printed at London in 1570, mentions Algebra as a mystery scarcely heard of by the studious in Mathematics here. In 1558, Peletarius published at Paris a very ingenious and masterly composition, entitled Jacobi Peletarii Cenomani, de occulta parte Numerorum, quam Algebram vocant, Lib. duo; in which he ably treats of all the parts of the subject then known, excepting Cubic Equations, and teaches some curious properties of square and cube numbers, with the method of constructing a table of each, by addition only; how to reduce trinomial surds, to rational quantities, and even to simple ones, by means of certain compound multipliers; and that the root of an Equation is one of the divisors of the known or absolute term.

The Stratioticos of Mr. Thomas Digges', containing

elected fellow of Trinity College. His great application to Astronomy, together with some ingenious mechanical inventions with which he occasionally amused himself, gave rise to a suspicion that he was a conjurer, and he was obliged in consequence to quit the country. He went to the University of Louvain, thence to the College of Rheims, where he read lectures upon Euclid; in 1551 he returned to England, and had the rectory of Upton upon Severn: afterwards, in consequence of a correspondence he had with Elizabeth, he was accused of practising enchantment against the life of Queen Mary her sister, and suffered a tedious confinement. On the accession of Queen Elizabeth, he was introduced to her, and (agreeably to the superstitious customs of that period) consulted respecting a propitious day for the coronation. She employed him afterwards in making geographical descriptions and maps of the countries to which England might have any claim; in this he acquitted himself with credit, as he did in his labours respecting the reformation of the calendar. In 1581, meeting with Edward Kelly, a credulous alchymist, our eccentric author and he performed together divers imaginary incantations, and held a pretended intercourse with angels and spirits. Our two conjurers asserted, that they were in possession of the secret of transmuting the baser metals into gold; and meeting with one Albert Laski, a Polish Nobleman, as credulous and ridiculous as themselves, they all three set out together for the Continent: here they imposed upon such of the rich and affluent as were silly enough to believe them, and lived on the profits of their trade in great affluence. Some disputes arising, Dee returned to England, and was graciously received by the Queen, who in 1595 made him Warden of Manchester College. He died at Mortlake in 1608, leaving some valuable works behind him.

1 Thomas Digges flourished in the reign of Elizabeth, but the times of his

tract on Algebra, was published in 1579; the author was Muster Master General of the forces, and a man of great credit, so that, in all probability his work gave a fresh impulse to the study of Algebra in England, where it had for many years been on the decline; at least we know, that it now began to be studied and cultivated with more ardour than heretofore.

The next writers of note were Ramus", Bombelli", and Clavius, whose excellence consisted in their com

birth and death are not known. Having studied for some time at Oxford, in consequence of what he acquired there, and the subsequent instructions of his learned father, he became one of the best mathematicians of that time; we have several very useful mathematical works of his still in print, and he left several others in manuscript.

m Peter Ramus was born at Vermandois in Picardy, in 1515. A thirst for learning, accompanied with extreme poverty, (for although he was of a good family, a series of misfortunes had made him poor,) urged him to become a servant in the College of Navarre, where he spent the day in performing the duties of his office, and most part of the night in study; by this means he acquired Classical learning, Rhetoric, Mathematics, and a knowledge of Philo'sophy. On taking his Master of Arts' degree, he defended a thesis, which went to overturn the whole doctrine of Aristotle, which at that time prevailed in the schools; this of course gave offence, but the force of his arguments proved an over-match for those of his adversaries. He was a great orator, sober, temperate, and chaste. He lay upon straw, rose early, and studied hard; being a Protestant, he endeavoured to shelter himself by concealment, during the dreadful massacre of St. Bartholomew in 1572; but was unfortunately discovered, dragged out, and murdered with circumstances of inhuman barbarity too shocking to relate,

The mathematical works of Ramus were enlarged, improved, and published in 2 volumes 4to. by Schoner; his Geometry, which is chiefly practical, was translated into English by Bedwell, and published at London, 4to,

1636.

D

Raphael Bombelli was a mathematician of Italy; his Algebra was written in 1572, and published seven years after at Bologna.

• Christopher Clavius was born at Bamberg in Germany in 1537: he was a Jesuit, and cultivated mathematical learning, which he laboured at for more than 50 years; he assisted under Pope Gregory XIII. in the reformation of the calendar, which he afterwards defended against Scaliger, Vieta, and others. His stile of writing is considered as heavy, and his works are mostly elementary, forming a complete system, in 5 large volumes folio. He died at Rome in 1612.

ments on, and explanations of, preceding authors, rather than in any material improvements of their own.

Simon Stevinus ", of Bruges, mathematician to Prince Maurice of Nassau, and inspector of the Dykes in Holland, was the author of several useful treatises in various branches of the Mathematics; among which, one is on Arithmetic, published in 1585, and another shortly after on Algebra: the latter, with which we are now particularly concerned, is an original and ingenious work, containing a variety of improvements. He here introduces the use of fractional exponents, whereby all sorts of roots are denoted, like powers by numeral indices: the notation of coefficients by including fractions, radicals, and numbers of every description, he greatly improved, and gave a general method of resolving all Equations by numbers; he likewise first applied the word nomial to all compound algebraic expressions, as binomial, trinomial, quadrinomial, multinomial, &c. the former of which, as has been observed, was first employed by Recorde.

