Concept
Calculus
Overview
branch of mathematics that works on how things change
Overview adapted from Wikipedia (CC BY-SA 4.0; see the article history for authors).
In the original texts
Passages from public-domain books where Calculus is discussed.
The differential calculus is evidently the logical basis of the integral calculus; for we do not and cannot know how to integrate directly any other differential expressions than those produced by the differentiation of the ten simple functions which constitute the general elements of our analysis. The art of integration consists, then, essentially in bringing all the other cases, as far as is possible, to finally…
Auguste Comte, The philosophy of mathematics
names the idea; states what it is; opens on it
Again, having divided the calculus into algebraic and arithmetical, M. Comte admits, as perforce he must, that the algebraic is more general than the arithmetical; yet he will not say that algebra preceded arithmetic in point of time. And again, having divided the calculus of functions into the calculus of direct functions (common algebra) and the calculus of indirect functions (transcendental analysis), he is…
Herbert Spencer, Essays on education and kindred subjects
names the idea; opens on it
And, indeed, it is the distinctive peculiarity of the calculus in general, that it proceeds on the hypothesis of that absolute equality of its abstract units, which no real units possess; and that the exactness of its results holds only in virtue of this hypothesis. The first ideas of number must necessarily then have been derived from like or equal magnitudes as seen chiefly in organic objects; and as the like…
Herbert Spencer, Illustrations of Universal Progress
names the idea
We first establish a theorem for _n_ = 1; then we show that if it is true of _n_ - 1, it is true of _n_, and thence conclude that it is true for all the whole numbers. We have just seen how it may be used to demonstrate the rules of addition and multiplication, that is to say, the rules of the algebraic calculus; this calculus is an instrument of transformation, which lends itself to many more differing combinations…
Henri Poincaré, The Foundations of Science
states what it is; names the idea
In these various transformations, the propositions of the science of number do but fulfill the function proper to all propositions forming a train of reasoning, viz., that of enabling us to arrive in an indirect method, by marks of marks, at such of the properties of objects as we can not directly ascertain (or not so conveniently) by experiment. We travel from a given visible or tangible fact, through the truths of…
John Stuart Mill, A System of Logic, Ratiocinative and Inductive
names the idea
Philosophers who discussed Calculus
- George Berkeley
- Gottfried Wilhelm Leibniz
- Zeno of Elea
- René Descartes
- George Boole
- Blaise Pascal
- Jules Vuillemin
Related ideas
- Force
- George Berkeley
- General relativity
- Gottfried Wilhelm Leibniz
- Differential equation
- Zeno of Elea
- Isaac Newton
- Ancient Greek
- Ancient Greek mathematics
- Johannes Kepler
- John von Neumann
- Infinitesimal
- Ibn al-Haytham
- Method of exhaustion
- Gravitational field
- Law of excluded middle
- Latin
- Propositional logic
- Archimedes
- Indian mathematics
- Function (mathematics)
- Algebra
- Mathematics
- Medicine
Opposing perspectives
Place in the tradition
Part of German philosophy.