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of their cathedral school, which he accordingly governed for five years. A skillful teacher, and a devourer of books, Odo possessed extraordinary powers of labor, and when any literary work was in hand, he rested neither day nor night till it was accomplished. He was also a great friend of method and good moral discipline, but as yet he had been too exclusively taken up with the cares and pleasures of his profession to give much thought to spiritual things. Or perhaps we might rather say that he hardly knew of their existence. Like other busy, hard-working men, he was swept along in the tide of daily life, and thought it much to preserve a character of stainless honor and respectability. His success as a teacher was so great, that disciples came to him from all parts of France, as well as from Flanders, Italy, and Saxony. The city of Tournai became literally filled with students, who might be seen disputing together in the public streets; and as you drew near the school you would see them walking with the master, or seated around him; or, in the evening, standing with him at the church door, while he taught them the various constellations, and explained to them the course of the stars.

Though skilled in all the liberal arts, Odo specially excelled in logic, on which science he composed three books. He followed the method of Boëthius and the ancients, maintaining that the objects of reasoning were not words, but things, in opposition to the rising school of Nominalists, who contended that the contrary was taught by Porphyry and Aristotle.

Odo was as remarkable for his virtue as his learning. He took all his disciples to the church with him daily. They never numbered fewer than 200 ; but he made them walk two-and-two through the streets, he himself bringing up the rear, and enforcing a discipline as strict as would have been observed in the most regular monastery. No one ventured to speak to his companion, or to look right or left, and in choir they might have been taken for monks of Cluny. He did not allow them to frequent the society of women, or to wear any kind of finery; and if they transgressed his orders in these respeets, he turned them out of his school. At the hours when he gave his lectures no layman was allowed to enter the cloisters, which were at other times the resort of the public. So strict was he in this, that he did not hesitate to exclude Everard, the Castellan of Tournai, a pobleman of power and influence; for it was Odo's principle that a man must not deviate a hair's breadth from his duty, from the motive of human respect. By these means he won the love and esteem of every one; canons and people alike spoke well of him, though some were found to say that his regularity of life sprang rather from philosoplıy than religion.

He bad directed his school for about five years, when one day, a clerk having brought him St. Augustine's "Treatise on Free-will,” be purchased it, merely with the view of increasing his library, and threw it into a coffer among some other books without looking at it, for his taste inclined him rather to the study of Plato than of the Fathers. About two months afterwards, however, as he was explaining Boëthius to his disciples, he came to the fourth book of the

Consolations of Philosophy," in which the author treats of Free-will. Remembering the book he had lately purchased on the same subject, he sent for it, and having read two or three pages, was struck with the beauty of the style; and calling his pupils, said to them, 'I own that until now I was igno. rant how agreeable and eloquent are the writings of St. Augustine,' and that day and the following he read to them from this work.

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Two Irish scholars, Dungal and Clement, arrived in France soon after the retirement of Alcuin from court—who on landing excited curiosity by crying aloud, Wisdom to sell ! Who'll buy? Charlemagne attached them both to his service-Clement at Paris, where he soon was put in charge of the Palatino School, and Dungal at Pavia, where he opened a school in the monastery of St. Augustine, and in 811 addressed a letter to the emperor on the solar eclipse, which was predicted for the next year. Clenzent seems to have been deeply imbued with the learned mystịcism of the school of Toulouse, and in a treatise on the eight parts of speech, which is still preserved, quotes the rules of the grammarian Virgil, and tlie writings of the noble doctors Glengus, Galbungus, Eneas, and the rest. Alcuin complained much of the disorder introduced into the studies of the court school after his departure. 'I left them Latins,' he exclaimed, and now I find them Egyptians.' This was a double hit at the gibberish of the twelve Latinites, which Alcuin could not abide, and at the hankering which the Irish professors always displayed, both in science and theology, for the teaching of the school of Alexandria, many of them hav. ing embraced the peculiar views of the Neo-Platonists. The Egyptians, however, found a welcome at the court of Charlemagne in spite of their eccentricities; for there no one was ever coldly received who could calculate eclipses, or charm the ears of the learned monarch with Latin hexameters. And it is perhaps to one of these Irish professors that we must attribute those verses preserved by Mar and professing to be written by an Irish exile which contain such agreeable flattery of the Frankish sovereign and of his people, and which were presented to the emperor as he held one of those solemn New-year courts, at which bis subjects vied one with another in offer. ing him jewels, tissues, horses, and bags of money.

The School of the Palace declined under the management of Clement, and of his successor Claud, bishop of Turin, and during the reign of Louis le Debonnaire. It revived under Charles the Bald, when it was much resorted to by Irish and English scholars.


