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 thus, . Albert Girard,
a pupil of Stevin, in 1629 uses the point on one occasion. John Wallis in 1657 writes 12345, 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
invented by John Napier, Baron of Merchiston, in Scotland
(1550–1617). It is one of the greatest curiosities of the history of science that Napier constructed logarithms before exponents were used. To be sure, Stifel and Stevin made
some attempts to denote powers by indices, but this notation was not generally known,–-not even to Harriot, whose algebra
appeared long after Napier's death. That logarithms flow naturally from the exponential symbol was not observed until much later. It was Euler who first considered logarithms as being indices of powers. What, then, was Napier's line of thought?
Let be a definite line, a line extending from indefinitely. Imagine two points starting at the same
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moment; the one moving from A toward B , the other from D toward E . Let the velocity during the first moment be the same for both: let that of the point on line D E be uniform; but the velocity of the point on