#### Henri Poincaré: On the Partial Differential Equations of Mathematical Physics – Law of cooling of an isolated solid body in space

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Suppose we are looking for the law of cooling of an isolated solid body in space. It will be a question of finding a function V satisfying the equation dV/dt = kΔV, and which moreover is given for t = … Read More

#### Poincaré: On the Partial Differential Equations of Mathematical Physics – Laplace equation for magnets

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Suppose one or more permanent magnets placed in the presence of a perfectly magnetically soft body M. It is a question of finding a function V (the magnetic potential) which satisfies the Laplace equation in all the portion of space … Read More

#### Poincaré: The problem of the pulsating spheres of Bjerknes

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We will first cite the following problem; a liquid is contained in a vessel which it completely fills; various moving solid bodies are immersed in this liquid; we know the movements of these bodies and we suppose that there is … Read More

#### Henri Poincaré, Mathematical physics: 1 – Dirichlet’s problem

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When we consider the various problems of integral calculus which naturally arise when we want to go deeper into the most different parts of physics, it is impossible not to be struck by the analogies that all these problems present … Read More

#### Major types of logic

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Syllogistic logic Organon is Aristotle’s principal work of logic, including the Prior Analytics; it constitutes the first explicit work of formal logic, with in particular the introduction of syllogistics. The works of Aristotle are considered in Europe and the Middle … Read More

#### Henri Poincaré, Mathematics and logic

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A few years ago, I had the opportunity to expose some ideas about the logic of the infinite; on the use of the infinite in Mathematics, on the use made of it since Cantor; I explained why I did not … Read More

#### Henri Poincaré, The logic of infinity: The use of infinity

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Is it possible to reason about objects that can notbe defined in a finite number of words? Is it even possible to talk about it knowing what one is talking about, and by saying something other than empty words? Or … Read More

#### Henri Poincaré, The logic of infinity: The cardinal number

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We must not forget the preceding considerations when defining the cardinal number. If we consider two collections, we may seek to establish a law of correspondence between the objects of these two collections, so that any object of the first … Read More

#### Henri Poincaré, Why space with three dimensions – Analysis Situs (Topology)

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Geometers usually distinguish two kinds of geometries, which they call the first of metric and the second of projective; metric geometry is based on the notion of distance; two figures are regarded as equivalent when they are “equal” in the … Read More

#### Propositional logic

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Propositional logic (propositional calculus, statement logic, sentential calculus, sentential logic, or sometimes zeroth-order logic) is part of the mathematical logic. Its purpose is the study of the logical relations between “propositions” and defines the formal laws according to which the … Read More