THE NATURE OF MATHEMATICS 13

211. Mathematics is a science continually expanding; and its
growth, unlike some political and industrial events, is attended
by universal acclamation. WHITE, H. S.

Congress of Arts and Sciences (Boston and
New York, 1905), Vol. 1, p. 455.

212. Mathematics accomplishes really nothing outside of the
realm of magnitude; marvellous, however, is the skill with
which it masters magnitude wherever it finds it. We recall at
once the network of lines which it has spun about heavens and
earth; the system of lines to which azimuth and altitude, dec-
lination and right ascension, longitude and latitude are re-
ferred; those abscissas and ordinates, tangents and normals,
circles of curvature and evolutes; those 'trigonometric and
logarithmic functions which have been prepared in advance and
await application. A look at this apparatus is sufficient to
show that mathematicians are not magicians, but that every-
thing is accomplished by natural means; one is rather impressed
by the multitude of skilful machines, numerous witnesses of a
manifold and intensely active industry, admirably fitted for the
acquisition of true and lasting treasures. HERBART, J. F.

Werke [Kehrbach] (Langensalza, 1890), Bd.
5, p. 101.

213. They [mathematicians] only take those things into
consideration, of which they have clear and distinct ideas,
designating them by proper, adequate, and invariable names,
and premising only a few axioms which are most noted and
certain to investigate their affections and draw conclusions from
them, and agreeably laying down a very few hypotheses, such as
are in the highest degree consonant with reason and not to be
denied by anyone in his right mind. In like manner they assign
generations or causes easy to be understood and readily ad-
mitted by all, they preserve a most accurate order, every
proposition immediately following from what is supposed and
proved before, and reject all things howsoever specious and
probable which can not be inferred and deduced after the same
manner. BARROW, ISAAC.

Mathematical Lectures (London, 1734), P- 66.

Source: Memorabilia mathematica; or, The philomath's quotation-book - Moritz, Robert Édouard, 1868-1940