CLASSICS OF SCIENCE

25

56

**DESAGULIERS, J. T.** A Dissertation concerning Electricity. London, 1742. 8vo. Title + 6 pp. + 50 pp. + 1 leaf. Sewn. £2.15.

Original edition of this prize-winning dissertation by the French scientist, J. T. Desaguliers (1683-1744), who spent his life in England. It is important as originating the term ‘conductors’ and ‘non-conductors’ (called ‘electrics and non-electrics per se’), and contains numerous experiments in illustration, as well as on electric attraction and repulsion. At the end a chapter on the ‘Several Authors who have treated of Electricity,’ mentioning their works and essays in scientific periodicals (with detailed references).

57

*(DESCARTES, RENE)*. Discours de la Méthode pour bien conduire sa raison, et chercher la verité dans les sciences. Plus la Dioptrique, les Méteores et la Géometrie, qui sont des essais de cete Méthode. Leyden, Jan Maire, 1637. 4to. 78 pp. Title, 413 pp. + 17 ll. (the last, a blank, missing). With numerous woodcut diagrams in the text. Old vellum. £52.10.

FIRST EDITION of Descartes' epoch-making work, of outstanding rarity. It was also his first published book, issued anonymously. It contains for the first time his treatises on Optics, Meteors and Geometry, the last, the most celebrated, setting out his Invention of analytical Geometry. His explanation of irradiation is now generally accepted.

Bibl. Osleriana 928:—"... In 1638 however, when 40 years of age, he felt that it was time to bring his views before the public and publish them abroad. ... Descartes endeavoured to preserve the anonymity of his work with scrupulous care, and was annoyed by his zealous but fussy friend Mersenne showing the work to others, and announcing the author's name, with the ostensible object of obtaining from the King of France permission for its publication. In the end he found himself compelled to avow the authorship." There is a passage alluding to the invention of the telescope about thirty years before by a person named James Metius.

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CLASSICS OF SCIENCE

60

**DIGGES, THOMAS.** Alae seu Scaleae Mathematicae, quibus visibilium
remotissima Coelorum Theatra conoscendi, et Planetarum omnium itinera
novis et inauditis Methodis explorari . . . possit. London, apud Thomam
Marsh, 1573. 4to. With full-page astronomical woodcut and woodcuts of
the arms of William Cecil, Lord Burghley (the Elizabethan chancellor), to
whom the book is dedicated, and the arms of Digges.

Bound with:

DEE, JOHN. Parallaticae Commentationis Praxeosque nucleus quidam. London, apud J. Dayum, 1573. 4to. With woodcut on title and many diagrams. Old vellum.

£21.

Short Title Catalogue I, 6871; II, 6462.

I. First edition. This book is most interesting on account of the fact, that is probably the first English book dealing with Copernicus. In the preface Digges quotes the longitudes and latitudes of the fixed stars as worked out by Copernicus in his "De lateribus 1542" (see No. 49) and later on he speaks of him as "divino illo, ingenii plusquam humani Copernico." In fact Digges prepared "Commentaries upon the Revolutions of Copernicus," never finished, as it is said of him: "Had not the infernall furies, envying such his felicite and happie societie with his mathematical muses, for many yeares so tormented him with lawe-brables, that he hath been enforced to discontinue those his delectable studies." (D.N.B.).

II. First edition. "The appearance of a new star in November 1572 gave Dee an excellent opportunity of displaying his skill in astronomy." He wrote this mathematical-astronomical tract on parallaxes, and his friend Digges added the introduction to it. Dee had brought with him in 1547 from the Low Countries the first astronomer's staff of brass and given it to Trinity College, Cambridge, and contributed very much to the development of astronomy in this country.

Fine copies in contemporary vellum, with Lalande's the great XVIIIth century astronomer's autograph on title.

John Dee his Mathematicall Preſace.

Forme reſulting, by this mixture of C, and E. As, if from 4. ye abate 1. there reſteth 3. the halfe of 3. is 1¼: Adde to 1. this 1¼: you haue 2¼. Or subtraſt from 4. this 1¼: you haue likewife 2¼: remayning. Which declareth, the Forme reſul-
ting, to be Heate, in the middle of the third degree.

But if the Quantities of two things Commixt, be diuerſe, and the Intenſi-
ons (of their Formes Mifcible) be in diuerſe degrees, and heigthes. (Whether
thofe Formes be of one kinde, or of Contrary kindes, or of a Temperate and a
Contrary, What proportion is of the leſſe quantitie to the greater, the ſame ſhall be of the
difference, which is betwene the degree of the Forme reſulting, and the degree of the greater
quantitie of the thing miſcible, to the difference, which is betwene the ſame degree of the
Forme reſulting, and the degree of the leſſe quantitie. As for example. Let two pound
of Liquor be geuen, hote in the 4. degree: & one pound of Liquor be geuen, hote
in the third degree. I would gladly know the Forme reſulting, in the Mixture of
theſe two Liquors. Set downe your núbers in order, thus.
The Se-
cond
Rule.

