As one Who vers’d in geometric lore, would fain Measure the circle; and, though pondering long And deeply, that beginning, which he needs, Finds not; e’en such was I, intent to scan The novel wonder, and trace out the form, How to the circle fitted, and therein How plac’d: but the flight was not for my wing; --DANTE. _Paradise [Carey] Canto 33, lines 122-129._ =1859.= If geometry were as much opposed to our passions and present interests as is ethics, we should contest it and violate it but little less, notwithstanding all the demonstrations of Euclid and of Archimedes, which you would call dreams and believe full of paralogisms; and Joseph Scaliger, Hobbes, and others, who have written against Euclid and Archimedes, would not find themselves in such a small company as at present.--LEIBNITZ. _New Essays concerning Human Understanding [Langley], Bk. 1, chap. 2, sect. 12._ =1860.= I have no fault to find with those who teach geometry. That science is the only one which has not produced sects; it is founded on analysis and on synthesis and on the calculus; it does not occupy itself with probable truth; moreover it has the same method in every country.--FREDERICK THE GREAT. _Oeuvres (Decker), t. 7, p. 100._ =1861.= There are, undoubtedly, the most ample reasons for stating both the principles and theorems [of geometry] in their general form, .... But, that an unpractised learner, even in making use of one theorem to demonstrate another, reasons rather from particular to particular than from the general proposition, is manifest from the difficulty he finds in applying a theorem to a case in which the configuration of the diagram is extremely unlike that of the diagram by which the original theorem was demonstrated. A difficulty which, except in cases of unusual mental powers, long practice can alone remove, and removes chiefly by rendering us familiar with all the configurations consistent with the general conditions of the theorem.--MILL, J. S. _System of Logic, Bk. 2, chap. 3, sect. 3._