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Pisa flourished toward the end of the fourteenth century but Mr. Cossali, a canon of Parma, has discovered and quoted* a manuscript by that algebraist dated 1202, which was enlarged and rewritten in 1228. Leonard of Pisa was very skilful in algebra, particularly in the analysis of problems of the Diophantine kind. The extract from his manuscript, which Mr. Cossali has given, shows, that the author had proceeded as far as the resolution of cubic equations, and those of higher powers capable of being reduced to the second or third order.

This impulse given to algebra was propagated through Europe, and extended to all parts of the mathematics. The thirteenth century produced a great number of learned men in every branch, in Italy, France, Germany, and England. The chief of those, who rendered any service to the mathematics, I shall proceed to mention.

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Jordanus Nemorarius was eminent for his time [A. D. 1230] in arithmetic and geometry, as may be judged by his treatise On the Planisphere, and his ten books of Arithmetic.

He had a contemporary much better known, John of Halifax, vulgarly called Sacrobosco, which siguifies the same thing in the barbarous latin of those days. Sacrobosco, who was born in England, came to reside as professor of the mathematics at Paris, We have a treatise of his on the sphere, which has been commented on by Clavius the jesuit, and re

* Origine, Transporto in Italia, e primi Progressi in Essa del Algebra, &c. 1797.


printed a great number of times. He likewise left us treatises on the Astrolabe, on the Calendar, and on the Arithmetic of the Arabs. He died at Paris in 1256, and his tomb was still to be seen in the cloister of the Mathurins before the french revolution.

A. D. 1250, Campanus of Novara translated and commented on Euclid's Elements, and wrote a treatise on the Sphere; another on the Theories of the Planets, the object of which was to make known the ancient astronomy, and the corrections introduced in it by the arabs; &c.

A. D. 1260, Vitellio, a native of Poland, but settled in Italy, wrote a treatise on Optics in ten books. This work is, in fact, nothing more than that of Alhazen, only rendered more perspicuous and methodical.

We have another work of the same period on Optics by Thomas Pecham, who from a simple observantine monk became archbishop of Canterbury. This work has been repeatedly printed, and was for a long time a classical book.

The sciences found a zealous patron in the great emperor Frederic 11, amid the continual wars he had to sustain against the popes. This prince ascended the throne in 1219, and died in 1250. He founded the university of Naples, composed several works, and caused those of Aristotle, with the Almagest of Ptolemy, to be translated into latin. For these translations he employed Gerard of Sabionetta, commonly called Gerard of Cremona, by whom we have also a translation of Geber's commentary on the Almagest, and of Alhazen's treatise on Twilight. To him like

wise is ascribed a treatise on the Theories of the Planets.

I should say nothing of Albertus Magnus, as he was named by his little contemporaries [A. D. 1260], if he had not written works on arithmetic, geometry, astronomy, and mechanics, useful in their day, but now lost. He distinguished himself chiefly in the construction of machines. It is reported, that he made an automaton figure of a man, which went and opened the door when any person knocked at it, and uttered some sounds, as if speaking to the person who entered.

Roger Bacon, an english cordelier, who was born in 1214, and died in 1294, has still more claim to the notice of posterity. He enjoyed a very high reputation among his contemporaries, and still retains it in the eyes of the learned. His numerous works, in which great genius and invention are displayed, have been successively printed. His treatise on Optics is particularly remarkable for the ingenious, just, and at that time new ideas it offers on the subjects of astronomical refraction, the apparent magnitudes of objects, the extraordinary size of the Sun and Moon near the horizon, the place of spherical foci, &c. Some english writers, a little too much prejudiced in favour of their countryman, have fancied they discovered in this treatise, that the author knew the use of spectacles, and even of the telescope: but Mr. Smith, an englishman of more impartiality, and an irrefragable judge, has controverted this opinion by an accurate and critical discussion of the passages, that gave rise to it. Others have been desirous of attributing to


Bacon likewise the discovery of gunpowder: in fact he was on the verge of it, being a great chemist for his time, and was acquainted with the effects of saltpetre; but it was not explained, and thoroughly known, till some years afterward. By the monks

he was persecuted, accused of magic, and confined in a dungeon; from which he was not liberated, till he had fully convinced his superiours and the pope, Nicholas IV, that he had never held any correspondence with the Devil.

The invention of spectacles is due to the close of the thirteenth century, and we are indebted for it to the italians. Incontestable proofs exist, that the first glasses of this kind were constructed by Alexander de Spina, a jacobin friar, who died at Pisa in 1313.



State of the Sciences among the Christians in the West continued through the fourteenth and fifteenth Cen


THE fourteenth century, fertile in theologians, alchymists, and even men of reputation in the department of letters, was barren of mathematicians among all the western nations of Europe. It is true a few geometricians, and astronomical observers or theorists appear, who, though they did not advance the sciences, at least maintained their honour, till they could receive more effectual assistance.

In Italy, Peter of Albano, a celebrated physician, wrote a treatise on the Astrolabe: Cecchi Ascoli, professor of mathematics at Bologna, composed a commentary on the Sphere of Sacrobosco, which was several times reprinted. Both these acquired the reputation of sorcerers and heretics, and Albano was burnt in effigy, as the more unfortunate Ascoli was in person at Bologna, in the year 1328, at the age of seventy.

In England there were many geometricians and astronomers; but of their works or observations we have only a few fragments, most of which are dispersed in manuscript in different libraries.

In Germany, John of Saxony, an augustin friar, wrote on the Alphonsine Tables, and on eclipses;


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