On the History of Gunter's Scale and the Slide Rule During the Seventeenth Century

Chapter II: Front Matter (2)

Text size

“Shortly after my gift to Elias Allen, I chanced to meet with Richard
Delamain in the street (it was at Alhallontide) and as we walked together
I told him what an Instrument I had given to Master Allen, both of the
Logarithmes projected into circles, which being lesse then one foot
diameter would performe as much as one of Master Gunters Rulers of sixe
feet long: and also of the Prostaphaereses of the Plannets and second
motions. Such an invention have I said he: for now his intentions (that
is his ambition) beganne to worke: . . . But he saith, Then after my
comming home I sent him a sight of my projection drawne in past-board.
See how notoriously he jugleth without an Instrument. Then after: how
long after? a sight of my projection: of how much? More then seven weekes
after on December 23, he sent to mee the line of numbers onely set upon a
circle: . . . and so much onely he presented to his Majesty: but as for
Sine or tangent of his, there was not the least shew of any. Neither
could he give to Master Allen any direction for the composure of the
circles of his Ring, or for the division of them: as upon his oath Master
Allen will testify how hee misled him, and made him labour in vain above
three weeks together, until Master Allen himselfe found out his ignorance
and mistaking, which is more cleare then is possible with any impudence
to be outfaced.”

Oughtred makes a further statement (Epistle, p. (24)) as follows:

Delamain hearing that Brown with his Serpentine had another line by which
he could worke to minutes in the 90 degree of sines . . . gave the [his]
booke to Browne: who in thankfulnesse could not but gratify Delamain with
his Lines also: and teach him the use of them, but especially of the
great Line: with this caution on both sides, that one should not meddle
with the others invention. Two dayes after Delamain . . . because he had
found some things to be altered therin, . . . asked for the booke . . .
but as soone as he had got it in his hands he rent out all the middle
part with the two Schemes & put them up in his pocket & went his way . .
. and . . . laboureth to recall all the bookes he had given forth . . .
And shortly after this he got a new Printer (who was ignorant of his
former Schemes) to print him new: giving him an especiall charge of the
outermost line newly graven in the Plate, which indeed is Brownes very
line: and then altering his book . . .

This and other statements made by Oughtred seem damaging to Delamain’s reputation. But it is quite possible that Oughtred’s guesses as to Delamain’s motives are wrong. Moreover, some of Oughtred’s statements are not first hand knowledge with him, but mere hearsay. One may accept his first hand facts and still clear Delamain of wrong doing. There is always danger that rival claimants of an invention or discovery will proceed on the assumption that no one else could possibly have come independently upon the same devices that they themselves did; the history of science proves the opposite. Seldom is an invention of any note made by only one man. We do not feel competent to judge Delamain’s case. We know too little about him as a man. We incline to the opinion that the hypothesis of independent invention is the most plausible. At any rate, Delamain figures in the history of the slide rule as the publisher of the earliest book thereon and as an enthusiastic and skillful designer of slide rules.

The effect of this controversy upon interested friends was probably small. Doubtless few people read both sides. Oughtred says:[21] “this scandall . . . hath with them, to whom I am not knowne, wrought me much prejudice and disadvantage . .” Aubrey,[22] a friend of Oughtred, refers to Delamain “who was so sawcy to write against him” and remembers having seen “many yeares since, twenty or more good verses made” against Delamain. Another friend of Oughtred, William Robinson, who had seen some of Delamain’s publications, but not his Grammelogia IV, wrote in a letter to Oughtred, shortly before the appearance of the latter’s Epistle:

I cannot but wonder at the indiscretion of Rich. Delamain, who being
conscious to himself that he is but the pickpurse of another man’s wit,
would thus inconsiderately provoke and awake a sleeping lion . . . he
hath so weakly (though in my judgment, vaingloriously enough) commended
his own labour . . .[23]

Delamain presented King Charles I with one of his sun-dials, also with a manuscript and, later, with a printed copy of his book of 1630. A drawing of his improved slide rule was sent to the King and the Grammelogia IV is dedicated to him. The King must have been favorably impressed, for Delamain was appointed tutor to the King in mathematics. His widow petitioned the House of Lords in 1645 for relief; he had ten children.[24]

Anthony Wood states that Charles I, on the day of his execution, commanded his friend Thomas Herbert “to give his son the duke of York his large ring-sundial of silver, a jewel his maj. much valued.” Anthony Wood adds, “it was invented and made by Rich. Delamaine a very able mathematician, who projected it, and in a little printed book did shew its excellent use in resolving many questions in arithmetic and other rare operations to be wrought by it in the mathematics.”[25]

