## Of Motion: An Elementary Treatise |

### From inside the book

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**ᏧᎾ**- 2 sin 0 r sin e ↑ COS Ө dt dt dt de2 dt dzy dt d2r dr de d20 = sin 0 + 2 cos 0 ' d Ꮎ 2 dť2 dt dt + r cos 0 r sin dt2 dt ; and therefore the acceleration along OP d2x = cos 0 + dzy sin dt2 dt2 de * 2 = r dt 2 d2r dt2 and the ... Page 42

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**ᏧᎾ**+ u2 = h2 и C , or ( velocity ) 2 = 2λ.u — h2C ' ; .. if v1 , v , be the velocities at 42 DETERMINATION OF THE AXES . 80 Acceleration (distance) -2: determination of the path Determination of the constants from the initial ... Page 45

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**ᏧᎾ**du 2 Also u2 de 1/1 = - 1/1 2 1 1 = - a b2 cos 20 . ...... ... ( 2 ) - b2 2 2 ( 1 – - cos2 20 ) - - + ( − } ) " - { ~ = 2 - u3 = ( 1 + + z ) u - Also from ( 1 ) and ( 2 ) , we get И du do 2 1/1 - ( + } ) } " 2 1 ˇ ... Page 83

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**ᏧᎾ**dt 20 ; a whence , by Arts . 51-54 , the motion will be oscillatory , and the therefore a pen- time of a complete oscillation will be 2π dulum oscillating in a circle may be considered as one oscillating in a cycloid , when the arc ... Page 112

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**ᏧᎾ**' + u = λ ( u ̃3 — a'u ̄1 ) . h2u2 λ ( μ3 — aˆr ) 6 a in a the fixed du Initially do 2 ( du ) * + u3 = 0 , u = 1 du do - a = 3 = 3 2a8 3 2a8 - 1 6 Зив . : C = 0 ; a 4 ----- 1 2a u 3u .. 0 - ẞ = √2 . a * 14 + - a из ๕ ) + C. u2 ; ...### 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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Page 1 - The Greek Testament : with a critically revised Text ; a Digest of Various Readings ; Marginal References to Verbal and Idiomatic Usage ; Prolegomena ;"and a Critical and Exegetical Commentary. For the Use of Theological Students and Ministers. By HENRY ALFORD, DD, Dean of Canterbury. Vol. I., containing the Four Gospels.

Page 11 - Progressive Exercises in Greek Tragic Senarii, followed by a Selection from the Greek Verses of Shrewsbury School, and prefaced by a short Account of the Iambic Metre and Style of Greek Tragedy. For the use of Schools and Private Students. Second Edition, altered and revised. 8vo. 8*.

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Page 10 - THIS series is intended to supply for the use of Schools and Students cheap and accurate editions of the Classics, which shall be superior in mechanical execution to the small German editions now current in this country, and more convenient in form. The texts of the " Bibliotheca Classica" and " GrammarSchool Classics" so far as they have been published, will be adopted.

Page 12 - This work, in illustration of the biography of notable and eminent men who have been members of the University of Cambridge, comprehends notices of : — 1. Authors. 2. Cardinals, archbishops, bishops, abbots, heads of religious houses and other church dignitaries. 3. Statesmen, diplomatists, military and naval commanders.