infinitesimals

D'Alembert firmly rejected the idea of infinitesimals as fixed quantities, and saw the idea of limit as supplying the methodological root of the differential calculus.

Continuity and Infinitesimals Bell, John L. 2009

It provides a rigorous framework for mathematical analysis in which every function between spaces is smooth (i.e., differentiable arbitrarily many times, and so in particular continuous) and in which the use of limits in defining the basic notions of the calculus is replaced by nilpotent infinitesimals, that is, of quantities so small (but not actually zero) that some power ” most usefully, the square ” vanishes.

Continuity and Infinitesimals Bell, John L. 2009

He studied the properties of the cycloid and attempted the problem of its quadrature; while in the "infinitesimals", which he was one of the first to introduce into geometrical demonstrations, was contained the germ of the calculus.

The Catholic Encyclopedia, Volume 6: Fathers of the Church-Gregory XI 1840-1916 1913

In this work Archimedes uses infinitesimals, and shows how breaking up a figure into an infinite number of infinitely small parts can be used to determine its area or volume.

Archive 2009-03-01 Jonathan Aquino 2009

In this work Archimedes uses infinitesimals, and shows how breaking up a figure into an infinite number of infinitely small parts can be used to determine its area or volume.

Capsule Summaries of the Great Books of the Western World Jonathan Aquino 2009

As the law of infinitesimals would predict, nothing.

Want to Help Save 34 Billion a Year in Health Care Costs? Be a Skeptic Ph.D. David Brenders 2010

That is, the notion of similars (like cures like) confuses symptoms with the underlying cause of disease and the law of infinitesimals (extreme dilution of the active ingredient increases its effects) often produces products where not one molecule of the original ingredient remains.

Want to Help Save 34 Billion a Year in Health Care Costs? Be a Skeptic Ph.D. David Brenders 2010

Furthermore, he claimed that he had proved the consistency of introducing infinitesimals into the system of real numbers in such a way as to form a new system in which there were infinitely many entities that were not equal to zero and yet were all smaller than any real number r that is not equal to zero, no matter how small r might be.

Nobody Knows Nothing 2009

(Quite possibly, it is Peirce's lattice theory that holds the key to his technical theory of infinitesimals and the continuum.)

Nobody Knows Nothing 2009

Accordingly, to do full justice to Leibniz's (as well as Nieuwentijdt's) conception, two sorts of infinitesimals are required: first,

Continuity and Infinitesimals Bell, John L. 2009