=1929.= The principal advantage arising from the use of hyperbolic functions is that they bring to light some curious analogies between the integrals of certain irrational functions. --BYERLY, W. E. _Integral Calculus (Boston, 1890), p. 30._ =1930.= Hyperbolic functions are extremely useful in every branch of pure physics and in the applications of physics whether to observational and experimental sciences or to technology. Thus whenever an entity (such as light, velocity, electricity, or radio-activity) is subject to gradual absorption or extinction, the decay is represented by some form of hyperbolic functions. Mercator’s projection is likewise computed by hyperbolic functions. Whenever mechanical strains are regarded great enough to be measured they are most simply expressed in terms of hyperbolic functions. Hence geological deformations invariably lead to such expressions....--WALCOTT, C. D. _Smithsonian Mathematical Tables, Hyperbolic Functions (Washington, 1909), Advertisement._ =1931.= Geometry may sometimes appear to take the lead over analysis, but in fact precedes it only as a servant goes before his master to clear the path and light him on the way. The interval between the two is as wide as between empiricism and science, as between the understanding and the reason, or as between the finite and the infinite.--SYLVESTER, J. J. _Philosophic Magazine, Vol. 31 (1866), p. 521._ =1932.= Nature herself exhibits to us measurable and observable quantities in definite mathematical dependence; the conception of a function is suggested by all the processes of nature where we observe natural phenomena varying according to distance or to time. Nearly all the “known” functions have presented themselves in the attempt to solve geometrical, mechanical, or physical problems.--MERZ, J. T. _A History of European Thought in the Nineteenth Century (Edinburgh and London, 1903), p. 696._ =1933.= That flower of modern mathematical thought--the notion of a function.--MCCORMACK, THOMAS J. _On the Nature of Scientific Law and Scientific Explanation, Monist, Vol. 10 (1899-1900), p. 555._ =1934.= Fuchs. Ich bin von alledem so consterniert, Als würde mir ein Kreis im Kopfe quadriert.