But the latter contented hilnself with an annual stipend which would enable him to devote all his time to his favorite studies of mathematics and astronomy.

Published in 1524, and subsequently edited and added to by Gemma Frisius under the title of Cosmographia, based the whole science on mathematics and measurement.

Peano (with various collaborators of the Italian school), Formulaire de mathematiques (Turin, various editions, 1894-1908; the earlier editions are the more interesting philosophically); Felix Klein, Lectures on Mathematics (New York, 1894); W.

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Jacobi and other mathematicians have developed to a great extent, and as a question of pure mathematics only, Hamilton's processes, and have thus made extensive additions to our knowledge of differential equations.

The comprehensive scheme of study included mathematics also, in which he advanced as far as the conic sections in the treatise of L'Hopital.

After serving as instructor in mathematics to the young prince Louis, he took part with credit in the expedition into Holland, and was given the order Pour le merite.

After that, apparently, logic was to be treated; then, possibly, mathematics and physics; then speculative alchemy and experimental science.

The young prince also studied at the gymnasium at Augsburg, where his love of work and his mental qualities were gradually revealed; he was less successful in mathematics than in literary subjects, and he became an adept at physical exercises, such as fencing, riding and swimming.

Where he took the first prize in mathematics and physics; at the Ecole Polytechnique, where he stood first at the exit examination in 1819; and at the Ecole des Mines (1819-1822), where he began to show a decided preference for the science with which his name is associated.

Some portion of his labours in those sciences and give them to the world, an incalculable impulse would have been given to all those enquiries by which mankind has since been striving to understand the laws of its being and control the conditions of its environment, - to mathematics and astronomy, to mechanics, hydraulics, and physics generally, to geology, geography, and cosmology, to anatomy and the sciences of life.