VI. OUGHTRED’S GAUGING LINE, 1633

It has not been generally known, hitherto, that Oughtred designed a rectilinear slide rule for gauging and published a description thereof in 1633.[26] In his Circles of Proportion, chapter IX, Oughtred had offered a closer approximation than that of Gunter for the capacity of casks. The Gauger of London expostulated with Oughtred for presuming to question anything that Gunter had written. The ensuing discussion led to an invitation extended by the Company of Vintners to the instrument maker Elias Allen to request Oughtred to design a gauging rod.[27] This he did, and Allen received an order for “threescore” instruments. On page 19 Oughtred describes his ‘Gauging Rod:’

It consisteth of two rulers of brasse about 32 ynches of length, which
also are halfe an ynch broad, and a quarter of an ynch thick . . . At one
end of both those rulers are two little sockets of brasse fastened on
strongly: by which the rulers are held together, and made to move one
upon another, and to bee drawne out unto any length, as occasion shall
require: and when you have them at the just length, there is upon one of
the sockets a long Scrue-pin to scrue them fast.

There are graduations on three sides of the rulers, one graduation being the logarithmic line of numbers. He says (p. 39), “the maner of computing the Gauge-divisions I have concealed.” W. Robinson, who was a friend of Oughtred, wrote him as follows:[28]

I have light upon your little book of artificial gauging, wherewith I am
much taken, but I want the rod, neither could I get a sight of one of
them at the time, because Mr. Allen had none left . . . I forgot to ask
Mr. Allen the price of one of them, which if not much I would have one of
them.” Oughtred annotated this passage thus: “Or in wood, if any be made
in wood by Thompson or any other.”

Another of Oughtred’s admirers, Sir Charles Cavendish, wrote, on February 11, 1635 thus:[29]

I thank you for your little book, but especially for the way of
calculating the divisions of your gauging rod. I wish, both for their own
sakes and yours, that the citizens were as capable of the acuteness of
this invention, as they are commonly greedy of gain, and then I doubt not
but they would give you a better recompense than I doubt now they will.

On April 20, 1638, we find Oughtred giving Elias Allen directions[30] “about the making of the two rulers.” As in 1633,[31] so now, Oughtred takes one ruler longer than the other. This 1633 instrument was used also as “a crosse-staffe to take the height of the Sunne, or any Starre above the Horizon, and also their distances.” The longer ruler was called staffe, the shorter transversarie. While in 1633 he took the lengths of the two in the ratio “almost 3 to 2,” in 1638, he took “the transversary three quarters of the staff’s length, . . . that the divisions may be larger.”

VII. OTHER SEVENTEENTH CENTURY SLIDE RULES

In my History of the Slide Rule I treat of Seth Partridge, Thomas Everard, Henry Coggeshall, W. Hunt and Sir Isaac Newton.[32] Of Partridge’s Double Scale of Proportion, London, I have examined a copy dated 1661, which is the earliest date for this book that I have seen. As far as we know, 1661 is the earliest date of publications on the slide rule, since Oughtred and Delamain. But it would not be surprising if the intervening 28 years were found not so barren as they seem at present. The 1661 and 1662 impressions of Partridge are identical, except for the date on the title-page. William Leybourn, who printed Partridge’s book, speaks in high appreciation of it in his own book.[33]

In 1661 was published also John Brown’s first book, Description and Use of a Joynt-Rule, previously mentioned. In Chapter XVIII he describes the use of “Mr. Whites rule” for the measuring of board and timber, round and square. He calls this a “sliding rule.” The existence, in 1661, of a “Whites rule” indicates activities in designing of which we know as yet very little. In his book of 1761, previously quoted, Brown gives a drawing of “White’s sliding rule” (p. 193); also a special contrivance of his own, as indicated by him in these words:

A further improvement of the Triangular Quadrant, as I have made it
several times, with a sliding Cover on the in-side, when made hollow, to
carry Ink, Pens, and Compasses; then on the sliding Cover, and Edges, is
put the Line of Numbers, according to Mr. White’s first Contrivance for
manner of operation; but much augmented, and made easie, by John Brown.

He gives no drawing of his “triangular quadrant,” hence his account of it is unsatisfactory. He explains the use of “gage-points.” His placing logarithmic lines on the edges of instrument boxes was outdone in oddity later by Everard who placed them on tobacco-boxes.[34] In Brown’s publication of 1704 the White slide rule is given again, “being as neat and ready a way as ever was used.” He tells also of a “glasier’s sliding rule.” William Leybourn explains in 1673 how Wingate’s double and triple lines for squaring and cubing, or square and cube root, can be used on slide rules.[35]

Beginning early in the history of the slide rule, when Oughtred designed his “gauging rod,” we notice the designing of rules intended for very special purposes. Another such contrivance, which enjoyed long popularity, was the Timber Measure by a Line, by Hen. Coggeshall, Gent., London, 1677, a booklet of 35 pages. Coggeshall says in his preface:

For what can be more ready and easie, then having set twelve to the
length, to see the Content exactly against the Girt or Side of the
Square. Whereas on Mr. Partridge’s Scale the Content is the Sixth Number,
which is far more troublesome then [even] with Compasses.

