Footnotes

[1]F. Cajori, History of the Logarithmic Slide Rule and Allied Instruments, New York, 1909, pp. 7-14, also Addenda i-vi.

[2]F. Cajori, “On the Invention of the Slide Rule,” in Colorado College Publication, Engineering Series Vol. 1, 1910. An abstract of this is given in Nature (London), Vol. 82, 1909, p. 267.

[3]F. Cajori, History etc., p. 14.

[4]Art. “Slide Rule” in the Penny Cyclopaedia and in the English Cyclopaedia [Arts and Sciences].

[5]Anthony Wood, Athenae oxonienses (Ed. P. Bliss), London, Vol. III, 1817, p. 423.

[6]The full title of the book which Wingate published on this subject in Paris is as follows:

Εἂν ἧς φιλεμαθὴς, ἕση ἥση πολυμαθὴς.

In tenui, sed nõ tenuis vsusve, laborne. |

Back of the title page is the announcement:

Notez que la Reigle de Proportion en toutes façons se vend à Paris chez Melchior Tauernier, Graueur & Imprimeur du Roy pour les Tailles douces, demeurant en l’Isle du Palais sur le Quay qui regarde la Megisserie à l’Espic d’or.

[7]The title-page of the edition of 1658 is as follows:

The Use of the Rule of Proportion in Arithmetick & Geometrie. First published at Paris in the French tongue, and dedicated to Monsieur, the then king’s onely Brother (now Duke of Orleance). By Edm. Wingate, an English Gent. And now translated into English by the Author. Whereinto is now also inserted the Construction of the same Rule, & a farther use thereof . . . 2nd edition inlarged and amended. London, 1658.

[8]Memories of the Life of that Learned Antiquary, Elias Ashmole, Esq.; Drawn up by himself by way of Diary. With Appendix of original Letters. Publish’d by Charles Burman, Esq., London, 1717, p. 23.

[9]Mathematical Tables, 1811, p. 36, and art. “Gunter’s Line” in his Phil. and Math. Dictionary, London, 1815.

[10]To the English Gentrie, and all others studious of the Mathematicks, which shall bee readers hereof. The just Apologie of Wil: Ovghtred, against the slaunderous insimulations of Richard Delamain, in a Pamphlet called Grammelogia, or the Mathematicall Ring, or Mirifica logarithmorum projectio circularis. We shall refer to this document as Epistle. It was published without date in 32 unnumbered pages of fine print, and was bound in with Oughtred’s Circles of Proportion, in the editions of 1633 and 1639. In the 1633 edition it is inserted at the end of the volume just after the Addition vnto the Vse of the Instrument etc., and in that of 1639 immediately after the preface. It was omitted from the Oxford edition of 1660. The Epistle was also published separately. There is a separate copy in the British Museum, London. Aubrey, in his Brief Lives, edited by A. Clark, Vol. II, Oxford, 1898, p. 113, says quaintly, “He writt a stitch’t pamphlet about 163(?4) against . . . Delamaine.”

[11]Thomas Browne is mentioned by Stone in his Mathematical Instruments, London 1723, p. 16. See also Cajori, History of the Slide Rule, New York, 1909, p. 15.

[12]The Description and Use of a Joynt-Rule: . . . also the use of Mr. White’s Rule for measuring of Board and Timber, round and square; With the manner of Vsing the Serpentine-line of Numbers, Sines, Tangents, and Versed Sines. By J. Brown, Philom., London, 1661.

[13]A Collection of Centers and Useful Proportions on the Line of Numbers, by John Brown, 1662(?), 16 pages; Description and Use of the Triangular Quadrant, by John Brown, London, 1671; Wingate’s Rule of Proportion in Arithmetick and Geometry: or Gunter’s Line. Newly rectified by Mr. Brown and Mr. Atkinson, Teachers of the Mathematicks, London, 1683; The Description and Use of the Carpenter’s-Rule: Together with the Use of the Line of Numbers commonly call’d Gunter’s-Line, by John Brown, London, 1704.

[14]William Leybourn, op. cit., pp. 129, 130, 132, 133.

[15]James Atkinson’s edition of Andrew Wakely’s The Mariners Compass Rectified, London, 1694 [Wakely’s preface dated 1664, Atkinson’s preface, 1693]. Atkinson adds An Appendix containing Use of Instruments most useful in Navigation. Our quotation is from this Appendix, p. 199.

[16]R. Delamain, The Making, Description, and Use of a small portable Instrument . . . called a Horizontall Quadrant, etc., London, 1631.

[17]Oughtred’s description of his circular slide rule of 1632 and his rectilinear slide rule of 1633, as well as a drawing of the circular slide rule, are reproduced in Cajori’s History of the Slide Rule, Addenda, pp. ii-vi.

[18]The full title of the Grammelogia I is as follows:

[19]Grammelogia III is the same as Grammelogia I, except for the addition of an appendix, entitled:

. . . The next line or two of this title-page which probably contained the date of publication, were cut off by the binder in trimming the edges of this and several other pamphlets for binding into one volume.

