Florian Cajori - On the History of Gunter's Scale and the Slide Rule during the Seventeenth Century

Grammelogia IV answers fully to the description of Delamain’s pamphlet contained in Oughtred’s Epistle . It was brought out in 1632 or 1633, for what appears to be the latest part of it contains a reference (page 99) to the Grammelogia I (1630) as “being now more then two yeares past.” Moreover, it refers to Oughtred’s Circles of Proportion , 1632, and Oughtred’s reply in the Epistle was bound in the Circles of Proportion having the Addition of 1633. For convenience of reference we number the two title-pages of Grammelogia IV , “page (1)” and “page (2),” as is done by Oughtred in his Epistle . Grammelogia IV contains, then, 113 pages. The page numbers which we assign will be placed in parentheses, to distinguish them from the page numbers which are printed in Grammelogia IV . The pages (44) – (65) are the same as the pages 1-22, and the pages (68) – (83) are the same as the pages 53-68. Thus only thirty-eight pages have page numbers printed on them. The pages (67) and (83) are identical in wording, except for some printer’s errors; they contain verses in praise of the Ring , and have near the bottom the word “Finis.” Also, pages (22) and (23) are together identical in wording with page (113), which is set up in finer type, containing an advertisement of a part of Grammelogia IV explaining the mode of graduating the circular rules. There are altogether six parts of Grammelogia IV which begin or end by an address to the reader, thus: “To the Reader,” “Courteous Reader,” or “To the courteous and benevolent Reader.,” namely the pages (8), (22), (68), (89), (90), (108). In his Epistle (page 2), Oughtred characterizes the make up of the book in the following terms:

In reading it.. I met with such a patchery and confusion of disjoynted stuffe, that I was striken with a new wonder, that any man should be so simple, as to shame himselfe to the world with such a hotch-potch.

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

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.

F. Cajori, History etc., p. 14.

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

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

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

L’Vsage | de la | Reigle de | Proportion | en l’Arithmetique & | Geometrie. | Par Edmond Vvingate, | Gentil-homme Anglois. |

Εἂν ἧς φιλεμαθὴς, ἕση ἥση πολυμαθὴς.

In tenui, sed nõ tenuis vsusve, laborne. |

A Paris, | Chez Melchior Mondiere, | demeurant en l’Isle du Palais, | à la | ruë de Harlay aux deux Viperes. | M. DC. XXIV. | Auec Priuilege du Roy. |

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.

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.

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.

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

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.”

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.

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.

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.

William Leybourn, op. cit. , pp. 129, 130, 132, 133.

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.