Algebra, Part 2 (Edinburgh, 1889), Preface, p. 8.
[608]. The large collection of problems which our modern Cambridge books supply will be found to be almost an exclusive peculiarity of these books; such collections scarcely exist in foreign treatises on mathematics, nor even in English treatises of an earlier date. This fact shows, I think, that a knowledge of mathematics may be gained without the perpetual working of examples.... Do not trouble yourselves with the examples, make it your main business, I might almost say your exclusive business, to understand the text of your author.—Todhunter, Isaac.
Private Study of Mathematics; Conflict of Studies and other Essays (London, 1873), p. 74.
[609]. In my opinion the English excel in the art of writing text-books for mathematical teaching; as regards the clear exposition of theories and the abundance of excellent examples, carefully selected, very few books exist in other countries which can compete with those of Salmon and many other distinguished English authors that could be named.—Cremona, L.
Projective Geometry [Leudesdorf] (Oxford, 1885), Preface.
[610]. The solution of fallacies, which give rise to absurdities, should be to him who is not a first beginner in mathematics an excellent means of testing for a proper intelligible insight into mathematical truth, of sharpening the wit, and of confining the judgment and reason within strictly orderly limits.—Viola, J.
Mathematische Sophismen (Wien, 1864), Vorwort.
[611]. Success in the solution of a problem generally depends in a great measure on the selection of the most appropriate method of approaching it; many properties of conic sections (for instance) being demonstrable by a few steps of pure geometry which would involve the most laborious operations with trilinear co-ordinates, while other properties are almost self-evident under the method of trilinear co-ordinates, which it would perhaps be actually impossible to prove by the old geometry.—Whitworth, W. A.
Modern Analytic Geometry (Cambridge, 1866), p. 154.