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had taught him, that he might place this confidence in himself without any danger of disappointment; and for this singular power, he was probably more indebted to the activity of his invention, than the mere tenaciousness of his memory.

Though he was extremely studious, he read few books, and verified the observation of M. D'Alembert, that, of all the men of letters, mathematicians read least of the writings of one another. His own investigations occupied him sufficiently; and, indeed, the world would have had reason to regret the misapplication of his talents, had he employed, in the mere acquisition of knowledge, that time which he could dedicate to works of invention.

It was his custom to spend the summer at a delightful retreat in Ayrshire, where, after the academical labours of the winter were ended, he found the leisure necessary for the prosecution of his researches. In his way thither, he frequently made a visit to Dr Simson at Glasgow, with whom he had lived from his youth in the most cordial and uninterrupted friendship. It was pleasing to observe, in these two profound mathematicians, the most perfect esteem and affection for each other, and the most entire absence of jealousy, though no two men ever trode more nearly in the same path. The similitude of their pursuits, as it will ever do with men superior to envy, served only to endear them to one another. Their sentiments and views

of the science they cultivated were nearly the same; they were both profound geometers; they equally admired the ancient mathematicians, and were equally versed in their methods of investigation; and they were both apprehensive that the beauty of their favourite science would be forgotten for the less elegant methods of algebraic computation. * This innovation they endeavoured to oppose; the one, by reviving those books of the ancient geometry which were lost; the other, by extending that geometry to the most difficult inquiries of the moderns. Dr Stewart, in particular, had remarked the intricacies in which many of the greatest of the modern mathematicians had involved themselves in the application of the calculus, which a little attention to the ancient geometry would certainly have enabled them to avoid. He had observed, too, the elegant synthetical demonstrations that, on many occasions, may be given of the most difficult propositions, investigated by the inverse method of

* On the reverse of a miniature picture of Dr Simson, now in the possession of Mr Professor Stewart, is an inscription written by Dr Moore, late Professor of Greek at Glasgow, an intimate friend of Dr Simson, and a greàt admirer of the ancient geometry:




fluxions. These circumstances had, perhaps, made a stronger impression than they ought, on a mind already filled with admiration of the ancient geometry, and produced too unfavourable an opinion of the modern analysis. But, if it be confessed that Dr Stewart rated, in any respect too high, the merit of the former of these sciences, this may well be excused in the man whom it had conducted to the discovery of the General Theorems, to the solution of Kepler's Problem, and to an accurate determination of the sun's disturbing force. His great modesty made him ascribe to the method he used that success which he owed to his own abilities.





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