[30]See F. Cajori, “The Cross × as a Symbol of Multiplication,” in Nature, Vol. XCIV (1914), p. 363. [31]See Elementi decimi Euclidis declaratio, 1652, p. 2. [32]See Johannis Wallisii Operum mathematicorum pars prima, Oxonii, 1657, p. 247. [33]Clavis of 1631, chap. xix, sec. 5, p. 50. [34]We have noticed the representation of known quantities by consonants and the unknown by vowels in Wingate’s Arithmetick made easie, edited by John Kersey, London, 1650, algebra, p. 382; and in the second part, section 19, of Jonas Moore’s Arithmetick in two parts, London, 1660, Moore suggests as an alternative the use of z, y, x, etc., for the unknowns. The practice of representing unknowns by vowels did not spread widely in England. [35]Philosophical Transactions, Vol. XIX, No. 231, London, p. 652. [36]Ibid., Vol. XIX, p. 56. [37]There are two title-pages to the edition of 1632. The first title-page is as follows: The Circles of Proportion and The Horizontall Instrument. Both invented, and the vses of both Written in Latine by Mr. W. O. Translated into English: and set forth for the publique benefit by William Forster. London. Printed for Elias Allen maker of these and all other mathematical Instruments, and are to be sold at his shop over against St. Clements church with out Temple-barr. 1632. T. Cecill Sculp. In 1633 there was added the following, with a separate title-page: An addition vnto the Vse of the Instrvment called the Circles of Proportion. . . . . London, 1633, this being followed by Oughtred’s To the English Gentrie etc. In the British Museum there is a copy of another impression of the Circles of Proportion, dated 1639, with the Addition vnto the Vse of the Instrument etc., bearing the original date, 1633, and with the epistle, To the English Gentrie, etc., inserted immediately after Forster’s dedication, instead of at the end of the volume. [38]The complete title of the English edition is as follows: Trigonometrie, or, The manner of calculating the Sides and Angles of Triangles, by the Mathematical Canon, demonstrated. By William Oughtred Etonens. And published by Richard Stokes Fellow of Kings Colledge in Cambridge, and Arthur Haughton Gentleman. London, Printed by R. and W. Leybourn, for Thomas Johnson at the Golden Key in St. Pauls Church-yard. M.DC.LVII. [39]Jer. Collier, The Great Historical, Geographical, Genealogical and Poetical Dictionary, Vol. II, London, 1701, art. “Oughtred.” [40]Rigaud op. cit., Vol. I, p. 82. [41]A. De Morgan, Budget of Paradoxes, London, 1872, p. 451; 2d ed., Chicago, 1915, Vol. II, p. 303. [42]E. Gunter, Description and Use of the Sector, the Crosse-staffe and other Instruments, London, 1624, second book, p. 31. [43]F. Cajori, “On the History of a Notation in Trigonometry,” Nature, Vol. XCIV, 1915, pp. 642, 643.