22 DISSERTATION SECOND. [part i. 



of being derived from no source with which we are at all 

 acquainted. 



Before the time of Leonardo of Pisa, an important ac- 

 quisition, also from the East, had greatly improved the 

 science of arithmetick. This was the use of the Arabick 

 notalion, and the contrivance of making the same charac- 

 ter 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. Ger- 

 bert was afterwards Pope, by the name of Silvester the 

 Second ; but from that high dignity derived much less glo- 

 ry, than from having instructed his countrymen in the de- 

 cimal notation. 



The writings of Leonardo, above mentioned, have re- 

 mained in manuscript ; and the first printed book in Alge- 

 bra is that of Lucas, <le Bursro, a Franciscan, who, towards 

 the end of the fifteenth century, travelled, like Leonardo, 

 into the East, and was there instructed in the principles of 

 Algebra. The characters emploj ed in his work, as in those 

 of Leonardo, are mere abbreviations of words. The let- 

 ters p and m denote plus and minus ; aud the rule is laid 

 down, that, in multiplication, plus into minus gives mi- 

 nus, 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, ap- 

 plied to the solution of arithmetical problems. It was a 

 contrivance merely to save trouble ; and yet to this con- 

 trivance we are indebted for the most philosophical and 

 refined art which men have yet employed for the ex- 

 pression cf their thoughts. This scientifick language, 

 therefore, like those in common use, has grown up slowly. 