[20]Grammelogia IV has two title pages. The first is Mirifica Logarithmoru’ Projectio Circularis. There follows a diagram of a circular slide rule, with the inscription within the innermost ring: Nil Finis, Motvs, Circvlvs vllvs Habet. The second title page is as follows:

Grammelogia | Or, the Mathematicall Ring. | Extracted from the Logarythmes, and projected Circular: Now published in the | inlargement thereof unto any magnitude fit for use: shewing any reason- | able capacity that hath not Arithmeticke how to resolve and worke, | all ordinary operations of Arithmeticke: | And those that are most difficult with greatest facilitie, the extracti- | on of Rootes, the valuation of Leases, &c. the measuring of Plaines and Solids, | with the resolution of Plaine and Sphericall Triangles applied to the | Practicall parts of Geometrie, Horologographie, Geographie | Fortification, Navigation, Astronomie, &c. | And that onely by an ocular inspection, and a Circular motion, Invented and first published, by R. Delamain, Teacher, and Student of the Mathematicks. | Naturae secreta tempus aperit. |

There is no date. There follows the diagram of a second circular slide rule, with the inscription within the innermost ring: Typus proiectionis Annuli adaucti vt in Conslusione Lybri praelo commissi, Anno 1630 promisi. There are numerous drawings in the Grammelogia, all of which, excepting the drawings of slide rules on the engraved title-pages of Grammelogia IV and V, were printed upon separate pieces of paper and then inserted by hand into the vacant spaces on the printed pages reserved for them. Some drawings are missing, so that the Bodleian Grammelogia IV differs in this respect slightly from the copy in the British Museum and from the British Museum copy of Grammelogia V.

[21]Epistle, p. (8).

[22]Aubrey, op. cit., Vol. II., p. 111.

[23]Rigaud, Correspondence of Scientific Men during the 17th Century, Vol. I, Oxford, 1841, p. 11.

[24]Dictionary of National Biography, Art. “Delamain, Richard.” See also Rev. Charles J. Robinson, Taylors’ School, from A.D. 1562 to 1874, Vol. I, 1882, p. 151; Journal of the House of Commons, Vol. IV., p. 197b; Sixth Report of the Royal Commission on Historical Manuscripts, Part I, Report and Appendix, London, 1877. In this Appendix, p. 82, we read the following:

Oct. 22 [1645] Petition of Sarah Delamain, relict of Richard Delamain. Petitioner’s husband was servant to the King, and one of His Majesty’s engineers for the fortification of the kingdom, and his tutor in mathematical arts; but upon the breaking out of the war he deserted the Court, and was called by the State to several employments, in fortifying the towns of Northampton, Newport, and Abingdon; and was also abroad with the armies as Quartermaster-General of the Foot, and therein died. Petitioner is left a disconsolate widow with ten children, the four least of whom are now afflicted with sickness, and petitioner has nothing left to support them. There are several considerable sums of money due to the petitioner, as well from the King as the State. Prays that she may have some relief amongst other widows. See L. J., VII. 6. 657.

[25]Anthony Wood, Athenae Oxonienses (Edition Bliss) Vol. IV., London, 1820, p. 34.

[26]The New Artificial Gauging Line or Rod: together with rules concerning the use thereof: Invented and written by WILLIAM OUGHTRED, etc., London, 1633. The copy we have seen is in the Bodleian Library, Oxford. The book is small sized and has 40 pages.

[27]Oughtred, op. cit., p. 11.

[28]S. J. Rigaud, Correspondence of Scientific Men of the 17th Century, Oxford, Vol. I, 1841, p. 17.

[29]Rigaud, loc. cit., p. 22.

[30]Rigaud, loc. cit., pp. 30, 31.

[31]Oughtred, An Addition vnto the Vse of the Instrument called the Circles of Proportion, London, 1633, p. 63.

[32]F. Cajori, History of the Slide Rule, New York, 1909, pp. 16-22, Addenda, pp. vi-ix.

[33]W. Leybourn, op. cit., 1673, Preface, and pp. 128-29.

[34]Cajori op. cit., Addenda, p. ix.

[35]William Leybourn, op. cit., 1673, p. 35.

[36]See Cajori, op. cit., pp. 20, 28, Addenda, p. ix.

[37]See F. Cajori, “A Note on the History of the Slide Rule,” Bibliotheca mathematica, 3 F., Vol. 10, pp. 161-163.

[38]John Atkinson, op. cit., 1694, p. 204.

[39]Probably the oldest slide rule now in existence is owned by St. John’s College, Oxford, and is in the form of a brass disc, 1 ft. 6 in. in diameter. It was exhibited along with other instruments in May, 1919. According to the Catalogue of a Loan Exhibition of Early Scientific Instruments in Oxford, opened May 16, 1919, the instrument is inscribed with the name of the maker (“Elias Allen fecit”) and with the name of the donor, Georgius Barkham. It is dated 1635, which is only three years after the first publication of Oughtred’s description of his circular slide rule. It is stated in the Catalogue: “Unfortunately all the movable parts but the base-plate and a couple of thumb-screws are missing. The face of the instrument is engraved with Oughtred’s Horizontal Instrument. The back is engraved with eleven Circles of Proportion as described in Arthur Haughton’s book, a copy of which was presented to St. John’s College by George Barkham, to explain the use of the instrument.” As Arthur Haughton’s Oxford edition of Oughtred’s Circles of Proportion did not appear until 1660, it would seem that the instrument was probably not presented to the College before 1660. As far as is known, the next oldest slide rule is of the year 1654, kept in the South Kensington Museum, London, and is described in Nature of March 5, 1914. It is a rectilinear rule, “of boxwood, well made, and bound together with brass at the two ends. It is of the square type, a little more than 2 ft. in length, and bears the logarithmic lines first described by Edmund Gunter. Of these, the num, sin and tan lines are arranged in pairs, identical and contiguous, one line in each pair being on the fixed part, and the other on the slide.” The instrument is inscribed, “Made by Robert Bissaker for T. W., 1654.” Nowhere else have we seen reference to Robert Bissaker. His slide rule seems to antedate the “Whites rule” mentioned above. [This foot-note was added on October 15, 1919.]