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HISTORY OF ALGEBRA.

TRACT 33 .

contradistinction to the ancient analysis, which chiefly re*spected geometry, and its applications.

There have arisen great controversies and sharp disputesamong authors, concerning the history of the progress andimprovements of algebra; arising partly from the partialityand prejudices which are natural to all nations, and partlyfrom the want of a closer examination of the works of theolder authors on this subject. From these causes it has hap-pened, that the improvements made by the writers of onenation, have been ascribed to those of another ; and thediscoveries of an earlier author, to some one of much laterdate. Add to this also, that the peculiar methods of manyauthors have been described so little in detail, that our in-formation derived from such histories, is but very imperfgct,and amounting only to some general and vague ideas of thetrue state of the arts. To remedy this inconvenience there-fore, and to reform this article, I have taken the pains care-fully to read over in succession all the older authors on thissubject, which I have been able to meet with, and to writedown distinctly a particular account and description of theirseveral compositions, as to their contents, notation, im-provements, and peculiarities; from the comparison of allwhich, I have acquired an idea more precise and accuratethan it w'as possible to obtain from other histories, and in agreat many instances very different from them. The fulldetail of these descriptions would employ a volume of itself,and would be far too extensive for this place : I must there-fore limit this article to a very brief abridgment of my notes,remarking only the most material circumstances in each au-thor ; from which a general idea of the chain of improve-ments may be perceived, from the first rude beginnings,down to the more perfect state; from which it will appearthat the discoveries and improvements made by any one-single author, are scarcely ever either very great or numer-ous ; but that, on the contrary, the improvements are al-most always very slow and gradual, from former writers,