An Introduction to Mathematics (New York, 1911), p. 122.
[1891]. It is often said that an equation contains only what has been put into it. It is easy to reply that the new form under which things are found often constitutes by itself an important discovery. But there is something more: analysis, by the simple play of its symbols, may suggest generalizations far beyond the original limits.—Picard, E.
Bulletin American Mathematical Society, Vol. 2 (1905), p. 409.
[1892]. It is not the Simplicity of the Equation, but the Easiness of the Description, which is to determine the Choice of our Lines for the Constructions of Problems. For the Equation that expresses a Parabola is more simple than that that expresses the Circle, and yet the Circle, by its more simple Construction, is admitted before it.—Newton.
The Linear Constructions of Equations; Universal Arithmetic (London, 1769), Vol. 2, p. 468.
[1893]. The pursuit of mathematics unfolds its formative power completely only with the transition from the elementary subjects to analytical geometry. Unquestionably the simplest geometry and algebra already accustom the mind to sharp quantitative thinking, as also to assume as true only axioms and what has been proven. But the representation of functions by curves or surfaces reveals a new world of concepts and teaches the use of one of the most fruitful methods, which the human mind ever employed to increase its own effectiveness. What the discovery of this method by Vieta and Descartes brought to humanity, that it brings today to every one who is in any measure endowed for such things: a life-epoch-making beam of light [Lichtblick]. This method has its roots in the farthest depths of human cognition and so has an entirely different significance, than the most ingenious artifice which serves a special purpose.—Bois-Reymond, Emil du.
Reden, Bd. 1 (Leipzig, 1885), p. 287.
Song of the Screw.