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Psellus, who lived in the ninth century, wrote a compendium of the ancient Arithmetic in Greek, which was published by Xylander, A. D. 1556, in Latin; and a similar work was written shortly after in the same language by Iodocus Willichius. These works are at present objects rather of learned curiosity than use; few persons will take the trouble to understand them.

The Arabs, who had shewn themselves the most inveterate enemies of learning, by a revolution of sentiments not uncommon, became its most zealous supporters. From them Arithmetic received some of its most useful improvements; among which the method of notation at present in use may be considered as the chief. It does not appear, however, that the Arabians ever laid claim to the invention; they refer us to the Indians; and hence the figures employed in our calculations are sometimes called Indian characters.

The Arabs were in possession of the Indian method of notation probably for the space of three centuries before the Europeans knew any thing of the matter. The latter were involved in the darkest ignorance, which the genius and learning of the few great men this age of blindness produced were unable to dispel, and which served only to render that mental darkness visible in all its horrors.

Among the few illustrious characters which appeared at this period, Gerbert' deserves the first place. This

1 Gerbert was born of mean parents, but it is uncertain in what year.

Having spent several years among the Saracens at Corduba, during which he industriously collected all that was valuable of their Geometry, Astronomy, and Arithmetic, he returned to France in 970, where he was caressed by the wiser part of his countrymen; but the generality of them treated him as a redoubtable Magician : and the credulous writers of those times relate many ridiculous stories about him; as that he understood the language of birds; that he could raise the Devil, was very familiar with him, and bequeathed his soul to him after death, &c. &c. See

Pincent's Lectures against Popery, Lect, VII. p. 191, a book in which many stories of the kind are to be found.

literary hero possessed an enlargement of mind, and a thirst for knowledge, rarely to be met with. He was educated in the monastery of Fleury; but soon discovering the incapacity of his teachers, he fled from his monastery, and went to Spain, which was then under the dominion of the Arabs. Having fixed himself at Corduba, he applied with ardour to the acquisition of the Arabian language, and the sciences which that people almost exclusively possessed; he succeeded so well, that in a few years he returned to France, and enriched the Christian world with the literary spoils obtained from the Mahometans, A. D. 960. To him the nations of Europe are indebted for the most valuable of all his acquisitions, a knowledge of the Arabian numeral figures, on the use of which depends every subsequent improvement in Arithmetic. The Arabian method of notation introduced from Spain by Gerbert, notwithstanding its advantages, was not so eagerly adopted as one might be led to expect; 150 years having elapsed before it was known in Britain, and nearly 100 more before it was brought into common use, as is shewn by Dr. Wallis. The first writer of note after the reception of the Arabian method, was Jordanus of Namur in Flanders, about the year 1200; his work was commented on, and published shortly after the invention of printing, by Johannes Faber Stapulensis, viz. in 1480. Johannes de Sacro Bosco, an Englishman, wrote a treatise on Arithmetic in the thirteenth century; as did Maximus

Gerbert was preceptor to Robert I. King of France, and to Otho III. Emperor of Germany. He was Bishop of Rheims, and afterwards Archbishop of Ravenna. At length, on the death of Pope Gregory V. A. D. 998, Gerbert was, by the influence of his pupil Otho, chosen to succeed him on the Papal throne, under the name of Sylvester II. He died about the year 1003.

Planudes, the Scholiast, either in that century or the next. After the introduction of printing, the diffusion of knowledge necessarily became much more extensive than it had been at any former period, from the number of books which were successively published. The earliest authors who wrote on Arithmetic were Lucas De Burgo, 1470. Cardan, Purbach, Stifelius, Scheábelius, Tartalea, Maurolycus, Peletarius, &c. these were foreigners. Of our own countrymen, Recorde, Bulkley, Digges, and Dee, were among the earliest writers. The doctrine of Decimal Fractions was introduced about 1464, by Regiomontanus": but the first

" John Muller was horn at Mons Regius, in Koningsberg, in 1436, and received the name of Regiomontanus from his birth-place, where, and at Leipsic, he acquired the rudiments of Mathematics and Astronomy. At fifteen he went to Vienna, where he studied to good purpose, under the celebrated Purbach, to whom he became a useful assistant, and an affectionate friend. He afterwards accompanied Cardinal Bessarion, the friend and patron of science, to Rome, where our author studied the Greek language, and at the same time continued his Astronomical labours. In 1463 he went to Padua, where he became a member of the University, and explained the works of the Arabian philosopher Alfraganus. Having collected a great number of Manuscripts, he returned to Vienna, and resumed the duties of his office: at length he retired to Noremberg, and set up a press, intending to print and publish the valuable books he had written or collected, and of which the catalogue is still in being. Here he became acquainted with Bernard Walther, a sincere lover of the sciences, who, entering heartily into his views, undertook the expence of erecting a printing-house, and constructing Astronomical instruments. He now printed The new Theories of Purbach, The Astronomicon of Manlius, The Cosmography of Ptolemy, with select Commentaries on the Almagest; also The new Calendar, and Ephemerides of his own composing.

