Journal of Speculative Philosophy, Vol. 5, p. 175.
[1613]. That arithmetic rests on pure intuition of time is not so obvious as that geometry is based on pure intuition of space, but it may be readily proved as follows. All counting consists in the repeated positing of unity; only in order to know how often it has been posited, we mark it each time with a different word: these are the numerals. Now repetition is possible only through succession: but succession rests on the immediate intuition of time, it is intelligible only by means of this latter concept: hence counting is possible only by means of time.—This dependence of counting on time is evidenced by the fact that in all languages multiplication is expressed by “times” [mal], that is, by a concept of time; sexies, ἑξακις, six fois, six times.—Schopenhauer, A.
Die Welt als Vorstellung und Wille; Werke (Frauenstaedt) (Leipzig, 1877), Bd. 3, p. 39.
[1614]. The miraculous powers of modern calculation are due to three inventions: the Arabic Notation, Decimal Fractions and Logarithms.—Cajori, F.
History of Mathematics (New York, 1897), p. 161.
[1615]. The grandest achievement of the Hindoos and the one which, of all mathematical investigations, has contributed most to the general progress of intelligence, is the invention of the principle of position in writing numbers.—Cajori, F.
History of Mathematics (New York, 1897), p. 87.
[1616]. The invention of logarithms and the calculation of the earlier tables form a very striking episode in the history of exact science, and, with the exception of the Principia of Newton, there is no mathematical work published in the country which has produced such important consequences, or to which so much interest attaches as to Napier’s Descriptio.—Glaisher, J. W. L.
Encyclopedia Britannica, 9th Edition; Article “Logarithms.”
[1617]. All minds are equally capable of attaining the science of numbers: yet we find a prodigious difference in the powers of different men, in that respect, after they have grown up, because their minds have been more or less exercised in it.—Johnson, Samuel.