page xii

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**Tangent**to a cycloid at any point 3. Length of arc , measured from vertex 4. Mode of describing a cycloid by a string 5. Equations to the cycloid . 6. Involute to a cycloid . PROBLEMS 95 · ༄ ༤ ༈༙ ༈༙ ib . 96 ib . 97 99 ΙΟΙ OF MOTION ... Page 14

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**tangent**, and bearing in mind that the corresponding elements of the arc and**tangent**are coincident . The other equations cannot be assumed to be true , because the change Relation between space, time, and variable velocity. Page 15

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**tangent**. A. 31. If , in the enunciation of Newton's 10th Lemma , we read " point " instead of " body , " and " acceleration " instead of " force , " the reasoning still holds good , and we have a = 2 limit S If t be considered ... Page 17

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**tangent**and normal . y Then we have cos PTx = dx ds ' sin PTx = dy ds and the velocity in direction of the**tangent**is direction of the normal is 0 . 7 Also the acceleration along the**tangent**L. = = = dx dx dy d'y ds dt2 + ds dt2 " 1 dx ... Page 23

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**tangent**to the path at A , therefore the above equation shews that the path is a parabola whose axis is parallel to yA the direction of the acceleration , the concavity being turned in that direction , and the distance of A from the v'2 ...### Other editions - View all

### Common terms and phrases

acceleration produced apse axes axis balls called center of force circle complete oscillation conic section considered constant acceleration cos² curve cycloid d²r d²x described determine the motion Differential Calculus direction of motion distance ds dt dt dt dt dt² dx dy elastic ellipse equal equation experiments fixed point force acting geometrical h²C horizontal hyperbola idea impact impulse inclined plane initial direction initial position initial velocity initially at rest latus rectum Law of Motion mass material bodies measure moving point NEWTON obtained orbit parabola parallelogram particle path perpendicular point be moving quantity of matter radius vector Second Edition semi-latus rectum shew sin² space passed Statics straight line string supposed tangent tion Treatise Trinity College units of space University of Cambridge v'cos v₁ velocity acquired vertex vertical vis viva weight whence