The Method of Fluxions and Infinite Series: With Its Application to the Geometry of Curve-lines. By ... Sir Isaac Newton, ... Translated from the Author's Latin Original Not Yet Made Publick. To which is Subjoin'd, a Perpetual Comment Upon the Whole Work, ... By John Colson, ...
Abſciſs AFDB aggregate Series alſo Area ariſe Arithmetical Progreſſion aſcending aſſume becauſe caſe Concluſion conſequently conſtant converge converging Series correſponding Curvature Curve decreaſe Demonſtration deſcending deſcribed Dimenſions diſpoſed diſtance Diviſion eaſily eaſy Equa equal expreſs'd external Terms extracted finite firſt Term flowing Quantities Fluxional Equation Fraćtion given Equation greateſt illuſtrate impoſſible increaſe infinite Series inſtance inſtead itſelf juſt laſt Laſtly leaſt leſs likewiſe Method of Fluxions moſt multiply'd muſt neceſſary Numbers obſerved occaſion Ordinate Parabola Parallelograms perpendicular pleaſe preſent Prob Produćt propoſed ratio reaſon Redućtion relation repreſent Reſolution reſolved reſpectively reſt reſulting right Line ſame ſecond Term ſee ſet ſeveral ſhall ſhew ſhould ſmall ſome ſtand ſtill ſubſtitute ſuch ſufficient ſuppos'd ſuppoſe taking the Fluents taking the Fluxions Tangent thence Theorem theſe third Term thoſe tion uſe vaniſhing Velocity whence whoſe
Page 20 - I shall have no regard to time formally considered, but shall suppose some one of the quantities proposed, being of the same kind, to be increased by an equable fluxion. to which the rest may be referred, as it were to time; and therefore by way of analogy it may not improperly receive the name of Time.
Page 46 - Then take TB to BD in the Ratio of the Fluxion of AB to the Fluxion of BD, and TD will touch the Curve in the Point D.
Page 44 - Then making x = o, there will remain — 3^* -j- ajx=o, or 3^'* =ax. By the help of this you may exterminate either x or y out of the primary Equation, and by the refulting Equation you may determine the other, and then both of them by — 3^* -f* ax=Q.
Page 130 - The fluxion of the Length is determin'd by putting it equal to the squareroot of the sum of the squares of the fluxion of the Absciss and of the Ordinate.
Page 25 - But whereas zero is supposed to be infinitely little, that it may represent the moments of quantities, the terms that are multiplied by it will be nothing in respect of the rest...
Page 21 - A Memorial Volume, ed. by WJ Greenstreet (London, 1927), 122-124. the Velocity of the Motion at the Time proposed." Problem II: " The Velocity of the Motion being continually given ; to find the Length of the Space described at any Time proposed," Restated, Problem I reads : " The Relation of Flowing quantities to one another being given, to determine the Relation of their Fluxions.
Page 116 - ... the synthetical method, which is apparent even in the most analytical of his works. In his Fluxions, when he is treating of the quadrature of curves, he says, " After the area of a curve has been found and constructed, we should consider about the demonstration of the construction, that, laying aside all algebraical calculation, as much as may be, the theorem may be adorned and made elegant, so as to become fit for public view.
Page xii - Quantities that are relatively fbj which he arrives at by beginning with finite Quantities, and proceeding by a gradual and neceflary progrefs of diminution. His Computations always commence by finite and intelligible Quantities; and then at ilaft he inquires what will be the refult in certain circumftances, when fuch:or fuch Quantities are diminifh'd ;';; infinitutn.