A Quote by W. W. Rouse Ball
Foreshadowings of the principles and even of the language of [the infinitesimal] calculus can be found in the writings of Napier, Kepler, Cavalieri, Pascal, Fermat, Wallis, and Barrow. It was Newton's good luck to come at a time when everything was ripe for the discovery, and his ability enabled him to construct almost at once a complete calculus.
Related Quotes
It may be said that the conceptions of differential quotient and
integral, which in their origin certainly go back to Archimedes,
were introduced into science by the investigations of Kepler,
Descartes, Cavalieri, Fermat and Wallis. . . .
You'll remember Newton was furious at Leibniz, because he developed calculus at the same time. And he went to his death believing that he had copied him. And no, it's because all the elements were there, so it's almost inevitable that the next discovery - as long as people are free and allowed to experiment and try new things.
Even the simplest calculation in the purest mathematics can have terrible consequences. Without the invention of the infinitesimal calculus most of our technology would have been impossible. Should we say therefore that calculus is bad?
With an absurd oversimplification, the 'invention' of the calculus is sometimes ascribed to two men, Newton and Leibniz. In reality, the calculus is the product of a long evolution that was neither initiated nor terminated by Newton and Leibniz, but in which both played a decisive part.
When I was about thirteen, the library was going to get 'Calculus for the Practical Man.' By this time I knew, from reading the encyclopedia, that calculus was an important and interesting subject, and I ought to learn it.
Newton, of course, was the inventor of differential calculus so his place in the tale is quite special.
Ask yourself whether our language is complete--whether it was so before the symbolism of chemistry and the notation of the infinitesimal calculus were incorporated in it; for these are, so to speak, suburbs of our language. (And how many houses or streets does it take before a town begins to be a town?) Our language can be seen as an ancient city: a maze of little streets and squares, of old and new houses, and of houses with additions from various periods; and this surrounded by a multitude of new boroughs with straight regular streets and uniform houses.
Science is the Differential Calculus of the mind. Art the Integral Calculus; they may be beautiful when apart, but are greatest only when combined.
We do not live in a time when knowledge can be extended along a pathway smooth and free from obstacles, as at the time of the discovery of the infinitesimal calculus, and in a measure also when in the development of projective geometry obstacles were suddenly removed which, having hemmed progress for a long time, permitted a stream of investigators to pour in upon virgin soil. There is no longer any browsing along the beaten paths; and into the primeval forest only those may venture who are equipped with the sharpest tools.
Love can reach the same level of talent, and even genius, as the discovery of differential calculus.
The analytical geometry of Descartes and the calculus of Newton and Leibniz have expanded into the marvelous mathematical method
...from the time of Kepler to that of Newton, and from Newton to Hartley, not only all things in external nature, but the subtlest mysteries of life and organization, and even of the intellect and moral being, were conjured within the magic circle of mathematical formulae.
With an absurd oversimplification, the "invention" of calculus [method in mathematics] is sometimes ascribed to two men, Newton and Leibniz.
Kepler's discovery would not have been possible without the doctrine of conics. Now contemporaries of Kepler-such penetrating minds as Descartes and Pascal-were abandoning the study of geometry ... because they said it was so UTTERLY USELESS. There was the future of the human race almost trembling in the balance; for had not the geometry of conic sections already been worked out in large measure, and had their opinion that only sciences apparently useful ought to be pursued, the nineteenth century would have had none of those characters which distinguish it from the ancien régime.
Throughout the 1960s and 1970s devoted Beckett readers greeted each successively shorter volume from the master with a mixture of awe and apprehensiveness; it was like watching a great mathematician wielding an infinitesimal calculus, his equations approaching nearer and still nearer to the null point.
The change began with John Stuart Mill and the Utopians . When Mill pointed out that economics had no ultimate solution to the problem of distribution , that society might do with the fruits of its toil as it saw fit, he introduced into the mechanical calculus of the market a conflicting calculus of moral judgment.
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