Page:A History of Mathematics (1893).djvu/180

 Decimalis. With Bürgi, a zero placed underneath the digit in unit's place answers as sign of separation. Beyer's notation resembles Stevin's. The decimal point, says Peacock, is due to Napier, who in 1617 published his Rabdologia, containing a treatise on decimals, wherein the decimal point is used in one or two instances. In the English translation of Napier's Mirifici logarithmorum canonis descriptio, executed by Edward Wright in 1616, and corrected by the author, the decimal point occurs in the tables. There is no mention of decimals in English arithmetics between 1619 and 1631. Oughtred in 1631 designates the fraction .56 thus, $$\scriptstyle{0|\underline{56}}$$. Albert Girard, a pupil of Stevin, in 1629 uses the point on one occasion. John Wallis in 1657 writes $$\scriptstyle{12|\underline{345}}$$, but afterwards in his algebra adopts the usual point. De Morgan says that "to the first quarter of the eighteenth century we must refer not only the complete and final victory of the decimal point, but also that of the now universal method of performing the operations of division and extraction of the square root."[27] We have dwelt at some length on the progress of the decimal notation, because "the history of language…is of the highest order of interest, as well as utility: its suggestions are the best lesson for the future which a reflecting mind can have."[27]

The miraculous powers of modern calculation are due to three inventions: the Arabic Notation, Decimal Fractions, and Logarithms. The invention of logarithms in the first quarter of the seventeenth century was admirably timed, for Kepler was then examining planetary orbits, and Galileo had just turned the telescope to the stars. During the Renaissance German mathematicians had constructed trigonometrical tables of great accuracy, but this greater precision enormously increased the work of the calculator. It is no exaggeration to say that the invention of logarithms "by shortening the labours doubled the life of the astronomer." Logarithms were