history of algebra.

TRACT 33.

J5D

unknown letter or character, which he chooses or assumesso ingeniously, that all the other unknown quantities in thequestion are easily expressed by it, and the final equationreduced to the simplest form which it seems the question canadmit of. Sometimes he substitutes for a number soughtimmediately, and then expresses the other numbers or con-ditions by it: at other times he substitutes for the sum ordifference, &c, and thence derives the rest, so as always toobtain the expressions in the simplest form. Thus, if thesum of two numbers be given, he substitutes for their differ-ence ; and if the difference be given, he substitutes fortheir sum : in both cases he has the two numbers easily ex-pressed by adding and subtracting the half sum and half dif-ference ; and so in other cases he uses other similar inge-nious notations. In short, the chief excellence in this col-lection of questions, which seems to be only a set of exer-cises to some rules which had been given elsewhere, is theneat mode of, substitution or notation ; which being oncemade, the reduction to the final equation is easy and evi-dent : and there he leaves the solution, only mentioningthat the root or apiSpoi is so much. Upon the whole, thiswork is treated in a very able and masterly manner, mani-festing the utmost address and knowledge in the solutions,and forcing a persuasion that the author was deeply skilledin the science of algebra, to some of the most abstruse partsof which these questions or exercises relate. However, ashe contrives his assumptions and notations so as to reduce allhis conditions to a simple equation, or at least a simple qua-dratic, it does not appear what his knowledge was in the re-solution of compound or affected equations.

But though Diopbantus was the first author on algebrathat we nowknow of, it was not from him, but from the Moorsor Arabians that we received the knowledge of algebra inEurope, as well as that of most other sciences. And it ismatter of dispute who were the first inventors of it; someascribing the invention to the Greeks, while others say thatfhe Arabians had it from the Persians, and these from the