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.
[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:
Gram̄elogia | or, | The Mathematicall Ring. | Shewing (any
reasonable Capacity that hath | not Arithmeticke) how to resolve and
worke | all ordinary operations of Arithmeticke. | And those which are
most difficult with greatest | facilitie: The extraction of Roots, the
valuation of | Leases, &c. The measuring of Plaines | and Solids. | With
the resolution of Plaine and Sphericall | Triangles. | And that onely by
an Ocular Inspection, | and a Circular Motion. | Naturae secreta tempus
aperit. | London printed by John Haviland, 1630.
[19]Grammelogia III is the same as Grammelogia I, except for the addition
of an appendix, entitled:
De la Mains | Appendix | Vpon his | Mathematicall | Ring. Attribuit
nullo (praescripto tempore) vitae | vsuram nobis ingeniique Deus. |
London, |
. . . 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.]