Trigonometry and Double Algebra (London, 1849), Bk. 1, chap. 1.
[1886]. Sin2φ is odious to me, even though Laplace made use of it; should it be feared that sinφ2 might become ambiguous, which would perhaps never occur, or at most very rarely when speaking of sin (φ2), well then, let us write (sinφ)2, but not sin2φ, which by analogy should signify sin(sinφ).—Gauss.
Gauss-Schumacher Briefwechsel, Bd. 3, p. 292; Bd. 4, p. 63.
[1887]. Perhaps to the student there is no part of elementary mathematics so repulsive as is spherical trigonometry.—Tait, P. G.
Encyclopedia Britannica, 9th Edition; Article “Quaternions”
[1888]. “Napier’s Rule of circular parts” is perhaps the happiest example of artificial memory that is known.—Cajori, F.
History of Mathematics (New York, 1897), p. 165.
[1889]. The analytical equations, unknown to the ancients, which Descartes first introduced into the study of curves and surfaces, are not restricted to the properties of figures, and to those properties which are the object of rational mechanics; they apply to all phenomena in general. There cannot be a language more universal and more simple, more free from errors and obscurities, that is to say, better adapted to express the invariable relations of nature.—Fourier.
Théorie Analytique de la Chaleur, Discours Préliminaire.
[1890]. It is impossible not to feel stirred at the thought of the emotions of men at certain historic moments of adventure and discovery—Columbus when he first saw the Western shore, Pizarro when he stared at the Pacific Ocean, Franklin when the electric spark came from the string of his kite, Galileo when he first turned his telescope to the heavens. Such moments are also granted to students in the abstract regions of thought, and high among them must be placed the morning when Descartes lay in bed and invented the method of co-ordinate geometry.—Whitehead, A. N.