The fame of Purbach, as a mathematical professor, was soon widely diffused, and brought numerous students to attend his lectures at Vienna. Among others was the celebrated Regiomontanus, who secured the esteem of his master, and was chosen the assistant and companion of his labours. From this time they maintained a union of studies, in their endeavours to improve the different branches of mathematical science, and more particularly astronomy. This science they would, no doubt, have materially improved by their joint labours, had Purbach's life been prolonged. His first essay was to amend the Latin translation of Ptolemy's Almagest. After this he wrote "An introduction to Arithmetic,' and proceeded to draw up another" on Gnomonics," or dialing with tables suited to the difference of climates and latitudes. This was followed by a small tract "Concerning the Altitudes of the Sun," with a table, and "Astrolobic Canons." After this he made solid spheres or celestial globes, and not only explained their instructions and uses, but added to them a new table of fixed stars, with the longitude by which every star had increased, from the time of Ptolemy to the middle of the fifth century. He also invented various other instruments, among which was a 66 gnomon," or geometrical square, with canons, and a table for the use of it, which he sent to the archbishop of Strigonia, who was himself a man of great erudition, and entertained a high opinion of Purbach. Our author made considerable improvements in trigonometry; prepared tables of the fixed stars, and undertook to reform those of the planets, and constructed some entirely new ones. When these tables were finished, he drew up a kind of perpetual almanack, chiefly for the moon, answering to the periods of Meton and Calippus; also an almanack for the planets, or, as it was afterwards called, an Ephemeris for many years. He finished his "Theoria Novæ Planetarum," which was made a text book in all the schools, and was commented upon by some of the most eminent mathematicians. Purbach died in the thirty-eighth year of his age, in 1461.

The following inscription on his tomb, is said to have been written by himself:

Extinctum dulces quid me defletis amici;
Fata vocant; Lachesis sic sua fila trahit.
Destituit terras animus, cœlumque revisit;

Quæ semper coluit, liber et astra petit.

ANTONY TORQUATO, a famous astrologer, was born at Ferrara. He gave Matthias, king of Hungary, a prediction in the year 1480, which was very fatal to Christendom; for he threatened with an entire ruin the Ottoman empire after a

fixed time, which caused the Hungarians to engage in a war that ruined them,

ANGLO CATTHO, of Tarentum, was in the service of the duke of Burgundy, and of Lewis XI., as astrologer and physician. He pretended to foretel future events, and died at Beneventum, in 1497.

BERNARD WALTHER, an eminent astronomer was born in the year 1430, and having applied principally to the study of mathematics, and more especially to the study of astronomy, under Regiomontanus, was eminently useful by his talents and opulence in encouraging the inventions and aiding the observations of his preceptor, whilst he continued at Nuremberg; and when by the invitation of pope Sixtus IV. he removed to Rome, with a view to the reformation of the calendar, he continued his observations for nearly forty years, viz, from 1475, to the time of his death in 1504. His instruments were of the most perfect kind which he could then proeure, and he was skilful and persevering, as well as successful in the use of them. He was the inventor of a chronometer, or clock with wheels, which indicated the time of noon with an accuracy corresponding to the result of calculation; and he is also celebrated as the first of moderns who observed refraction. The singularity of his character, however, restricted the benefit which astronomy might otherwise have derived from his own observations and those of his preceptor Regiomontanus, or John Muller. After the death of Muller, he purchased his papers and instruments, which he kept in his own possession, without allowing any one to see them; and after his death, they were neglected by his heirs, so that many of them were lost. At length the senate of Nuremberg purchased all the writings of these two mathematicians which they could procure, and deposited them in the library of that city. Several parts of them were afterwards extracted, and published by Schoner and his son.

PAUL TOSCANELLA, a most celebrated Italian astronomer, who erected in the cathedral of Florence, the famous Gnomon, which is still reckoned the best in Europe, and of which Ximenes gave a particular description. He died in 1490.

JOHN MULLER, commonly called REGIOMONTANUS, from Mons Regius, or Koningsberg, where he was born, in 1436. He made so great a progress in learning, that, when a boy, he was admitted into the academy at Leipsic. From thence he removed to Vienna, where he studied the mathematics under Purbach, whom he assisted in his observations. At the desire of cardinal Bessarion, Regiomontanus and his master went to Rome, to complete the Latin version of Ptolemy's Almagest; but, while there, Purbach died, and the

whole task devolved upon his associate. After a long stay in Italy, he went to Buda; but on the breaking out of a war with the Turks he removed to Nuremberg, where he constructed an observatory, and founded a printing-office.

In 1474, pope Pius IV. conceived a design of reforming the calendar, and sent for Regiomontanus to Rome, as the most able person to accomplish his purpose. The philosopher was exceedingly unwilling to leave his own pursuits, but having received the most magnificent promises from his holiness, who also nominated him bishop of Ratisbon, he set out, and arrived at Rome in 1475, but died the following year, at the age of forty. He was buried in the Pantheon, and his memory was celebrated by the best poets of the time. It may be observed that Purbach was the first mathematician who reduced the trigonometrical tables of fines to the decimal scale. This project was perfected by Regiomontanus, who not only extended the fines to every minute, the radius being 600,000, as designed by Purbach, but afterwards computed them to the radius of 1,000,000 for every minute of the quadrant. He also introduced the tangents into trigonometry, and enriched this part of science with many theorems and precepts. His "Treatise on plane and spherical Trigonometry," consists of five books; in the fifth are various problems concerning rectilinear triangles, some of which are resolved by means of algebra. Regiomontanus was author of several other works. Of his mechanical projects, we are told by Peter Ramus, that in his workshop at Nuremberg there was an automaton in perpetual motion: a fly, which, after escaping from his hand, flew round the room, and returned again; he also formed an eagle, which, on the emperor's approach to the city, he sent out, high in the air, a considerable distance to meet him, and which kept him company to the very gates of the city. "Let us no more wonder," adds Ramus," at the dove of Archytas, since Nuremberg can shew a fly and an eagle armed with geometrical wings."

