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nydus/A History of MathematicsPublic

This text examines the transition from the Middle Ages to the Modern era, highlighting how the fall of Constantinople and the invention of the printing press catalyzed a revival of classical learning. It traces the shift toward scientific inquiry through the rise of pure mathematics and astronomy, detailing the intellectual struggle against established scholastic and ecclesiastical authority.

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Table of Contents

Applied Mathematics

Notwithstanding the beautiful developments of celestial mechanics reached by Laplace at the close of the eighteenth

century, there was made a discovery on the first day of the present century which presented a problem seemingly beyond the power of that analysis. We refer to the discovery of Ceres by Piazzi in Italy, which became known in Germany just after

the philosopher Hegel had published a dissertation proving a priori

that such a discovery could not be made. From the positions of the planet observed by Piazzi its orbit could not be satisfactorily calculated by the old methods, and it remained for the genius of Gauss to devise a method of calculating

elliptic orbits which was free from the assumption of a small eccentricity and inclination. Gauss' method was developed further in his Theoria Motus. The new planet was re-discovered with aid of Gauss' data by Olbers, an astronomer

who promoted science not only by his own astronomical studies, but also by discerning and directing towards astronomical pursuits the genius of Bessel.

Friedrich Wilhelm Bessel[]91 (1784–1846) was a native of Minden in Westphalia. Fondness for figures, and a distaste for Latin grammar led him to the choice of a mercantile career. In his fifteenth year he became an apprenticed clerk in Bremen, and for nearly seven years he devoted his days to mastering the details of his business, and part of his nights to study. Hoping some day to become a supercargo on trading expeditions, he became interested in observations at sea. With a sextant constructed by him and an ordinary clock he determined the latitude of Bremen. His success in this inspired him for astronomical study. One work after another was mastered by him, unaided, during the hours snatched from

sleep. From old observations he calculated the orbit of Halley's comet. Bessel introduced himself to Olbers, and

submitted to him the calculation, which Olbers immediately sent for publication. Encouraged by Olbers, Bessel turned his back to the prospect of affluence, chose poverty and the stars, and became assistant in J. H. Schröter's observatory at

Lilienthal. Four years later he was chosen to superintend the construction of the new observatory at Königsberg.92 In the absence of an adequate mathematical teaching force, Bessel was obliged to lecture on mathematics to prepare students for astronomy. He was relieved of this work in 1825 by the arrival of Jacobi. We shall not recount the labours by which

Bessel earned the title of founder of modern practical astronomy and geodesy. As an observer he towered far above Gauss, but as a mathematician he reverently bowed before the genius of his great contemporary. Of Bessel's papers, the one of greatest mathematical interest is an "Untersuchung des Theils der planetarischen

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