He who seeks for immediate practical use in the pursuit of science, may be reasonably sure, that he will seek in vain. Complete knowledge and complete understanding of the action of forces of nature and of the mind, is the only thing that science can aim at. The individual investigator must find his reward in the joy of new discoveries, as new victories of thought over resisting matter, in the esthetic beauty which a well-ordered domain of knowledge affords, where all parts are intellectually related, where one thing evolves from another, and all show the marks of the mind’s supremacy; he must find his reward in the consciousness of having contributed to the growing capital of knowledge on which depends the supremacy of man over the forces hostile to the spirit.--HELMHOLTZ, H. _Vorträge und Reden (Braunschweig, 1884), Bd. 1, p. 142._ =1546.= When the time comes that knowledge will not be sought for its own sake, and men will not press forward simply in a desire of achievement, without hope of gain, to extend the limits of human knowledge and information, then, indeed, will the race enter upon its decadence.--HUGHES, C. E. _Quoted in D. E. Smith’s Teaching of Geometry (Boston, 1911), p. 9._ =1547.= [In the Opus Majus of Roger Bacon] there is a chapter, in which it is proved by reason, that all sciences require mathematics. And the arguments which are used to establish this doctrine, show a most just appreciation of the office of mathematics in science. They are such as follows: That other sciences use examples taken from mathematics as the most evident:--That mathematical knowledge is, as it were, innate to us, on which point he refers to the well-known dialogue of Plato, as quoted by Cicero:--That this science, being the easiest, offers the best introduction to the more difficult:--That in mathematics, things as known to us are identical with things as known to nature:--That we can here entirely avoid doubt and error, and obtain certainty and truth:--That mathematics is prior to other sciences in nature, because it takes cognizance of quantity, which is apprehended by intuition (_intuitu intellectus_). “Moreover,” he adds, “there have been found famous men, as Robert, bishop of Lincoln, and Brother Adam Marshman (de Marisco), and many others, who by the power of mathematics have been able to explain the causes of things; as may be seen in the writings of these men, for instance, concerning the Rainbow and Comets, and the generation of heat, and climates, and the celestial bodies.”--WHEWELL, W. _History of the Inductive Sciences (New York, 1894), Vol. 1, p. 519. Bacon, Roger: Opus Majus, Part 4, Distinctia Prima, cap. 3._