## Of Motion; an elementary treatise1859 |

### From inside the book

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**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 v'2 focus - 1. ( 2 ) - D α = 43. The position of the focus S is determined as ... Page 24

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**parabola**cuts Ax 12 v'sin = 2 x v'cos i = sin 21 . α a The directrix of the**parabola**will be parallel to Ax , and will cut Ay at a point E whose distance from A = AS : 212 = 2aR 47. The velocity at Pin direction Ax will be v'cos , and ... Page 26

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**parabola**, the co - ordinates of v'2 2α whose vertex are sin 2 , v'2 and sin , whose axis is in the 2α negative direction of y , i . e . in the direction of the acceleration ; and whose latus rectum = 20 ' cos2 α A. CHAPTER IV . * OF ... Page 41

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**parabola**, or hyperbola , according as Ah2 λ is < = or > 1 . 77. This might have been obtained , as in Art . 52 , by putting λ - h2 = w , whence d'w dt + w = 0 ; .. w = A cos ( 0 – B ) . 78. We have also ( du \ 2 do + u2 = 42 sin2 ( 0-8 ) ... Page 43

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**parabola**, we should have Ah h2 83 . e ; = እ v2 2λ λ ( v ' _ 27 +12 ) ( Art . 79 ) . r ' v'h3 2h1 λ2 λη +1 12 v ' ' sin ' 2 ' ' sin ' = 1 + +1 λ λε ~ { v'3r ' — 2λ } , v'r ' sin 12 which is 1 , according as v ' = DETERMINATION OF THE ...### Other editions - View all

### Common terms and phrases

acceleration produced apse axes axis balls called center of force circle complete oscillation conic section considered constant acceleration cos² curve cycloid d²r d²x described determine the motion Differential Calculus direction of motion distance ds dt dt dt dt dt² dx dy elastic ellipse equal equation experiments fixed point force acting geometrical h²C horizontal hyperbola idea impact impulse inclined plane initial direction initial position initial velocity initially at rest latus rectum Law of Motion mass material bodies measure moving point NEWTON obtained orbit parabola parallelogram particle path perpendicular point be moving quantity of matter radius vector Second Edition semi-latus rectum shew sin² 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