William Oughtred

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.

44

A. von Braunmühl, Geschichte der Trigonometrie, 2. Teil, Leipzig, 1903, pp. 42, 91.

45

H. Hankel, Geschichte der Mathematik in Alterthum und Mittelalter, Leipzig, 1874, pp. 369, 370.

46

M. Cantor, Vorlesungen über Geschichte der Mathematik, II, 1900, pp. 640, 641.

47

This matter has been discussed in a paper by F. Cajori, “A History of the Arithmetical Methods of Approximation, etc., Colorado College Publication, General Series No. 51, 1910, pp. 182-84. Later this subject was again treated by G. Eneström in Bibliotheca mathematica, 3. Folge, Vol. XI, 1911, pp. 234, 235.

48

See F. Cajori, op. cit., p. 193.

49

See William Oughtred’s Key of the Mathematicks, London, 1694, pp. 173-75, tract, “Of the Resolution of the Affected Equations,” or any edition of the Clavis after the first.

50

A. De Morgan, op. cit., p. 451; 2d ed., Vol. II, p. 303.

51

See F. Cajori, History of the Logarithmic Slide Rule, New York, 1909, pp. 7-14, Addenda, p. ii.

52

Rigaud, op. cit., Vol. I, p. 12.

53

The New Artificial Gauging Line or Rod: together with rules concerning the use thereof: Invented and written by William Oughtred, London, 1633.

54

W. Oughtred, Apologeticall Epistle, p. 13.

55

Quarterly Journal of Pure and Applied Mathematics, Vol. XLVI, (1915), p. 169. In this article Glaisher republishes the “Appendix” in full.

56

Aubrey, op. cit., Vol. II, 1898, p. 108.

57

Wood’s Athenae Oxonienses (ed. P. Bliss), Vol. IV, 1820, p. 247.