=1524.= All applications of mathematics consist in extending the empirical knowledge which we possess of a limited number or region of accessible phenomena into the region of the unknown and inaccessible; and much of the progress of pure analysis consists in inventing definite conceptions, marked by symbols, of complicated operations; in ascertaining their properties as independent objects of research; and in extending their meaning beyond the limits they were originally invented for,--thus opening out new and larger regions of thought.--MERZ, J. T. _History of European Thought in the 19th Century (Edinburgh and London, 1903), Vol. 1, p. 698._ =1525.= All the effects of nature are only mathematical results of a small number of immutable laws.--LAPLACE. _A Philosophical Essay on Probabilities [Truscott and Emory] (New York, 1902), p. 177; Oeuvres, t. 7, p. 139._ =1526.= What logarithms are to mathematics that mathematics are to the other sciences.--NOVALIS. _Schriften (Berlin, 1901), Teil 2, p. 222._ =1527.= Any intelligent man may now, by resolutely applying himself for a few years to mathematics, learn more than the great Newton knew after half a century of study and meditation. --MACAULAY. _Milton; Critical and Miscellaneous Essays (New York, 1879), Vol. 1, p. 13._ =1528.= In questions of science the authority of a thousand is not worth the humble reasoning of a single individual.--GALILEO. _Quoted in Arago’s Eulogy on Laplace; Smithsonian Report, 1874, p. 164._ =1529.= Behind the artisan is the chemist, behind the chemist a physicist, behind the physicist a mathematician.--WHITE, W. F. _Scrap-book of Elementary Mathematics (Chicago, 1908), p. 217._ =1530.= The advance in our knowledge of physics is largely due to the application to it of mathematics, and every year it becomes more difficult for an experimenter to make any mark in the subject unless he is also a mathematician.--BALL, W. W. R. _History of Mathematics (London, 1901), p. 503._