MULLER (John)

, commonly called REGIOMONTANUS, from Mons Regius, or Koningsberg, a town in Franconia, where he was born in 1436, and became the greatest astronomer and mathematician of his time. He was indeed a very prodigy for genius and learning. Having first acquired grammatical learning in his own country, he was admitted, while yet a boy, into the academy at Leipsic, where he formed a strong attachment to the mathematical sciences, arithmetic, geometry, astronomy, &c. But not finding proper assistance in these studies at this place, he removed, at only 15 years of age, to Vienna, to study under the famous Purbach, the professor there, who read lectures in those sciences with the highest reputation. A strong and affectionate friendship soon took place between these two, and our author made such rapid improvement in the sciences, that he was able to be assisting to his master, and to become his companion in all his labours. In this manner they spent about ten years together; elucidating obscurities, observing the motions of the heavenly bodies, and comparing and correcting the tables of them; particularly those of Mars, which they found to disagree with the motions, sometimes as much as two degrees.

About this time there arrived at Vienna the cardinal Bessarion, who came to negociate some affairs for the pope; who, being a lover of astronomy, soon formed an acquaintance with Purbach and Regiomontanus. He had begun to form a Latin Version of Ptolomy's Almagest, or an Epitome of it; but not having time to go on with it himself, he requested Purbach to complete the work, and for that purpose to return with him into Italy, to make himself master of the Greek tongue, which he was as yet unacquainted with. To these proposals Purbach only assented, on condition that Regiomontanus would accompany him, and share in all the labours. They first however, by| means of an Arabic Version of Ptolomy, made some progress in the work; but this was soon interrupted by the death of Purbach, which happened in 1461, in the 39th year of his age. The whole task then devolved upon Regiomontanus, who finished the work, at the request of Purbach, made to him when on his death<*> bed. This work our author afterwards revised and perfected at Rome, when he had learned the Greek language, and consulted the commentator Theon, &c.

Regiomontanus accompanied the cardinal Bessarion in his return to Rome, being then near 30 years of age. Here he applied himself diligently to the study of the Greek language; not neglecting however to make astronomical observations and compose various works in that science; as his Dialogue against the Theories of Cremonensis. The cardinal going to Greece soon after, Regiomontanus went to Ferrara, where he continued the study of the Greek language under Theodore Gaza; who explained to him the text of Ptolomy, with the commentaries of Theon; till at length he became so perfect in it, that he could compose verses, and read it like a critic.—In 1463 he went to Padua, where he became a member of the university; and, at the request of the students, explained Alfraganus, an Arabian philosopher.—In 1464 he removed to Venice, to meet and attend his patron Bessarion. Here he wrote, with great accuracy, his Treatise of Triangles, and a Refutation of the Quadrature of the Circle, which Cardinal Cusan pretended he had demonstrated. The same year he returned with Bessarion to Rome; where he made some stay, to procure the most curious books: those he could not purchase, he took the pains to transcribe, for he wrote with great facility and elegance; and others he got copied at a great expence. For as he was certain that none of these books could be had in Germany, he thought on his return thither, he would at his leisure translat, and publish some of the best of them. During this time too he had a fierce contest with George Trabezonde, whom he had greatly offended by animadverting on some passages in his translation of Theon's Commentary.

Being now weary of rambling about, and having procured a great number of manuscripts, which was one great object of his travels, he returned to Vienna, and performed for some time the offices of his professorship, by reading of lectures &c. After being a while thus employed, he went to Buda, on the invitation of Matthias king of Hungary, who was a great lover of letters and the sciences, and had founded a rich and noble library there: for he had bought up all the Greek books that could be found on the sacking of Constantinople; also those that were brought from Athens, or wherever else they could be met with through the whole Turkish dominions, collecting them all together into a library at Buda. But a war breaking out in this country, he looked out for some other place to settle in, where he might pursue his studies, and for this purpose he retired to Noremberg. He tells us, that the reasons which induced him to desire to reside in this city the remainder of his life were, that the artists there were dextrous in fabricating his astronomical machines; and besides, he could from thence easily transmit his letters by the merchants into foreign countries. Being now well versed in all parts of learning, and made the utmost proficiency in mathematics, he determined to occupy himself in publishing the best of the ancient authors, as well as his own lucubrations. For this purpose he set up a printinghouse, and formed a nomenclature of the books he intended to publish, which still remains.