John Scotus Erigena; born in Ireland in 796, and educated at York and Lin. disfarne, resorted to Paris in 826, where he was placed by Charles the Bald over the Palatine school. He had early applied himself to the study of Greek,' and embraced the doctrines of the Neo-Platonic school. His translation of the works of St. Denys the Arcopagite, astonished the scholars at Rome, who looked upon all beyond the Alps as barbarians. In his philosophical treatise, De Natura Rerum, he sets forth the doctrines of the Greek Platonists, and flings defiance at his adversaries at Rome. “They are all deceived, owing to their ignorance of liberal studies. They have none of them studied Greek, and with a knowledge of the Latin language alone, it is impossible for them to understand the distinctions of science." In 855, certain propositions drawn from his writings were condemned as heretical by the Council of Valence. He withdrew from the school in 865, on the remonstrance of Pope Nicholas I., on the ground the perversion of his authority by the enemies of the church. He retired to England, where, according to some historians, he taught mathematics and astronomy at Oxford, and, to others, opened a school at Malmsbury.


GERBERT, better known in ecclesiastical history as Pope Sylvester, was born (about the year 950) of humble parentage, in Aurillac, in Auvergne, and entered at an early age the monastery of St. Gerard in his native town, where his remarkable parts and attainments attracted the attention of Borrel, Count of Barcelona, when on a pilgrimage to that monastery. The count took the young scholar back with him into Spain, where he was placed with Hatto, then bishop of Vich, in Catalonia, where he formed an intimate friendship with Warin, abbot of Cusan, one of the most learned men of his time. At that time mathematics and astronomy were more successfully cultivated in Spain, both in the Arabic Schools and the Christian monasteries, than elsewhere.

Gerbert made extraordinary progress in both; and when he accompanied Borrel and Hatto on their next pilgrimage to Rome, Pope John XIII. was not long in discovering his talents. The liberty of the subject seems not to have been much understood in the tenth century, for when it became known that the young monk was an adept both in music and mathematics, neither of which sciences were then taught in Italy, the Pope lost no time in communicating the fact to the emperor Otho I., who conjured him not to permit his return to Spain. Gerbert was accordingly most affectionately kidnapped and sent without delay to Otho's court, where being interrogated as to the extent of his knowledge, he replied that he was tolerably acquainted with mathematics, but was ignorant of logic, which science he greatly desired to study. It happened that at that time Gerard, archdeacon of Rheims, an excellent logician, had been sent as ambassador to Otho from Lothaire, king of France, and Gerbert at last won the emperor's consent to his returning home with him, that he might teach mathematics and study logic in the schools of that city. Adalberon was then archbishop of Rheims, and he forthwith committed the studies of his cathedral school to the direction of the young professor. Richer gives a very precise account of the method he followed. He began with the 'Dialectics of Aristotle,' going through and thoroughly explaining the propositions of each book. He particularly explained the Introduction of Porphyry; and passed on to the Categories,' and the 'Topics' of the same author, as translated out of Greek into Latin by Cicero, and commented on in six books by the Consul Manlius. In the same way he lectured on the four books of Topical differences, two of Categorical syllogisms, and book of Divisions, and one of Definitions. And here the reader will not fail to observe that these logical lectures must have been the fruit of studies pursued not in Spain, but in France, for previous to Gerbert's coming to Rheims, we have his own acknowledgment that he knew nothing of that science. After he had taken his scholars through this course, says Richer, he proceeded to initiate them into the art of rhetoric; and he set out on the principle, that in this branch of study a knowledge of the classical poets was essential. He therefore read and explained Virgil, Statius, and Terence; then the satirists, Juvenal, Persius, and Horace, and last of all, Lucan. After this, bis pupils were exercised in disputation, which he taught with such art, that the art was never apparent; a thing, observes his biographer, which is held to be the perfection of oratory. Then he popularized the science of

music; * and as to arithmetic, mathematics, and astronomy, he made these difficult studies easy and delightful Richer devotes several pages to the description of the various instruments which he constructed, and by which he contrived to render the science of astronomy, as it were, sensible to the eyes of his scholars. A round wooden ball, with its poles oblique to the horizon, figured the world, the various astronomical and geographical phenomena being represented by other circles. In fact, from the minute description of the writer, we are obliged to conclude that Gerbert exhibited at his lectures two very passable specimens of the terrestrial and celestial globes. But the great boon, which he is commonly represented as bestowing on the European schools, was the introduction of that wonderful table, in which nine figures represented all the numbers, and produced in their infinite combinations all multiplications and divisions. This was the mystic Abacus, the foundation, no doubt, of our present system of numeration. It consisted of a tablet, on which three columns were marked out, sometimes in fixed lines, sometimes in sand sprinkled over its surface; and in these columns figures were arranged in units, tens, and hundreds. The method in use for working out calculations, even with the assistance of this decimal system, as explained by. Gerbert in several treatises, was, however, extremely intricate, though it was probably a vast improvement on the clumsy contrivances which had been resorted to by former scholars. How far, however, the Abacus is to be regarded as a new invention, appears more than doubtful. Its history has been made the subject of interesting modern researches, and the result seenis to be that the system of numeration used and explained by Gerbert, contained nothing in it which had been unknown to Boëthius. Nevertheless, he certainly seems to have elucidated and popularized the science of arithmetic, which from this epoch began to be more seriously studied.

