DECIMAL FRACTIONS Forerunners.—The mediaeval computer who wished to find the square root of 7, having no decimal fractions with which to work, first multiplied the number by, say, i0,000, then found the square root of 70,00o to three figures, and then divided the result (246) by ioo, obtaining or 2H. The process was known to the Hindus and the Arabs and is found in Europe as early as the century. Even after the decimal fraction was known, such devices remained; this is seen, for example, in the custom of com paratively recent writers in taking the radius of a circle as 10,000,000 so as to avoid the use of decimals in the trigonometric functions. Early in the 15th century al-Kashi, assistant of the prince astronomer, Ulugh Beg of Samarkand, is said to have given the value of 7r as sah-hah I I 26 8 8 where 59-• S35 9 (modern Turkish sahib) means complete or integral. If the manu script of his work now in Constantinople goes back to his time, this is the earliest evidence we have of any precise knowledge of the decimal fraction. Pellos (1492) made use of the decimal point in cases like 9537959±70. He first placed a decimal point, then divided by 7, obtaining 136255 with a remainder, and finally wrote the result as I36255-. In Rudolff's Exempel Buchlin of 1530 an example in compound interest is solved by the aid of decimal fractions written in the form 393175, 41314375, and ,o on to 20 61640996972656250000, the operations being carried on as they are to-day. The first book devoted solely to these frac tions was De Thiende (Flemish; there was a French translation, la Disme, The Tenth, in the same year), written by Simon Stevin (Stevinus) and published in 1585. In this the decimal 27.847 (English) or 27.847 (American) appears as 27©8@4®7®. The first writer to use a decimal point with full understanding of its significance seems to have been Clavius. In the columns of differences of his table of sines printed in his work on the astrolabe in 1585, differences like 46.5 are given, this particular one being explained in the chapter "De parte proportionali sinuum, & arcuum" (p. 22q) as equivalent to 46-. The question as to what kind of decimal point to use has never been settled. The use of a separatrix of some kind was generally agreed upon early in the 17th century, but the precise form or position is still uncertain. The decimal (or centesimal) symbol % appears in the 15th cen tury under the form "per c°," the "per" being finally dropped and the c° becoming o in the 17th century. It is of Italian origin.