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HISTORY OF ALGEBRA.

TRACT 35.

construction adapted to it. He gives also a good tract onangular sections.

7. The work concludes with the numeral solution ofaffected equations, in which he follows the manner of Vieta,though he is more explicit.

OF DESCARTES.

Descartes’s Geometry was first published in 1637, beingsix years after the publication of Harriot’s Algebra. Thatwork was rather an application of Algebra to Geometry,than the science either of Algebra or Geometry itself, purelyand properly so called. And yet he made improvements inboth. We must observe, however, that all the propertiesof equations, Sec, which he sets down, are not to be con-sidered as even meant by himself for new inventions or dis-coveries ; but as statements and enumerations of properties,before known and taught by other authors, which he is aboutto make some use or application of, and for which reason itis that he mentions those properties.

Descartes’s Geometry consists of three books. The firstof these is, De Prvblematibus, qua construi possunt, adhibendotantum rectos lineas & circulos. He here accommodates orperforms arithmetical operations by Geometry, supposingsome line to represent unity, and then, by means of propor-tionals, showing how to multiply, divide, and extract roots,by lines. He next describes the notation he uses, but notbecause it is a new one, for it is the same as had been used byformer authors, viz, a + b for the addition of a and b, also

a — b for their subtraction, ab multiplication, —division, aa

or or the square of a, a 3 its cube, Stc : also */a z 4- b z for thesquare root of a 1 + b z , and A / c.a> — b 1 4- abb for the cube root,&e, with a bar over the quantities. He then observes, afterStifelius, that there must be as many equations as there areunknown lines or quantities; and that they must be reduced all