## Of Motion: An Elementary Treatise |

### From inside the book

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Page vii

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**parallelogram**of velocities 9. The parallelepiped of velocities IO . Resolution of a velocity II . Composition of velocities 12 . Resolved part of a given velocity in any given direction 13. Measure of a variable velocity 14. Relation ... Page 3

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**Parallelogram**of Velocities . " If two adjacent sides of a**parallelogram**represent in mag- nitude and direction two velocities simultaneously existing in the motion of a point , the resulting velocity will be represented in magnitude ... Page 4

... equiangular , i . e . the angles aAd , CAD are equal ; therefore d is in the diagonal AD , and consequently the moving point passes along AD . Also it describes AD uniformly , for Ad : AD 4

... equiangular , i . e . the angles aAd , CAD are equal ; therefore d is in the diagonal AD , and consequently the moving point passes along AD . Also it describes AD uniformly , for Ad : AD 4

**PARALLELOGRAM**OF VELOCITIES . Page 8

... be the greatest and least values of the velocity during the time St , it is plain that ds < v'dt , and > v'dt ; Ss < v ' , and > v " , δε and making ds , St indefinitely small , as v 8 VARYING VELOCITY . The

... be the greatest and least values of the velocity during the time St , it is plain that ds < v'dt , and > v'dt ; Ss < v ' , and > v " , δε and making ds , St indefinitely small , as v 8 VARYING VELOCITY . The

**parallelogram**of velocities. Page 9

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**parallelogram**and paral- lelepiped of velocities are equally true for varying velocities , as may be clearly seen by considering an indefinitely small**parallelogram**or parallelepiped similar to those in the figures of Arts . 8 , 9 , or ...### Other editions - View all

### Common terms and phrases

acceleration produced apse axes axis balls center of force chord circle co-ordinates complete oscillation conic section considered constant acceleration cos˛ curve cycloid described determine the motion Differential Calculus direction of motion ds dt dt˛ dx dy earth's elastic ellipse equal equation fixed point focus force acting geometrical horizontal hyperbola idea impact impulse inclined plane initial direction initial position initial velocity initially at rest instant under consideration latus rectum Law of Motion material bodies measure moving point negative NEWTON obtained Octavo orbit origin parabola parallelogram particle path perpendicular point be moving quantity of matter radius vector Second Edition Sermons shew sin˛ 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 ᏧᎾ

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