## Of Motion: An Elementary Treatise |

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Page viii

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**axes**of x , y , and z 33. Radial and transversal velocities 15 ib . 34. Radial and transversal accelerations 16 35. Tangential and normal velocities and accelerations 17 37. Dimensions of the measure of a velocity or acceleration . 19 ... Page ix

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**axes**of the path Velocity = √ ( semi - conjugate diameter ) • Determination of the**axes**from the initial circumstances 32 ib . ib . ˇ 33 34 35 ib . • 36 ˇ 37 38 39 40 2π 75 . Period = ib . √ 76 . 79 . 80 . Acceleration ( distance ) -2 ... Page 7

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**axes**, and as l ' , m ' , n ' , are the cosines of the angles between these and the second line , this proposition shews that the resolved part required may be correctly obtained by resolving the given velocity into three directions at ... Page 15

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**axes**of x , y , z , are dt dx dy dz ds ' ds ' ds ' and therefore ( Art . 10 ) the resolved parts of the velocity in the directions of the**axes**will be dx dy dz dt ' dt ' dt ' and therefore the accelerations in the same directions will ... Page 37

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**axes**are apses ; if the focus were the origin , the extremities of the major axis only are apses . + This case of motion may be easily solved in the following manner . We have the acceleration in x = -λr cos 0 = −λx , and that in y ...### 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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