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

By A Wolf

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It was left for the nineteenth-centuiy mathematicians, beginning with Robert Woodhouse, to combine on the contrary the elegant notation o f the Continental analysts with the valuable notion o f a limit, which had been developed in Britain during the eighteenth century, and to remove the geometrical and mechanical imagery which had surrounded the theory o f fluxions from the beginning. (See F. C a jo ri: A History o f the Conceptions o f Limits and Fluxions in Great Britain from Newton to Woodhouse.

By their treatment o f so-called isoperimetrical problems the Bernoullis laid the foundations upon which Euler, Lagrange, Legendre, and others were later able to construct the calculus o f variations. (For annotated German translations o f the chief contributions to the subject, down to 1837,^ see Ostwald’s Klassiker, Nos. ) Isoperimetrical problems (in the wider use o f the term) treat, in the first instance, o f curves which satisfy certain maximum and minimum conditions. T he oldest o f these problems was that o f finding which o f all the curves having a given perimeter encloses the greatest area.

Euler’s e q u a t io n s Euler introduced into Dynamics the important general equations which still bear his name and which relate to the motion o f a rigid body about a fixed point or about its mass-centre {Mem. de VAcad. R. , Berlin, 1758, X I V , p. 165). , pp. ). , V ol. 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.

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