Here that excellent man, Bernard Walther, one of the principal citizens, who was well skilled in the sciences, especially astronomy, cultivated an intimacy with Regiomontanus; and as soon as he understood those laudable designs of his, he took upon himself the expence of constructing the astronomical instruments, and of erecting a printing-house. And first he ordered astronomical rules to be made of tin, for observing the altitudes of the sun, moon and planets. He next constructed a rectangular, or astronomical radius, for taking the distances of those luminaries. Then an armillary astrolabe, such as was used by Ptolomy and Hipparchus, for observing the places and motions of the stars. Lastly, he made other smaller instruments, as the torquet, and Ptolomy's meteoroscope, with some others which had more of curiosity than utility in them. From this apparatus it evidently appears, that Regiomontanus was a most diligent observer of the laws and motions of the celestial bodies, if there were not still stronger evidences of it in the accounts of the observations themselves which he made with them.

With regard to the printing-house, which was the other part of his design in settling at Noremberg, as soon as he had completed it, he put to press two works of his own, and two others. The latter were, The New Theories of his master Purbach, and the Astronomicon of Manilius. And his own were, the New Calendar, in which were given (as he says in the Index of the books which he intended to publish) the true conjunctions and oppositions of the luminaries, their eclipses, their true places every day, &c. His other work was his Ephemerides, of which he thus speaks in the said index: “The Ephemerides, which they vulgarly call an Almanac, for 30 years: where you may every day see the true motion of all the planets, of the moon's nodes, with the aspects of the moon to the sun and planets, the eclipses of the luminaries; and in the fronts of the pages are marked the latitudes.” He published also most acute commentaries on Ptolomy's Almagest: a work which cardinal Bessarion so highly valued, that he scrupled not to esteem it worth a whole province. He prepared also new versions of Ptolomy's Cosmography; and at his leisure hours examined and explained works of another nature. He enquired how high the vapours are carried above the earth, which he fixed to be not more than 12 German miles. He set down observations of two comets that appeared in the years 1471 and 1472.

In 1474, pope Sixtus the 4th conceived a design of reforming the calendar; and sent for Regiomontanus to Rome, as the properest and ablest person to accomplish his purpose. Regiomontanus was very unwilling to interrupt the studies, and printing of books, he was engaged in at Noremberg; but receiving great promises from the pope, who also for the present named him bishop of Ratisbon, he at length consented to go. He arrived at Rome in 1475, but died there the year after, at only 40 years of age; not without <*>| suspicion of being poisoned by the sons of George Trabezonde, in revenge for the death of their father, which was said to have been caused by the grief he felt on account of the criticisms made by Regiomontanus on his translation of Ptolomy's Almagest.

Purbach first of any reduced the trigonometrical tables of fines, from the old sexagesimal division of the radius, to the decimal scale. He supposed the radius to be divided into 600000 equal parts, and computed the sines of the arcs to every ten minutes, in such equal parts of the radius, by the decimal notation. This project of Purbach was perfected by Regiomontanus; who not only extended the sines to every minute, the radius being 600000, as designed by Purbach, but afterwards, disliking that scheme, as evidently imperfect, he computed them likewise to the radius 1000000, for every minute of the quadrant. Regiomontanus also introduced the tangents into trigonometry, the canon of which he called fœcundus, because of the many great advantages arising from them. Beside these things, he enriched trigonometry with many theorems and precepts. Indeed, excepting for the use of logarithms, the trigonometry of Regiomontanus is but little inferior to that of our own time. His Treatise, on both Plane and Spherical Trigonometry, is in 5 books; it was written about the year 1464, and printed in folio at Noremberg in 1533. In the 5th book are various problems concerning rectilinear triangles, some of which are resolved by means of algebra: a proof that this science was not wholly unknown in Europe before the treatise of Lucas de Burgo.

Regiomontanus was author of some other works beside those before mentioned. Peter Ramus, in the account he gives of the admirable works attempted and performed by Regiomontanus, tells us, that in his workshop at Noremberg there was an automaton in perpetual motion: that he made an artisicial fly, which taking its flight from his hand, would fly round the room, and at last, as if weary, would return to his master's hand: that he fabricated an eagle, which, on the emperor's approach to the city, he sent out, high in the air, a great way to meet him, and that it kept him company to the gates of the city. Let us no more wonder, adds Ramus, at the dove of Archytas, since Noremberg can shew a fly, and an eagle, armed with geometrical wings. Nor are those famous artificers, who were formerly in Greece, and Egypt, any longer of such account, since Noremberg can boast of her Regiomontanuses. For Wernerus first, and then the Schoneri, father and son, afterwards, revived the spirit of Regiomontanus.

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Entry taken from A Mathematical and Philosophical Dictionary, by Charles Hutton, 1796.

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MOTION
MOTRIX
MOVEABLE
MOVEMENT
MOULDINGS
* MULLER (John)
MULTANGULAR Figure
MULTILATERAL Figures
MULTINOMIAL
MULTIPLE
MULTIPLICAND