It is not easy to convey any notion of the enthusiasm excited by Gerbert's lectures, or the tide of scholars that flocked to him not only from every part of France, but from Germany, Italy, and the British islands. . . . Not content with instructing his own scholars, le corresponded with the scholastics of Tours, Sens, Fleury, and Aurillac, and spared no pains or expense in the col. lection of his library. In this work he was generously assisted by his friends, scattered over the length and breadth of Europe. It is in his 'Epistles' that we catch a glimpse of that prodigious activity of mind which took cognizance

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Gerbert taught his disciples the use of the monochord ; a single string, which being struck at different intervals, gave out the different sounds of the gamut. These intervals were marked on the chord, and the words to be sung had written over them a cypher, showing to what interval on the monochord it corresponded. A person therefore could always set himself right by sounding the note he wanted, as we should use a pitch key. A description of this instrument is given by the monk Odoramn, whose works have been discovered and published by Cardinal Mai, nnd whose musical treatises are said to be based on the scientific principles of Boëthius and Euclid.

| The Arabs received the knowlege of the Indian numerals in the ninth century. "But the profound and important historical investigations to which a distinguished mathematician, M. Chasles, was led by his correct interpretation of the so-called Pythagorean table in the geometry of Boëthius,' says M. Humboldt, 'render it more than probuble that the Christians in the West were acquainted even earlier than the Arabians with the Indian system of numeration; the use of the nine figures, having their value determined by position, being known by them under the name of the System of the Abacus.' (Cosmos, vol. ii. p. 226, also noto 358. See also M. Chasles, Aperçu historique des méthodes en géométrie, 465-272, and his papers in the Complesrendus de l' Acad. des Sciences.

of all subjects, and never rested till it had sounded all to the depth. In one letter we find bim begging the loan of a Cæsar from his archbishop, and offering in exchange eight volumes of Boëthius and some excellent geometrical figures. In another he solicits the monks of Aurillac to furnish him with a Spanish treatise on the arts of multiplication and division, and directs them in the work of correcting a manuscript of Pliny. Then, again, we find him writing on the medical science, to which he and his disciples directed a good deal of attention, and in which they followed the Greek masters. In fact, it was the diversified character of his acquirements that made Gerbert the 'wonder of the world' in the eyes of his contemporaries. He knew all things, they said, and all things equally well. If this were an exaggeration, it is certain that he possessed the rare power of being able to direct his attention to a very wide range of studies, though natural philosophy was certainly his special attraction.

Whilst still presiding over his school, Gerbert produced several treatises on astronomy, mathematies, and geometry; on the formation of the astrolabe, the quadrant, and the sphere, as well as on rhetoric and logic. The monk Ditmar tells us that when at Magdeburg with his old pupil, Otho III., 'he made a clock, regulating it according to the movement of the polar star, which he observed through a kind of tube.' Another writer speaks of certain hydraulic organs which he constructed, in which the wind and necessary movements were introduced by means of boiling water: and these obscure notices seem to indicate that wheeled clocks, the telescope, and the power of steam, were known by Gerbert fully three centuries before what has been considered their earliest dis. covery by the monk Roger Bacon. Gerbert did not teach at Rheims alone. Crossing the Alps, he passed through most of the towns of Northern Italy, then subject to his great patron, Otho I. In 970 he also visited Rome in company with the bishop Adalberon, and at Pavia met the emperor, together with the celebrated Saxon, Otheric, who had honorably filled the office of scholas. ticus in the episcopal school of Magdeburg. Otheric had up to that time enjoyed the reputation of being the greatest scholar of his age, and perhaps re. garded himself somewhat in the light of a literary dictator. In the course of the previous year, he had felt no little uneasiness at the daily increasing renown of the French professor, and had dispatched one of his own Saxon pupils to Rheims to bring him an exact account of Gerbert's method of dividing the Sciences. The Saxon made an unsatisfactory report. It was Gerbert's custom to represent physics and mathematics as equal and independent sciences. But Otheric's disciple, whose head was none of the clearest, made bim teach that physics were subordinate to mathematics, as the species to the genus. On this, Otheric decided that he knew nothing of philosophy, and, proceeding to the court of the emperor, Otho I., he spoke to that effect before an assembly of learned men. Otho, who was himself passionately fond of these studies, was not satisfied, and resolved to sist the matter to the bottom. He therefore seized the occasion of Gerbert's presence at Pavia, to inaugurate a grand scien. tific tournament, and invited all the savants of his empire to witness the dispute between the first scholar of France and the first scholar of Germany. He himself presided at the conference, and opened it with a little allocution of his own, in which be very clearly explained the question in dispute. Then Otheric began his attack, first in words, and then in writing. The conference lasted the whole day, and Gerbert, who cited the authorities of Plato, Porphyry,

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