Mention should be made of trigonometric symbols used even earlier than any of the preceding, in “An Appendix to the Logarithmes, shewing the practise of the Calculation of Triangles, etc.,” printed in Edward Wright’s edition of Napier’s A Description of the Admirable Table of Logarithmes, London, 1618. We referred to this “Appendix” in tracing the origin of the sign ×. It contains, on p. 4, the following passage: “For the Logarithme of an arch or an angle I set before (s), for the antilogarithme or compliment thereof (s*) and for the Differential (t).” In further explanation of this rather unsatisfactory passage, the author (Oughtred?) says, “As for example: sB+BC=CA. that is, the Logarithme of an angle B. at the Base of a plane right-angled triangle, increased by the addition of the Logarithm of BC, the hypothenuse thereof, is equall to the Logarithme of CA the cathetus.” Here “logarithme of an angle B” evidently means “log sin B,” just as with Napier, “Logarithms of the arcs” signifies really “Logarithms of the sines of the angles.” In Napier’s table, the numbers in the column marked “Differentiae” signify log sine minus log cosine of an angle; that is, the logarithms of the tangents. This explains the contraction (t) in the “Appendix.” The conclusion of all this is that as early as 1618 the signs s, s*, t were used for sine, cosine, and tangent, respectively. John Speidell, in his Breefe Treatise of Sphaericall Triangles, London, 1627, uses Si. for sine, T. and Tan for tangent, Se. for secant, Si. Co. for cosine, Se. Co. for cosecant, T. Co. for cotangent. The innovation of designating the sides and angles of a triangle by A, B, C, and a, b, c, so that A was opposite a, B opposite b, and C opposite c, is attributed to Leonard Euler (1753), but was first used by Richard Rawlinson of Queen’s College, Oxford, sometimes after 1655 and before 1668. Oughtred did not use Rawlinson’s notation.[43] In trigonometry English writers of the first half of the seventeenth century used contractions more freely than their continental contemporaries; even more freely, indeed, than English writers of a later period. Von Braunmühl, the great historian of trigonometry, gives Oughtred much praise for his trigonometry, and points out that half a century later the army of writers on trigonometry had hardly yet reached the standard set by Oughtred’s analysis.[44] Oughtred must be credited also with the first complete proof that was given to the first two of “Napier’s analogies.” His trigonometry contains seven-place tables of sines, tangents, and secants, and six-place tables of logarithmic sines and tangents; also seven-place logarithmic tables of numbers. At the time of Oughtred there was some agitation in favor of a wider introduction of decimal systems. This movement is reflected in those tables which contain the centesimal division of the degree, a practice which is urged for general adoption in our own day, particularly by the French.