[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 Compa.s.s 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 t.i.tle 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, ent.i.tled:

De la Mains

Appendix

Vpon his

Mathematicall

Ring. Attribuit nullo (praescripto tempore) vitae

vsuram n.o.bis ingeniique Deus.

London,

... The next line or two of this t.i.tle-page which probably contained the date of publication, were cut off by the binder in tr.i.m.m.i.n.g the edges of this and several other pamphlets for binding into one volume.

[20]Grammelogia IV has two t.i.tle 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 t.i.tle 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 t.i.tle-pages of Grammelogia IV and V, were printed upon separate pieces of paper and then inserted by hand into the vacant s.p.a.ces 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 Ma.n.u.scripts, Part I, Report and Appendix, London, 1877. In this Appendix, p. 82, we read the following:

Oct. 22 [1645] Pet.i.tion of Sarah Delamain, relict of Richard Delamain.

Pet.i.tioner'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.

Pet.i.tioner is left a disconsolate widow with ten children, the four least of whom are now afflicted with sickness, and pet.i.tioner has nothing left to support them. There are several considerable sums of money due to the pet.i.tioner, 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 bra.s.s 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 bra.s.s 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.]