[107]. See Vol. II, p. 137.
[108]. The nearest English equivalent is perhaps the word “fear.” “Fearful” would correspond exactly but for the fact that in the second sense the word is objective instead of subjective. The word “shy” itself bears the second meaning in such trivial words as gun-shy, work-shy.—Tr.
[109]. The Relativity theory, a working hypothesis which is on the way to overthrowing Newton’s mechanics—which means at bottom his view of the problem of motion—admits cases in which the words “earlier” and “later” may be inverted. The mathematical foundation of this theory by Minkowski uses imaginary time units for measurement.
[110]. The dimensions are x, y, z (in respect of space) and t (in respect of time), and all four appear to be regarded as perfectly equivalent in transformations. [The English reader may be referred to A. Einstein, “Theory of Relativity,” Ch. XI and appendices I, II.—Tr.]
[111]. Si nemo ex me quaerat, scio; si quaerenti explicari velim, nescio. (Conf. XI, 14.)
[112]. Save in elementary mathematics. (It may be remarked that most philosophers since Schopenhauer have approached these questions[questions] with the prepossessions of elementary mathematics.)
[113]. The “inverse circular functions” of English text-books.—Tr.
[114]. The Newtonian form of the differential calculus was distinct from the Leibnizian, which is now in general use. Without going into unnecessary detail, the characteristic of Newton’s method was that it was meant not for the calculation of quadratures and tangents (which had occupied his predecessors), nor as an organ of functional theory as such (as the differential calculus became much later), but quite definitely as a method of dealing with rate of change in pure mechanics, with the “flowing” or “fluxion” of a dependent variable under the influence of a variable which for Newton was the “fluent,” and which we call the argument of a function.—Tr.
[115]. See Vol. II, pp. 13, 19.
[116]. See Vol. II, p. 16.