William Oughtred: A Great Seventeenth-Century Teacher of Mathematics

by Florian Cajori

LOGARITHMS

Oughtred’s treatment of logarithms is quite in accordance with the more recent practice.[49] He explains the finding of the “index” (our “characteristic”); he states that “the sum of two Logarithms is the Logarithm of the Product of their Valors; and their difference is the Logarithm of the Quotient,” that “the Logarithm of the side [436] drawn upon the Index number [2] of dimensions of any Potestas is the logarithm of the same Potestas” [436²], that “the logarithm of any Potestas [436²] divided by the number of its dimensions [2] affordeth the Logarithm of its Root [436].” These statements of Oughtred occur for the first time in the Key of the Mathematicks of 1647; the Clavis of 1631 contains no treatment of logarithms.

If the characteristic of a logarithm is negative, Oughtred indicates this fact by placing the - above the characteristic. He separates the characteristic and mantissa by a comma, but still uses the sign |_ to indicate decimal fractions. He uses the contraction “log.”