Of Motion: An Elementary Treatise |
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Page 27
... origin of distance ; and let a be the initial distance of the moving point , s its distance , and v its velocity at a time t , reckoned from the beginning of the motion . The acceleration will be expressed by As , where λ = the measure ...
... origin of distance ; and let a be the initial distance of the moving point , s its distance , and v its velocity at a time t , reckoned from the beginning of the motion . The acceleration will be expressed by As , where λ = the measure ...
Page 29
... origin and the velocity at that point . 54. The motion now takes place on the negative side of the origin , and will manifestly be the same as if the moving point's velocity ( - . a ) were suddenly reversed , and the motion were on the ...
... origin and the velocity at that point . 54. The motion now takes place on the negative side of the origin , and will manifestly be the same as if the moving point's velocity ( - . a ) were suddenly reversed , and the motion were on the ...
Page 30
... origin , α may be assumed to be of such magnitude as that , when this point arrives at the distance a from the origin , it may be moving with the same velocity as that which the first point initially has , which we will call v ' . Then ...
... origin , α may be assumed to be of such magnitude as that , when this point arrives at the distance a from the origin , it may be moving with the same velocity as that which the first point initially has , which we will call v ' . Then ...
Page 31
... " . -1 α The time of reaching the origin will be a α 蛋 2 • 3 π 2 2λ The velocity here will be ∞ . - * N.B. A is of 3 dimensions in space and -2 in time . 58. After this the motion is on the negative side RECTILINEAR MOTION . 31.
... " . -1 α The time of reaching the origin will be a α 蛋 2 • 3 π 2 2λ The velocity here will be ∞ . - * N.B. A is of 3 dimensions in space and -2 in time . 58. After this the motion is on the negative side RECTILINEAR MOTION . 31.
Page 32
... origin , and by reasoning similar to that used in the preceding case , the moving point will come to rest at a distance a from the origin , 8 after the lapse of a time . It is now in the same cir- cumstances as it initially was , but on ...
... origin , and by reasoning similar to that used in the preceding case , the moving point will come to rest at a distance a from the origin , 8 after the lapse of a time . It is now in the same cir- cumstances as it initially was , but on ...
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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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