Til ACT 33.

HISTORY OF ALGEBRA.

287

2. The common rules or operations of Arithmetic andAlgebra. In algebraic multiplication, he either joins theletters together like a word, or connects them by the markx , which is the first introduction of this character of multi-plication : thus ax a or aa or hq. But omitting the vincu-lum over compound factors, used by Vieta. He intro-duces here many neat and useful contractions in multiplica-tion and division of decimals: as that common one of invertingthe multiplier, to have fewer decimals, and abridge thework ; that of omitting always one figure at a time, of thedivisor, for the same purpose ; dividing by the componentfactors of a number, instead of the number itself ; as 4 and 6for 24 ; and many other neat contractions. He states hisproportions thus 7.9 :: 28.36, and denotes continued pro-portion thus -ff ; which is the first time I have observed thesecharacters.

3. Invents and describes various symbolical marks or ab-breviations, which are not now used.

4. The genesis and analysis of powers. Denotes powerslike Vieta, and also roots, thus \/q6, fc20, t/qq2i<, &c ;and much in his manner too performs the numeral extractionof roots. He here gives a table of the powers of the bino-mial a + e as far as the 10th power, with all their terms andcoefficients, or unciae as he calls them, after Vieta.

5. Equations. He here gives express and particular di-rections for the several sorts of reductions, according as theform of the equation may require. He uses the letter uafter V, for universal, instead of the vinculum of Vieta.And he observes that the signs of all the terms of the powersof a + e are positive, but those of a — e are alternately po-sitive and negative.

6. Next follow many properties of triangles and othergeometrical figures ; and the first instance of applying Al-gebra to Geometry, so as to investigate new geometricalproperties; also, after the algebraical resolution of eachproblem, he commonly deduces and gives a geometrical