One line on Coggeshall’s rule begins with 4 and extends to 40, these numbers being the “Girt” (a quarter of the circumference), which in ordinary practice of measuring round timber lies between 4 inches and 40 inches. This “Girt line” slides “against the line of Numbers in two Lengths, to which it is exactly equal.” A second edition, 1682, shows some changes in the rule, as well as an enlargement and change of title of the book itself: A Treatise of Measures, by a Two-foot Rule, by H. C. Gent, London, 1682. In this, the description of the rule is given thus:

There are four Lines on each flat of this Rule; two next the outward
edges, which are Lines of Measure; and two next the inward edges, which
are Lines of Proportion. On one flat, next the inward edges, is the
Square-line [Girt-line in round timber measurement] with the Line of
Numbers his fellow. Next the outward, a Line of Inches divided into
Halfs, Quarters, and Half-Quarters; from 1 to 12 on one Rule; and from 12
to 24 on the other. On the other flat, next the inward edges, is the
double Scale of Numbers [for solving proportions]. Next the outward on
one Rule a Line of Inches divided each into ten parts; and this for
gauging, etc. On the other a foot divided into 100 parts.

Later further changes were introduced in Coggeshall’s rule.[36]

It is worthy of note that Coggeshall’s slide rule book, The Art of Practical Measuring, was reviewed in the Acta eruditorum, anno 1691, p. 473; hence Leupold’s description[37] of the rectilinear slide rule in his Theatrum arithmetico-geometricum, Leipzig, 1727, Cap. XIII, p. 71, is not the earliest reference to the rectilinear rule found in German publications. The above date is earlier even than Biler’s reference to a circular slide rule in his Descriptio instrumenti mathematici universalis of 1696.

Two noted slide rules for gauging were described by Tho. Everard, Philomath, in his Stereometry made easie, London, 1684. He designates his lines by the capital letters A, B, C, D, E. On the first instrument, A on the rule, and B and C on the slide, have each two radiuses of numbers, D has only one, while E has three. The second rule is described in an Appendix; it is one foot long, with two slides enabling the rule to be extended to 3 feet.

Everard’s instruments were made in London by Isaac Carver who, soon after, himself wrote a sixteen-page Description and Use of a New Sliding Rule, projected from the Tables in the Gauger’s Magazine, London, 1687, which was “printed for William Hunt” and bound in one volume with a book by Hunt, called The Gauger’s Magazine, London, 1687. This appears to be the same William Hunt who later brought out descriptions of his own of slide rules. The instrument described by Carver “consists of three pieces, two whereof are moveable to be drawn out till the whole be 36 inches long.” It has several non-logarithmic graduations, together with logarithmic lines marked A, B, C, D, of which A, B, C are “double lines,” and D a “single line” used for squares and square roots. It is designed for the determination of the vacuity of a “spheroidal cask lying,” a “spheroidal cask standing,” and a “parabolical cask lying.”

Another seventeenth century writer on the slide rule is John Atkinson, whom we have mentioned earlier. He says:[38] “The Lines of Numbers, Sines and Tangents, are set double, that is, one on each side, as the middle piece slides: which middle piece is so contrived, to slip to and fro easily, to slide out, and to be put in any side uppermost, in order to bring those Lines together (or against one another) most proper for solving the Question, wrought by Sliding-Gunter.”

The data presented in this article show that, while the earliest slide rules were of the circular type, the later slide rules of the seventeenth century were of the rectilinear type.[39]

January 12, 1915.

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.]

UNIVERSITY OF CALIFORNIA PUBLICATIONS

Note.—The University of California Publications are offered in exchange for the publication of learned societies and institutions, universities and libraries. Complete lists of all the publications of the University will be sent upon request. For sample copies, lists of publications or other information, address the Manager of the University of California Press, Berkeley, California, U. S. A. All matter sent in exchange should be addressed to The Exchange Department, University Library, Berkeley, California, U. S. A.

MATHEMATICS.—Mellen W. Haskell, Editor. Price per volume, $5.00.

Cited as Univ. Calif. Publ. Math.