MARTIN BEHËM, BEHAIM, BÆHM, or BEHENIRA, a mathematician and cosmographer who, according to the Germans, first conceived the notion of a western continent, and afterwards proved its reality as the original discoverer. He was born of a noble family at Nuremberg, in Franconia. He was devoted from his infancy to the study of geography, astronomy, and navigation; and at a more mature age he often reflected on the possibility of the existence of a western continent, and of the antipodes. Filled with this notion, he applied, in 1459, to Isabella, daughter of John, the first king of Portugal, and regent of the duchy of Burgundy and Flanders, who supplied him with a vessel, in which he made the discovery of the island of Fayel, in 1460. On this island he established a colony of Flemings, whose descendants still exist in the

Azores, which were for some time the Flemish islands. After having obtained a grant of Fayal from the regent Isabella, and resided there about twenty years, during which he made small excursions of discovery, Behem applied in 1484, eight years before the expedition of Columbus, to John, the second king of Portugal, for the means of making a great expedition towards the south-west. This prince supplied him with some ships, with which he discovered that part of America which is now called Brazil; and sailed as far as the straits of Magellan, or to the country of some savage tribes, whom he called Patagonians, from the extremities of their bodies being covered with a skin more like a bear's paws than human hands and feet.

In 1492 the chevalier Behem, crowned with honours and riches, undertook a journey to Nuremberg, to visit his native country and family. He there made a globe of the earth, which is still preserved in the library of that city, and exhibits the outline of his discoveries under the name of western lands, from which it is seen that they are the present coast of Brazil, and the lands near the straits of Magellan. After having performed several other interesting voyages, Behem died at Lisbon in July 1506, leaving behind him no other work than his globe. It appears, however, that the king of Portugal possessed a chart of the coast of America, drawn by Behem, which was seen by Magellan before he undertook his voyage, and that certain letters are still extant at Nuremberg. The globe is made from the writings of Ptolemy, Pliny, Strabo, Marco Polo, and Mandeville, with the addition of his own discoveries in Africa and America.

MARTIN BENENA was the scholar of the celebrated John Muller, or Regiomontanus, and was very intimate with Christopher Columbus.

JOHN BAPTIST DANTE, a native of Perugia, was an excellent mathematician, and is memorable for having fitted a pair of wings so exactly to his body, as to be able to fly with them. He made the experiment several times over the lake Fralimenus; and succeeded so well, that he had the courage to perform before the whole city of Perugia, during the solemnity of the marriage of Bartholomew d'Alviano with the sister of John Paul Baglioni. He shot himself from the highest part of the city and directed his flight over the square, to the admiration of the spectators; but unfortunately the iron, with which he managed one of his wings, failed; and then, not being able to balance the weight of his body, he fell on a church, and broke his thigh. Boyle fancies, that the history of Dædalus, for so he was called, will not generally be credited; yet he observes, that it is said to have been practised at other places, for which he refers us to the "Journal des Scavans"

of 1678. Dante was afterwards invited to be professor of the mathematics at Venice. He flourished towards the end of this fifteenth century, and died before he was forty years old.

JOACHIM FORTIUS RINGELBERĞIUS, vernacu larly SLERCK, an eminent Flemish mathematician and philosopher, was born at Antwerp. He was patronised by the emperor Maximilian I., in whose place he had an apartment, and he there received his first instructions in the rudiments of learning. When he was seventeen years of age, he was sent to the university of Louvain, where he studied the learned. languages, philosophy, and the mathematical sciences. He became a public professor in that university, and taught rhetoric, cosmography, the mathematics, and the Greek language, with very high reputation. So numerous were the classes which attended his lectures, that they frequently occupied his attention twelve hours every day, for a month together. In the year 1528 he went into Germany, and taught the mathematical sciences and the Greek tongue in various seminaries of that country. From Germany he went to France, where he filled the professor's chair at Paris, Orleans, Bourdeaux, and other places. He died about the year 1536. He wrote a number of esteemed works, which were published at Basil, Antwerp, and other places, and reflected honour on his learning and judgment.

JOHN CARION, professor of mathematics in the university of Francfort upon the Oder, was born at Buetickheim, in Germany. He published Ephemerides, and Practice Astrologicæ. He gained but little reputation from these two pieces, but he became famous for a Chronicle in which he had no hand, and which the protestants highly extolled. He died at Berlin, in the year 1538.

JACOBUS STAPULENSIS, or JAMES LEFEVRE, FABER, born at Etaples in the Boulonnois, was an able mathematician, and one of the few writers on music which France could boast of at that early period. He was educated at Paris, and with a view to further improvement, he travelled through various parts of the world, that he might have an opportunity of conversing with the learned. On his return to France, he declared open war against the scholastic philosophy, and attempted to introduce genuine Aristotelianism, as well as to disseminate a taste for mathematical learning. The boldness with which he opposed the corruptions of philosophy brought upon him a suspicion of heresy, and the persecution of the doctors of the Sorbonne; but he found a secure asylum in the court of Margaret, queen of Navarre, where he is said to have lived to the age of 100 years; and where he died while veering between Protestant and Catholic. His chief works were theological, but his name is preserved by Protestants às a musical