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A controversy raged between the Cartesians and the Leibnizians for many years in which representatives o f almost every European nation took a share. Eventually D ’Alembert, in his Traite de dynamique, o f 1743, explained that the whole controversy was merely an empty dispute about words, it being equally legitimate to measure a force by the vis viva which it imparts to a body upon which it acts through a certain distance, or by the momentum which it imparts to a body upon which it acts for a certain length o f time.

Such strenuous exertions, however, combined with the rigour o f the climate, cost Euler the sight o f one eye. In 1741 he was invited by Frederick the Great to the Prussian Academ y o f Sciences at Berlin. Here for twenty-five years he lived in the Royal Palace, and worked with unexampled activity at the reformation o f mathematics. He published 121 papers, some o f considerable length, in the Transactions o f the Academy, the mathematical work o f which he superintended after the death o f Maupertuis.

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.

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