Of Motion: An Elementary Treatise |
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Page 3
... resulting velocity will be represented in magnitude and direction by the diagonal drawn through the point of intersection of those two sides . " In order to conceive the motion more clearly , let the point be supposed to be compelled to ...
... resulting velocity will be represented in magnitude and direction by the diagonal drawn through the point of intersection of those two sides . " In order to conceive the motion more clearly , let the point be supposed to be compelled to ...
Page 5
... resulting velocity in magnitude and direction ( Art . 7 ) . 9. This may be extended to space of three dimensions , as ... result from the coexistence of other velocities in two or three given directions , according as we deal with space ...
... resulting velocity in magnitude and direction ( Art . 7 ) . 9. This may be extended to space of three dimensions , as ... result from the coexistence of other velocities in two or three given directions , according as we deal with space ...
Page 6
... resulting velocity in magnitude and direction . This is called compounding the given velocities . For if in space of two dimensions , the velocities along Ox and Oy be given = v1 , v2 , respectively , we have OC2 = OA2 + OB2 , y C B OB ...
... resulting velocity in magnitude and direction . This is called compounding the given velocities . For if in space of two dimensions , the velocities along Ox and Oy be given = v1 , v2 , respectively , we have OC2 = OA2 + OB2 , y C B OB ...
Page 7
... results are obtained . If we consider space of three dimensions , and the velocities along Ox , Oy , Oz be given v1 , V2 , V3 , = = V1 , 2 we have B C O D E A 21 OD2 = OE + ED2 , = OA2 + OB2 + 002 , OB cos DOx = = OA OD ' ОС cos Doy ...
... results are obtained . If we consider space of three dimensions , and the velocities along Ox , Oy , Oz be given v1 , V2 , V3 , = = V1 , 2 we have B C O D E A 21 OD2 = OE + ED2 , = OA2 + OB2 + 002 , OB cos DOx = = OA OD ' ОС cos Doy ...
Page 8
... result . For if a space ds be described in a small time St immediately subsequent to the instant under consideration , and if v ' , v " be the greatest and least values of the velocity during the time St , it is plain that ds < v'dt ...
... result . For if a space ds be described in a small time St immediately subsequent to the instant under consideration , and if v ' , v " be the greatest and least values of the velocity during the time St , it is plain that ds < v'dt ...
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Common terms and phrases
accele acceleration produced axes axis balls center of force chord circle complete oscillation conic section constant acceleration cos² curve cycloid described determine the motion determined in Arts Differential Calculus direction of motion dt dt dt² earth's effect elastic ellipse equal equation fixed point focus force acting force of constraint force varying geometrical horizontal hyperbola impact impulse inclined plane inelastic initial direction initially at rest instant Ipswich School latus rectum Law of Motion length lowest point magnitude measure moving point NEWTON obtained Octavo orbit parabola parallelogram particle path perpendicular point of projection quantity of matter radius vector Second Edition Sermons shew sin² space passed straight line string supposed tangent tion Treatise Trinity College University of Cambridge v₁ versin vertex vis viva weight whence
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