In 1474 Pope Sixtus IV. invited our Author to Rome, to assist in reforming the Calendar. To induce him to leave his retreat, the Pope made him large promises, and nominated him Bishop of Ratisbon. He consented, and arrived at Rome in 1475, but died the next year, as it is supposed, by poison. The atrocious deed is ascribed to the sons of George Trabezond, in revenge for their father's death, who is said to have died of a broken heart, in consequence of some severe criticisms made by Regiomontanus, on his Translation of Ptolemy's Almagest.

who wrote expressly on the subject was Simon Stevinus, of Bruges, about 1582. Dr. Wallis, in 1657, published his mathematical works, wherein he has the first of any treated at large of Recurring Decimals. Some hundreds of books on the subject, possessing various degrees of merit, have from time to time appeared, in many of which the fundamental principles and rules have been laid down with much clearness and perspicuity, and their applications to mathematical, mechanical, and commercial subjects (which were mostly received from the Arabians) simplified, extended, and improved. Omitting a long list of names, we pass on to the next valuable discovery in Arithmetic, namely, the invention of Logarithms, or numbers whereby the most tedious and difficult calculations are performed with surprising ease and facility. For this invention the world is indebted to the skill and industry of John Lord Napier, a Scotch Nobleman, who first published it in 1614; and for a most important improvement in the system, which took place three years after, to Mr. Henry Briggs, Professor of Geometry at Gresham College. Further particulars of this interesting discovery will be given in its proper place; and we will conclude this sketch with the mention of a few names, to one or other of which most of our countrymen are indebted for their skill in the science. The Arithmetic of Mr. Edmund Wingate" was first published in 1629; and after, an edition of the same, improved and enlarged by John Kersey “, teacher of the Mathematics

* Mr. Wingate, a zealous cultivator and encourager of mathematical learning, flourished in the reigns of James and Charles the First. He carried the knowledge of Logarithms to France, where he published some Tracts on the subject: he likewise applied the Logarithms to two sliding rulers, so accommodated to each other, that problems may be mechanically performed by them without the assistance of compasses.

• Kersey lived in the reign of Charles the Second. He was the author of

in London: this book had a good sale, and was considered as a useful introduction when our grandfathers were boys at school. The arithmetical part of the Young Mathematician's Guide, by Mr. John Ward” of Chester, is remarkably plain and clear for the time in which it was written. This work, which appeared in 1706, has been much esteemed, and still maintains its reputation. Mr. Malcolm's New System of Arithmetic, theoretical and practical, published in 1730, is a very complete work, and served as a model to some of our best elementary writers. Dilworth's "Schoolmaster's Assistant, 1743, was much in use thirty or forty years ago; it contains an ample collection of easy examples under every rule, and is on the whole a good old-fashioned Schoolbook. Fenning's Arithmetic is a plain and easy system of rules, with very few examples. Walkingame's Tutor's Assistant has had a great run ; indeed it has been found more useful to the practical scholar than books more scientifically written. Its proprietors have taken great pains to render the work as perfect as possible: a few alterations in its structure would make it the best school book on practical arithmetic in print. Dr. Hutton's Treatise on Practical Arithmetic needs no better recommendation than his name. The same may be said of Mr. Bonnycastle's Scholar's Guide; in this work the rules are not only exemplified, but demonstrated, and the taste and science of the author appear

an excellent treatise on Algebra in folio, wherein the Diophantine Problems are very skilfully managed; he also wrote an English Dictionary. P John Ward was born in the year 1648. He appears from his manner and style of writing to have been a very respectable scholar, but I know no particulars of his life. * Thomas Dilworth was originally, as I have been informed, an assistant to the Rev. Thomas Dyche, who kept a school at Stratford le Bow; he afterwards was master of a school in Wapping, and published several elementary books, which are still considered as useful.

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