=1302.= In mathematics we see the conscious logical activity of our mind in its purest and most perfect form; here is made manifest to us all the labor and the great care with which it progresses, the precision which is necessary to determine exactly the source of the established general theorems, and the difficulty with which we form and comprehend abstract conceptions; but we also learn here to have confidence in the certainty, breadth, and fruitfulness of such intellectual labor. --HELMHOLTZ, H. _Vorträge und Reden, Bd. 1 (Braunschweig, 1896), p. 176._ =1303.= Mathematical demonstrations are a logic of as much or more use, than that commonly learned at schools, serving to a just formation of the mind, enlarging its capacity, and strengthening it so as to render the same capable of exact reasoning, and discerning truth from falsehood in all occurrences, even in subjects not mathematical. For which reason it is said, the Egyptians, Persians, and Lacedaemonians seldom elected any new kings, but such as had some knowledge in the mathematics, imagining those, who had not, men of imperfect judgments, and unfit to rule and govern.--FRANKLIN, BENJAMIN. _Usefulness of Mathematics; Works (Boston, 1840), Vol. 2, p. 68._ =1304.= The mathematical conception is, from its very nature, abstract; indeed its abstractness is usually of a higher order than the abstractness of the logician.--CHRYSTAL, GEORGE. _Encyclopedia Britannica (Ninth Edition), Article “Mathematics.”_ =1305.= Mathematics, that giant pincers of scientific logic.... --HALSTED, G. B. _Science (1905), p. 161._ =1306.= Logic has borrowed the rules of geometry without understanding its power.... I am far from placing logicians by the side of geometers who teach the true way to guide the reason.... The method of avoiding error is sought by every one. The logicians profess to lead the way, the geometers alone reach it, and aside from their science there is no true demonstration. --PASCAL. _Quoted by A. Rebière: Mathématiques et Mathématiciens (Paris, 1898), pp. 162-163._ =1307.= Mathematics, like dialectics, is an organ of the higher sense, in its execution it is an art like eloquence. To both nothing but the form is of value; neither cares anything for content. Whether mathematics considers pennies or guineas, whether rhetoric defends truth or error, is perfectly immaterial to either.--GOETHE. _Sprüche in Prosa, Natur IV, 946._