This paper contains a tutorial introduction to the ideas of geometric algebra, concentrating on its physical applications We show how the definition of a “geometric product” of vectors in 2-and 3-dimensional space provides precise geometrical interpretations of the imaginary numbers often used in conventional methods Reflections and rotations are analyzed in terms of bilinear spinor transformations, and are then related to the theory of analytic functions and their natural extension in more than two dimensions (monogenics), Physics is greatly facilitated by the use of Hestenes' spacetime algebra, which automatically incorporates the geometric structure of spacetime This is demonstrated by examples from electromagnetism In the course of this purely classical exposition many surprising results are obtained—results which are usually thought to belong to the preserve of quantum theory We conclude that geometric algebra is the most powerful and general language available for the development of mathematical physics

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Imaginary numbers are not real—The geometric algebra of spacetime

Eléments d'analyse de Karl Weierstrass

The history of eighteenth-century philosophy is a subject with its own history. However, the idea of what constitutes eighteenth-century philosophy has been remarkably stable over the two centuries that have elapsed since the period in question, and this stability has obscured the simple fact of its historicity and made it peculiarly difficult to question the historical adequacy of that idea. What is more, even now, when detailed scholarship has undertaken such questioning in earnest, tradition is so strong that works of synthesis and overview – not to mention teaching – have to pay it considerable respect in order to find an identifiable audience. During the last two centuries, two factors above all have lent the philosophy of the eighteenth century an identity, other than its place in time, and these two factors have often reinforced each other. One is the idea that the philosophy in question is the core of a wider cultural and social movement, namely ‘the Enlightenment’. The other is that the eighteenth century has to be seen as part of – in fact, as the high point of – a development of early-modern philosophy from Francis Bacon and Rene Descartes to Thomas Reid and Immanuel Kant. THE ENLIGHTENMENT AND PHILOSOPHY The attempt to identify the philosophy of the eighteenth century by means of the Enlightenment is as inadequate as it is popular. Apart from the danger of tautology – namely that the philosophy of the eighteenth century is the philosophy of the Enlightenment because the Enlightenment is the eighteenth century – the concept of Enlightenment is either too wide or too narrow to capture the philosophical riches of the century.

The history of eighteenth-century philosophy: history or philosophy?

https://hal.archives-ouvertes.fr/hal-00185537/document

Multivariate Fuss-Catalan numbers

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The Foundations of Morality

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Papers

Lazare Carnot, Réflexions sur la métaphysique du calcul infinitésimal, nouveau tirage augmenté d'une préface par Marcel Mayot, Paris, Blanchard, 1970

Sayili (Aydin). Abdülhamid ibn Türk'ün Katisik denklemlerde mantiki zaruretler adli yazisi ve zamanin cebri (Logical necessities in mixed equations by Abd al Hamid ibn Turk and the Algebra of his time)

Leonhard Euler und Christian Goldbach, Briefwechsel 1729-1764

Angiolo Procissi, I « Ragionamenti d'Algebra » di R. Canacci

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