Of Motion: An Elementary Treatise |
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Page 23
... 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 focus 1 == ˇ 22'2 ว = 12 4 α 2α • 43. The position of the focus S is determined as ...
... 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 focus 1 == ˇ 22'2 ว = 12 4 α 2α • 43. The position of the focus S is determined as ...
Page 24
... parabola cuts Ax v'sini 12 ย = 2 x v ' cos i = sin 21 . α α The directrix of the parabola will be parallel to Ax , and will cut Ay at a point E whose distance from A = AS = 212 2a 47. The velocity at Pin direction Ax will be v'cos ɩ ...
... parabola cuts Ax v'sini 12 ย = 2 x v ' cos i = sin 21 . α α The directrix of the parabola will be parallel to Ax , and will cut Ay at a point E whose distance from A = AS = 212 2a 47. The velocity at Pin direction Ax will be v'cos ɩ ...
Page 26
... parabola , the co - ordinates of 12 whose vertex are sin 21 , 2α v'2 and sin , whose axis is in the 2a negative direction of y , i . e . in the direction of the acceleration ; and whose latus rectum = 2v2 cos2 α A. CHAPTER IV . * OF THE ...
... parabola , the co - ordinates of 12 whose vertex are sin 21 , 2α v'2 and sin , whose axis is in the 2a negative direction of y , i . e . in the direction of the acceleration ; and whose latus rectum = 2v2 cos2 α A. CHAPTER IV . * OF THE ...
Page 41
... parabola , or hyperbola , according as Ah2 λ is < = or > 1 . 77. This might have been obtained , as in Art . 52 , by putting น - λ h2 = w , whence dow dt2 + w = 0 ; .. w = A cos ( 0 – B ) . 78. We have also 2 A2 ( du ) + u2 = 4a sin2 ...
... parabola , or hyperbola , according as Ah2 λ is < = or > 1 . 77. This might have been obtained , as in Art . 52 , by putting น - λ h2 = w , whence dow dt2 + w = 0 ; .. w = A cos ( 0 – B ) . 78. We have also 2 A2 ( du ) + u2 = 4a sin2 ...
Page 43
... parabola , we should have v2 2λ Ah h 83 . e : = λ e - 4- ( 2+ ) ( Art . 79 ) . = = v'3h3 2h2 - + 1 λι h v ' ' sin2 2v'r ' sin ' እ ። +1 λ v'r ' sin ' = 1 + ˇ { v'3⁄4r ' — 2λ } , 27 12 which is 1 , according as v ' • 43 DETERMINATION OF ...
... parabola , we should have v2 2λ Ah h 83 . e : = λ e - 4- ( 2+ ) ( Art . 79 ) . = = v'3h3 2h2 - + 1 λι h v ' ' sin2 2v'r ' sin ' እ ። +1 λ v'r ' sin ' = 1 + ˇ { v'3⁄4r ' — 2λ } , 27 12 which is 1 , according as v ' • 43 DETERMINATION OF ...
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accele acceleration produced axes axis balls center of force chord circle complete oscillation conic section constant acceleration cos˛ curve cycloid described determine the motion determined in Arts Differential Calculus direction of motion dt dt dt˛ 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 sin˛ 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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