Vol. 1. 1. On Numbers which Contain no Factors of the Form
p(kp+1), by Henry W. Stager. Pp. 1-26. May, 1912 $0.50

2. Constructive Theory of the Unicursal Plane Quartic by
Synthetic Methods, by Annie Dale Biddle. Pp. 27-54, 31
text-figures. September, 1912 .50

3. A Discussion by Synthetic Methods of Two Projective Pencils of
Conics, by Baldwin Munger Woods. Pp. 55-85. February, 1913 .50

4. A Complete Set of Postulates for the Logic of Classes
Expressed in Terms of the Operation “Exception”, and a
Proof of the Independence of a Set of Postulates due to Del
Ré, by B. A. Bernstein. Pp. 87-96. May, 1914 .10

5. On a Tabulation of Reduced Binary Quadratic Forms of a
Negative Determinant, by Harry N. Wright. Pp. 97-114. June,
1914 .20

6. The Abelian Equations of the Tenth Degree Irreducible in a
Given Domain of Rationality, by Charles G. P. Kuschke. Pp.
115-162. June, 1914 .50

7. Abridged Tables of Hyperbolic Functions, by F. E. Pernot.
Pp. 163-169. February, 1915 .10

8. A List of Oughtred’s Mathematical Symbols, with Historical
Notes, by Florian Cajori. Pp. 171-186. February, 1920 .25

9. On the History of Gunter’s Scale and the Slide Rule during the
Seventeenth Century, by Florian Cajori. Pp. 187-209.
February, 1920 .35

10. On a Birational Transformation Connected with a Pencil of
Cubics, by Arthur Robinson Williams. Pp. 211-222. February,
1920 .15

11. Classification of Involutory Cubic Space Transformations, by
Frank Ray Morris. Pp. 223-240. February, 1920 .25

AGRICULTURAL SCIENCES.—Charles B. Lipman, Ernest B. Babcock, and
John W. Gilmore, Editors. Price per volume, $5.00. Volumes I and
III completed. Volumes II and IV in progress.

AMERICAN ARCHAEOLOGY AND ETHNOLOGY.—Alfred L. Kroeber, Editor.
Volumes I-XII completed. Volumes XIII to XVI in progress.

ASTRONOMY.—William W. Campbell, Director of the Lick Observatory,
Editor.

Publications of the Lick Observatory (Quarto). Volumes I-XIII
completed. Price per volume, $3.00 (Volume VII, $4.00; Volume
VIII, $5.00; Volume IX, $2.25; Volume XIII, $0.00). Volumes I
and III are out of print.

Lick Observatory Bulletins (Quarto). Volumes I-IX completed.
Volume X current. Price, $2.50 per volume in advance. Volume I
is out of print.

BOTANY.—W. A. Setchell, Editor. Volumes I-IV completed. Volumes V
to VII in progress.

CLASSICAL PHILOLOGY.—William A. Merrill, Herbert C. Nutting, James
T. Allen, Editors. Price per volume, $2.50. Volumes I to IV, VI
and VII, completed. Volume V in progress.

ECONOMICS.—Volumes I ($5.00), II ($4.00), and III ($3.50)
completed. Volume IV in progress.

EDUCATION.—Volumes I ($3.50), III ($3.50), and IV ($2.50)
completed. Volumes II and V in progress.

ENGINEERING.—Charles Derleth, Jr., Editor. Volumes I and II in
progress.

GEOGRAPHY.—R. S. Holway, Editor. Price per volume, $5.00. Volume I
completed. Volume II in progress.

GEOLOGY.—Andrew C. Lawson and John C. Merriam, Editors. Price per
volume, $3.50. Volumes I-VII completed. Volume VIII in progress.

HISTORY.—Henry Morse Stephens, Editor. Volume I completed. Volumes
II and III in progress.

MODERN PHILOLOGY.—Charles M. Gayley, Hugo K. Schilling, and Rudolph
Schevill, Editors. Volumes I to VII completed. Volumes VIII and
IX in progress.

PATHOLOGY.—Frederick P. Gay, Editor. Price per volume, $2.50.
Volumes I and II completed.

PHILOSOPHY.—George H. Howison, Editor. Price per volume, $2.00.
Volume I completed. Volume II in progress.

PHYSIOLOGY.—S. S. Maxwell, Editor. Price per volume, $2.00. Volumes
I-IV completed. Volume V in progress.

PSYCHOLOGY.—George M. Stratton, Editor. Price per volume, $3.50.
Volumes I and II completed. Volume III in progress.

SEMITIC PHILOLOGY.—William Popper, Editor. Price per volume, $4.50.

ZOOLOGY.—William E. Ritter and Charles A. Kofoid, Editors. Volumes
I-XVII completed. Price per volume for first ten volumes, $3.50.
Price for Volume XI and subsequent volumes $5.00. Volumes XVIII
to XXI in progress.

MEMOIRS OF THE UNIVERSITY OF CALIFORNIA (Quarto). John C. Merriam,
Editor. Volume I (in progress).

1. Triassic Ichthyosauria, with Special Reference to the
American Forms, by John C. Merriam. September, 1908 $3.00

2. The Fauna of Rancho La Brea, by John C. Merriam.

Previous Next

Comments

On the History of Gunter's Scale and the Slide Rule During the Seventeenth CenturyChapter II: Front Matter (2)

0%21 min left in chapter