By A Wolf
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Extra info for A history of science, technology and philosophy in the eighteenth century
LEGENDRE Further important contributions to the calculus o f variations were made by Legendre (1786), who showed how to distinguish between maxima and minima, and by Jacobi (1837). Adrien M arie Legendre (1752-1833) forms a connecting link between the eighteenth and nineteenth centuries. He became Pro fessor o f Mathematics at the M ilitary School and later at the Normal School o f Paris, and held several Government appointments; but his career was blighted by the hostility o f Laplace, who, however, occasionally made unacknowledged use o f his results.
Maclaurin rejected the notions o f infinite and o f infinitesimal quantities, and sought to deduce the principles o f the subject from unexceptionable axioms, so as to match the rigour o f the ancients. T he great skill which Maclaurin showed in his purely geometrical treatment, by means o f fluxions, o f physical and astronomical problems, gave the synthetic methods which he employed a new lease o f life. Maclaurin also made notable advances in the pure geometry o f conics and higher plane curves, being a pioneer in the investigation o f pedal curves.
As conceived by Lagrange, the Principle was still beset by certain obscurities, and he made little use o f it; but in the nineteenth century it was clarified, and underwent important developments, at the hands o f Hamilton and Jacobi. Action has come to play a fundamentally important part in twentieth-century Physics; it is an absolute quantity, independent o f the way in which the space-time continuum is analysed by any particular observer; and the discovery o f its atomicity is the basis o f the Quantum Theory.