A Wolf's A History of Science, Technology, and Philosophy in the PDF

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Extra resources for A History of Science, Technology, and Philosophy in the Eighteenth Century

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While thereby developing analytical geometry, he was able, at the same time, to liberate the higher calculus from the geometrical fetters which were cramping its development, and to form it into an autonomous branch o f mathematics. His Institutiones (1755, 1768) summed up existing knowledge about the calculus. Euler was the first distinctly to conceive the notion o f a mathematical MATHEMATICS 53 function, with which the earlier chapters o f the Introductio deal. This conception has been well described as perhaps the most fundamental of all the creations o f modern mathematics.

X I). La g r a n g e ’ s e q u a t i o n s It was reserved for Lagrange to mould theoretical mechanics into a system, and, by combining the principle o f virtual velocities with D ’Alembert’s Principle, to derive fundamental mechanical equations which describe the motions o f any system o f bodies. These important results were set forth in Lagrange’s masterpiece, the Mecanique analytique (Paris, 1788), which laid the foundations o f modern mechanics, and which occupies a place in the history o f the subject second only to that o f Newton’s Principia.

Will be the motions o f the respective bodies in view o f their mutual reactions. In the latter part o f his book D ’Alembert makes numerous applications o f his Principle; and he also succeeded in relating to it the theory o f the motion o f fluids, in his Traite de Vequilibre et du mouvement des jtuides (Paris, 1744). He subscribed to the opinion, current in his time, that the principles o f mechanics are capable o f being proved; but the alleged proofs which he adduces merely amount to saying that the proposition in question is true because there is no adequate ground for maintaining the contrary.

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A History of Science, Technology, and Philosophy in the Eighteenth Century by A Wolf


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