Page:A History of Mathematics (1893).djvu/125

 The first notable author of mathematical books was, who lived during the reign of. He was engaged by the caliph in making extracts from the Sindhind, in revising the tablets of Ptolemæus, in taking observations at BagdadBaghdad [sic] and Damascus, and in measuring a degree of the earth's meridian. Important to us is his work on algebra and arithmetic. The portion on arithmetic is not extant in the original, and it was not till 1857 that a Latin translation of it was found. It begins thus: "Spoken has Algoritmi. Let us give deserved praise to God, our leader and defender." Here the name of the author,, has passed into Algoritmi, from which comes our modern word algorithm, signifying the art of computing in any particular way. The arithmetic of Hovarezmi, being based on the principle of position and the Hindoo method of calculation, "excels," says an Arabic writer, "all others in brevity and easiness, and exhibits the Hindoo intellect and sagacity in the grandest inventions." This book was followed by a large number of arithmetics by later authors, which differed from the earlier ones chiefly in the greater variety of methods. Arabian arithmetics generally contained the four operations with integers and fractions, modelled after the Indian processes. They explained the operation of casting out the 9's, which was sometimes called the "Hindoo proof." They contained also the regula falsa and the regula duorum falsorum, by which algebraical examples could be solved without algebra. Both these methods were known to the Indians. The regula falsa or falsa positio was the assigning of an assumed value to the unknown quantity, which value, if wrong, was corrected by some process like the "rule of three." Diophantus used a method almost identical with this. The regula duorum falsorum was as follows:[7] To solve an equation $$\scriptstyle{f(x)=V}$$, assume, for the moment, two values for x; namely, $$\scriptstyle{x=a}$$ and $$\scriptstyle{x=b}$$.