--DE MORGAN, A. _On the Study and Difficulties of Mathematics (Chicago, 1902), p. 231._ =1813.= Geometry is a true natural science:--only more simple, and therefore more perfect than any other. We must not suppose that, because it admits the application of mathematical analysis, it is therefore a purely logical science, independent of observation. Every body studied by geometers presents some primitive phenomena which, not being discoverable by reasoning, must be due to observation alone.--COMTE, A. _Positive Philosophy [Martineau], Bk. 1, chap. 3._ =1814.= Geometry in every proposition speaks a language which experience never dares to utter; and indeed of which she but half comprehends the meaning. Experience sees that the assertions are true, but she sees not how profound and absolute is their truth. She unhesitatingly assents to the laws which geometry delivers, but she does not pretend to see the origin of their obligation. She is always ready to acknowledge the sway of pure scientific principles as a matter of fact, but she does not dream of offering her opinion on their authority as a matter of right; still less can she justly claim to herself the source of that authority.--WHEWELL, WILLIAM. _The Philosophy of the Inductive Sciences, Part 1, Bk. 1, chap. 6, sect. 1 (London, 1858)._ =1815.= Geometry is the science created to give understanding and mastery of the external relations of things; to make easy the explanation and description of such relations and the transmission of this mastery.--HALSTED, G. B. _Proceedings of the American Association for the Advancement of Science (1904), p. 359._ =1816.= A mathematical point is the most indivisible and unique thing which art can present.--DONNE, JOHN. _Letters, 21._ =1817.= It is certain that from its completeness, uniformity and faultlessness, from its arrangement and progressive character, and from the universal adoption of the completest and best line of argument, Euclid’s “Elements” stand pre-eminently at the head of all human productions. In no science, in no department of knowledge, has anything appeared like this work: for upward of 2000 years it has commanded the admiration of mankind, and that period has suggested little toward its improvement.--KELLAND, P. _Lectures on the Principles of Demonstrative Mathematics (London, 1843), p. 17._