TRACT 33.

HISTORY OP ALGEBRA.

285

Having thus shown how to simplify equations, and preparethem for solution, Harriot enters next upon the second partof his work, being the

Exegetice Numerosa,

or the numeral resolution of all sorts of equations by a gene-ral method, which is exemplified in a great number ofequations, both simple and affected, as far as the 5th powerinclusive; and they are commonly prepared, by the fore-going parts, by freeing them from their 2d term, &c. Theseextractions are explained and performed in a way differentfrom that of V i eta ; and the examples are first in perfect orterui.nate roots, and afterwards for irrational or interminateones, to which Harriot approximates, by adding alwaysperiods of ciphers to the given number or resol vend, as faras necessary in decimals, which are continued and set downas such, but with their proper denominator 10, or 100, or1000, &c.

He then concludes the work with

Canones Directorii,

which form a collection of the cases or theorems for making:

O

the foregoing numeral extractions, ready arranged for use,under the various forms of equations, with the factors neces-sary to form the several resoivends and subtrahends.

Anri from a review of the whole work, it appears thatHarriot’s inventions, peculiarities, and improvements in alge-bra, may be comprized in the following particulars.

1st. He introduced the uniform use of the small letters,a, by c, d, &c, viz, the vowels a , e, 8tc, for unknown quan-tities, and the consonants b, c, d, f, Sec, for the knownones; which he joins together like the letters of a word, torepresent the multiplication or product of any number ofthese literal quantities, and prefixing the numeral coefficientas we do at present, except only separated by a point, thusS.bbc. For a root, he set the index of the root after the mark