Newton not only explicitly recognized a connection between derivation and tangents but also gave calculus a more rigorous approach when he complied the Methodus fluxionum et Serierum infinitarum into definite terms in 1671. This new method shaped and defined how fluxional calculus could be approached leading to a greater understanding of these phenomena in a more general and mathematical setting. This method used methodological tool in calculating fluxional calculus in explaining the physical world other than the existing instantaneous motion. His revised calculus became continuity like the continual flowing calculus. The Methodus Fluxionum defined the quantity generated (fluent). For instance, if x and y are fluents, then x and y and the velocity of this fluents was termed as fluxion. His inventions continued to develop gradually and were termed in 1676 as â€œDe Quadratura Curvarumâ€. This method defined the present day derivative as the ultimate ratios of change which defined the ratio between evanescent increments. He explained the ultimate ratio by appealing to motion-ratio as the increments vanish into nothingness (Smith, 2007).
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