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HISTORICAL VIEW OF THE

copied from one treatise to another, as to have becomeinvolved in real obscurity, and to have given ground forserious accusation against the science.

The greatest advance in this part of the science ofquantity was effected by Thomas Harriot , who wasborn at Oxford in 1560. Having graduated in theuniversity in 1579, he was employed afterwards in thesecond expedition sent out by Sir W. Raleigh to Vir-ginia ; and on his return published an account of thatcountry. He afterwards devoted himself entirely tothe study of mathematics and astronomy. His prin-cipal work is entitled “ Artis Analytics Praxis,” whichwas not published till after his death, in 1631. In thiswork we find, for the first time, the complete develope-ment of the apparently very simple truth, to whichVieta, Girard, and others we have named, had beenso long making their successive approximations; viz.the formation of general equations of all degrees, bythe multiplication together of as many simple equationsas amount to their dimension, or the highest powerof the unknown quantity involved. This, of course,includes the case where one or more of such factorsis an equation of a higher degree than the first, hutwhere, in general, the number of factors is such thatthe sum of their dimensions is the dimension of theresulting equation. The slow progress made in thedevelopement of this principle, which, when understood,does not appear to be of any very abstruse or difficultkind, is a remarkable fact in the history of discovery.It would seem as if these labourers in science had beenworking with, and gradually improving upon, an in-strument whose full powers they did not yet under-stand. It is to the further extension of those powers,and the full confidence with which the analyst maytrust himself to be passively borne along by the appa-ratus he has thus set in motion, that the great moderndiscoveries are owing.

Harriot introduced a minor improvement in the fa-cility of the notation, by using the smail Italic letters