[1829]. Geometry is nothing if it be not rigorous, and the whole educational value of the study is lost, if strictness of demonstration be trifled with. The methods of Euclid are, by almost universal consent, unexceptionable in point of rigour.—Smith, H. J. S.
Nature, Vol. 8, p. 450.
[1830]. To seek for proof of geometrical propositions by an appeal to observation proves nothing in reality, except that the person who has recourse to such grounds has no due apprehension of the nature of geometrical demonstration. We have heard of persons who convince themselves by measurement that the geometrical rule respecting the squares on the sides of a right-angles triangle was true: but these were persons whose minds had been engrossed by practical habits, and in whom speculative development of the idea of space had been stifled by other employments.—Whewell, William.
The Philosophy of the Inductive Sciences, (London, 1858), Part 1, Bk. 2, chap. 1, sect. 4.
[1831]. No one has ever given so easy and natural a chain of geometrical consequences [as Euclid]. There is a never-erring truth in the results.—De Morgan, A.
Smith’s Dictionary of Greek and Roman Biography and Mythology (London, 1902); Article “Eucleides”
[1832]. Beyond question, Egyptian geometry, such as it was, was eagerly studied by the early Greek philosophers, and was the germ from which in their hands grew that magnificent science to which every Englishman is indebted for his first lessons in right seeing and thinking.—Gow, James.
A Short History of Greek Mathematics (Cambridge, 1884), p. 131.