120

HISTORICAL VIEW OF THE

the Arabic ; but perceiving its value, as coining next toEuclid’s data in the order of elementary exposition ofthe subject, he entertained the project of translating itinto Latin : it does not, however, appear that he exe-cuted it.

Though later in time, the connection of our subjectleads us here to mention, that his steps were followedby Benedetto, an Italian mathematician, who continuedthe investigation of the subject, and published a treatiseon the geometrical analysis at Turin , in 1585. Mau-rolycus of Messina, also, who flourished in the middle ofthe sixteenth century, and may be regarded as the greatgeometer of that age, furnished several translationsfrom the ancients, and commentaries upon them : be-sides which, he wrote a treatise on the Conic Sections,of considerable value. He made an attempt also torestore the fifth book of Apollonius ’s Conic Sections, inwhich the subject of maxima and minima is treated.His writings indicate a man of clear conceptions, andof a strong understanding; though, in common withalmost all persons of that age, he was a believer in as-trology, and even an adept in the art.

One of the most eminent of the early cultivators ofalgebra, was Lucas de Burgo, a Franciscan , who, to-wards the end of the fifteenth century; travelled likeLeonards into the East, and was there instructed inthe principles of this science. On his return he pub-lished a treatise on the subject, in which he advances alittle in the art of notation ; employing more abbrevi-ations, and, in particular, using the letters p. and m.to stand for plus and minus, or the symbols of additionand subtraction : he also gives the rule for the signs inmultiplication. Though, as we have already seen, Dio-phantus had advanced to this point of symbolical algebra,yet Lucas de Burgo arrived at it independently; sincethe writings of Diophantus were not discovered till themiddle of the sixteenth century, when a Latin translationof the arithmetical questions was published by Xylander .Thus the origin of the algebraic notation was simply