History of Civilization in England (New York, 1891), Vol. 2, p. 342.
[1811]. It is the glory of geometry that from so few principles, fetched from without, it is able to accomplish so much.—Newton.
Philosophiae Naturalis Principia Mathematica, Praefat.
[1812]. Geometry is the application of strict logic to those properties of space and figure which are self-evident, and which therefore cannot be disputed. But the rigor of this science is carried one step further; for no property, however evident it may be, is allowed to pass without demonstration, if that can be given. The question is therefore to demonstrate all geometrical truths with the smallest possible number of assumptions.—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).