DISSERTATION.

the symbol for the note of radicality referring to the square root sign occurs in the first printed work, which is that of Paciolo. 1 Leonardo Bonacci of Pisa, the earliest scholar of the Arabians, 2 is said by Targioni Tozzetti to have used the small letters of the alphabet to denote quantities. 3 But Leonardo only does so because he represents quantities by straight lines, and designates those lines by letters, in elucidation of his Algebraic solutions of problems. 4

The Arabians termed the unknown (and they wrought but on one) shai thing. It is translated by Leonardo of Pisa and his disciples, by the correspondent Latin word res thing and Italian cosa thing; whence Regola de la Cosa Rule of the Thing, and Rule of Coss, with Cossike practise and Cossike number of our older authors, 5 for Algebra or Speculative practice, as Paciolo 6 denominates the analytic art; and Cossic number, in writers of a somewhat later date, for the root of an equation.

The Arabs termed the square of the unknown mál possession or wealth; translated by the Latin census and Italian censo as terms of the same import: for it is in the acceptation of amount of property or estate 7 that census was here used by Leonardo.

The cube was by the Arabs termed Cáb a die or cube; and they combined these terms mál and Cáb for compound names of the more elevated powers, in the manner of Diophantus by the sums of the powers, and not like the Hindus by their products. Such, indeed, is their method in the modern elementary works; but it is not clear that the same mode was observed by their earlier writers, for their Italian scholars denominated the biquadrate and higher powers Relato primo, secundo, tertio, etc.

Positive they call záid additional; and negative nákis deficient: and, as before observed, they have no discriminative marks for either of them.

The operation of restoring negative quantities, if any there be, to the positive form, which is an essential step with them, is termed jebr, or with the article Aljebr, the mending or restoration. That of comparing the terms and taking like from like, which is the next material step in the process of resolution,

1 Or Pacioli, Paciuolo, -li, etc. For the name is variously written by Italian authors.
2 See Note L.
3 Viaggi, 2d Edit. vol. 2, p. 62.
4 Cossali, Origine dell’Algebra, i.
5 Robert Recorde’s Whetstone of Witte.
6 According to us called Speculative Practice. Summa 8. 1.
7 Census, whatever property one possesses. Steph. Thes.