As early as 1575, Gulielmus Xylander published at Basil a Latin translation of the six first books, and part of the seventh, of the Arithmetics of Diophantus, ac

➤ Simon Stevin was very skilful in both Mathematics and Mechanics: he is said to have invented the sailing chariots sometimes used in Holland. His works on various branches of the Mathematics were written in Dutch, and translated into Latin by Snellius, making 2 volumes folio; but the best edition is that in French, with additions and notes, by Albert Girard, printed at Leyden in 1634. He died in 1633.

a Diophantus is supposed by some to have flourished before Christ, others place him in the second century after, and others again in the fourth, after; he lived at Alexandria, and is reputed to be the same who wrote the Canon Astronomicus, which was honoured with a commentary by Hypatia, the celebrated and unfortunate daughter of Theon, whom she succeeded as President of the Alexandrian school.

It does not appear in what manner the six books of Diophantus were recovered; Regiomontanus mentions them as being deposited in the Vatican Library in his time, and Bombelli proposed to translate them, but did not. That Diophantus was not the inventor of Algebra, as some have supposed, nor of the

companied with the Greek Scholia of Maximus Planudes, and notes. This work, which had been lost for many ages, consisted originally of thirteen books, but those only which we have mentioned have been published; the remainder, it is supposed, are irrecoverably lost. The Problems of Diophantus are of the kind called indeterminate, relating to square and cube numbers, right angled triangles, &c. and "so exceedingly curious and abstruse, that nothing less than the most refined Algebra, applied with the utmost skill and judgment, can surmount the difficulties which attend them."

The method of Diophantus was found to differ very widely from that of the Arabs, which had hitherto been followed, and it furnished succeeding algebraists with ample means of extending and perfecting the science. The first who availed himself of this advantage, was Franciscus Vieta', Master of the Requests to Mar

Analysis of indeterminate Problems, as M. Bossut asserts, appears from the nature of his problems, and the consummate skill their investigation requires, which indicate such a maturity in the science as would require ages to produce. Xylander was a native of Augsburg, and became Professor of Greek at Heidelberg; he translated Diophantus, Plato, Dion Cassius, Strabo, and Marcus Antoninus; "he was very learned, and very poor, and laboured rather for bread than for fame, which helps to account for the numerous errors found in his writings." Born 1532, died 1576. Melchior Adam, in Vitis Philosophorum. Bayle. Maximus Planudes, the Scholiast, was a Monk of the Greek Church, and flourished at Constantinople in the fourth century; he was author of a collection of Epigrams, and of some Fables, which he ascribed to Esop, whose life he wrote; but the account he has given is said to be full of anachronisms, absurdities, and lies.

Vieta was born in 1540 at Fontenai-le-Comté, in Lower Poitou; he excelled in various branches of learning, especially the Mathematics, scarcely any part of which is not indebted to his original and masterly genius for great and valuable improvements: to particularize them would require a volume; Algebra, Geometry, Trigonometry, Astronomy, are particularly indebted to him. By means of his angular sections, he resolved the famous problem of 45 dimensions, proposed by Adrian Romanus to all the world. His skill as a decipherer proved a great benefit to his country, during the troubles of the League, by disconcerting the councils of the Spanish court for more than two years.

garet, Queen to Henry IV. of France: his affection for the Mathematics was so great, that it is said he frequently passed three whole days and nights in study, without food or sleep; by him the Greek and Arabian methods were judiciously blended, and more improvements introduced than any former writer could claim. He was the first who introduced the general use of letters into Algebra, denoting the known quantities in a problem by the consonants, and unknown ones by vowels. He improved the method of reducing cubic and other Equations; shewed how to change the roots in a given proportion; how to raise cubic and biquadratic Equations from quadratics, by squaring and otherwise multiplying certain parts of the latter; he made various observations on the limits of the roots of Equations, and stated the general relation between the roots and coefficients, when the signs of the terms are alternately + and

and none of the terms wanting; he gave the construction of certain Equations, and exhibited their roots by means of angular sections, a method which had been before adverted to by Bombelli. He introduced the vinculum, and the names coefficient, affirmative, negative, pure, affected, unciæ, &c. and was, I believe, the first who extracted the roots of Equations by approximation. The next whose writings deserve to be mentioned, is Albert Girard, an ingenious Dutch mathematician; his Inven

The dark and crooked policy of the ambitious Philip induced him to support the Duke of Guise, and their correspondence was carried on by means of a cipher, consisting of above 500 different characters; this falling into the hands of the King's party, was successfully interpreted by Vieta, which was considered as so difficult a task, that many ascribed it to magic. Vieta died at Paris in 1603, and his works were collected and published at Leyden in 1646, by Schooten, besides a large folio volume mentioned by Dr. Hutton as published at Paris in 1573. Introduction to Hutton's Mathematical Tables, 2nd edit. p. 4. &c.

The time of his birth is not known; he died about the year 1633, leaving behind him the character of an ingenious and useful mathematician.