ALGEBRA..
It was not from Greece alone that the light proceeded which dispelled the darkness of the middle ages ; for, with the first dawn of that light, a mathematical science, of a name and character unknown to the geometers of antiquity, was received in Europe from Ara bia. As early as the beginning of the thirteenth century, Leonardo, a merchant of Pisa, having made frequent visits to the East, in the course of commercial adventure, returned to Italy enriched by the traffic, and instructed by the science of those countries. He brought with him the knowledge of Algebra ; and a late writer quotes a manuscript of his, bearing the date of 19.02, and another that of 028. The importation of Algebra Europe is thus carried back nearly 200 years farther than has generally been suppos ed, for Leonardo has been represented as flourishing in the end of the fourteenth century, instead of the very beginning of the thirteenth. It appears by an extract from his manu script, published by the above author, that his knowledge of Algebra extended as far as quadratic equations. The language was very imperfect, corresponding to the infancy of the science ; the quantities and the operations being expressed in words, with the help on ly of a few abbreviations. The rule for resolving quadratics by completing the square, is demonstrated geometrically.
Though Algebra was brought into Europe from Arabia, it is by no means certain that this last is its native country. There is, indeed, reason to think that its invention must be sought for much farther to the East, and probably not nearer than Indostan. We are assured by the Arabian writers, that Mahomet Ben Musa of Chorasan, distinguished for his mathematical knowledge, travelled, about the year 969, into India, for the purpose of receiving farther instruction in the science which he cultivated. It is likewise certain, that some books, which have lately been brought from India into this country, treat of al gebra in a manner that has every appearance of originality, or at least of being .derived from no source with which we are at all acquainted.
Before the time of Leonardo of Pisa, an important acquisition, from the East, had greatly improved the science of arithmetic. This was the use of the Arabic notation, and the contrivance of making the same character change its signification, according to a fixed rule, when it •changed its position, being increased tenfold for every place that it advanced towards the left. The knowledge of this simple but refined artifice was learned from the Moors by Gerbert, a monk of the Low Countries, in the tenth century, and by him-made known in Europe. Gerbert was afterwards Pope, by the name of Silvester the Second ;
but from that high dignity derived much less glory than from having instructed his coun trymen in the decimal notation.
The writings of Leonardo, above mentioned, have remained in manuscript ; and the first printed.book in Algebra is that of Lucas de Burgo, a Franciscan, who, towards the end of the fifteenth century, travelled, like Leonardo, into the East, and was there in structed in the principles of algebra. The characters employed in his work, as in those of Leonardo, are mere abbreviations of words. The letters p and m denote plus and mi nus; and the rule is laid down, that, in multiplication, plus into minus gives minus, but minus into minus gives plus. Thus the first appearance of Algebra is merely that of a system of short-hand writing, or an abbreviation of common language, applied to the so lution of arithmetical problems. It was a contrivance merely to save trouble ; and yet to this contrivance we are indebted for the most philosophical and refined art which men have yet employed for the expression of their thoughts. This scientific language, there fore, like those in common use," has grown up slowly, from a very weak and imperfect state, till it has reached the condition in which it is now found.