Now by the rule of Algiebar, haue I deuifed a very eaſie,
briefe, and generall maner of working in this caſe. Let vs
firſt, ſuppoſe that Middle Forme reſulting, to be 12: as that
Rule teacheth. And becauſe (by our Rule, here geuen) as
the weight of 1. is to 2: So is the difference betwene 4. (the
degree of the greater quantitie) and 12: to the difference betwene 12: and 3:
(the degree of the thing, in leſſe quâtitie. And with all, 12: being alwayes in a certaine middell, betwene the two heigthes or degrees). For the firſt difference, I ſet
4—12: and for the ſecond, I ſet 12:—3. And, now againe, I ſay, as 1. is to 2. ſo is
4—12: to 12:—3. Wherfore, of theſe ſoure proportionall numbers, the firſt and
the fourth Multiplied, one by the other, do make as much, as the ſecond and the
third Multiplied the one by the other. Let theſe Multiplications be made accor-
dingly. And of the firſt and the fourth, we haue 12:—3, and of the ſecond & the
third, 8—22: Wherfore, our Æquation is betwene 12:—3: and 8—22: Which
may be reduced, according to the Artie of Algiebar: as, here, adding 3. to eche part,
geueth the Æquation, thus, 12:—11—22: And yet againe, contracting, or Redu-
cing it: Adde to eche part, 22: Then haue you 32: æquall to 11: thus repreſen-
ted 32:—11. Wherefore, druiding 11. by 3: the Quotient is 3—1: the Valew of our
12: Cop, or Thing, firſt ſuppoſed. And that is the heigth, or Intenſion of the Forme
reſulting: which is, Heate, in two thirdes of the fourth degree: And here I ſet the
ſhow of the Worke in conclusion, thus. The prouſe hereof is eaſie by subtraacting
3. from 3—1, reſteth

Subtracte the
fame heigth of the
Forme reſulting,
(which is 3 1/4) fro
4, then reſteth 1/2.
You ſee, that
is double to 1 1/2.

as 2. r. is double to 1. r. So should it be: by the rule here geuen. Note. As you ad-
ded to eche part of the Æquation, 3: ſo if ye firſt added to eche part 2r, it would
ſtand, 3r—3=8. And now adding to eche part 3: you haue (as afore) 3r = 11.

And though I, here, ſpeake onely of two thyngs Mifcible: and moſt common-
ly, mo then thre ſoure, ſuue or ſix, (&c.) are to be Mixed: (and in one Compound
*illij. to

John Dee his Mathematicall Praeface.

Note.

to be reduced: & the Forme reſultyng of the fame, to ſerue the turne) yet theſe Ru-
les are ſufficient: ducely repeated and iterated. In procedyng firſt, with any two: and
then, with the Forme Reſulting, and an other: & ſo forth: For, the laſt worke, con-
cludeth the Forme reſultyng of them all: I nede nothing to ſpeake, of the Mixture
(here ſuppoſed) what it is. Common Philosophie hath defined it, ſaying, *Mixtio
eſt miſcibilium, alteratorum, per minima coniunctorum, Vnio.* Every word in the de-
ſinition, is of great importance. I nede not alſo ſpend any time, to ſhow, how, the
other manner of diſtributing of degrees, doth agree to theſe Rules. Neither nede I
of the ſarder vſe belonging to the Croſſe of Graduation (before deſcribed) in this
place declare, vnto ſuch as are capable of that, which I haue all ready ſayd. Neither
yet with examples ſpecifie the Manifold varieties, by the ſoreſayd two gene-
rall Rules, to be ordered. The witty and Studious, here, haue ſufficient: And they
which are not hable to atteine to this, without liuely teaching, and more in parti-
cular: would haue larger diſcourſing, then is mete in this place to be dealt withall:
And other (perchaunce) with a proude ſnuffe will diſdaine this litle: and would be
vnthankefull for much more. I, therfore conclude: and with ſuch as haue modeſt
and earneſt Philosophicall mindeſs, to laude God highly for this: and to Meruayle,
that the profoundeſt and ſubtleſt point, concerning *Mixture of Formes and Quali-
ties Naturall, is* ſo Matcht and maryed with the moſt ſimple, eaſie, and ſhort way of
the noble Rule of Algiebar. Who can remaine, therefore vnperſuaded, to loue, a-
low, and honor the excellent Science of Arithmetike? For, here, you may perceiue
that the litle finger of Arithmetike, is of more might and contriuing, then a hun-
derd thouſand mens wittes, of the middle ſorte, are hable to perſourme, or truely
to conclude, with our helpe thereof.

Taxliſt.

Now will we ſarder, by the wife and valiant Capitaine, be certified, what helpe
he hath, by the Rules of Arithmetike: in one of the Artes to him appertaining. And
of the Grekes named *Taxliſt*. That is, the Skill of Ording Souldiers in Battell ray
after the beſt maner to all purpoſes. This Art ſo much dependeth vppon Numbers
vſe, and the Mathematicals, that *Ælianus* (the beſt writer therof,) in his worke, to
the *Emperour Hadrianus*, by his perſection, in the Mathematicals, (beyng greater,
then other before him had,) thinketh his booke to paſſe all other the excellent
workes, written of that Art, vnto his dayes. For, of it, had written Æneas: Cyneas of
Theſaly: Pyrrhus Epirota: and Alexander his ſonne: Clearchus: Pauſanias: Euangelus:
Polybius, familier ſrende to Scipio: Europlemus: Iphicrates, Poſſidonius: and very many
other worthy Capitaines, Philosophers and Princes of Immortall fame and me-
mory: Whose ſayre ſtande of their garland (in this ſeat) was Arithmetike: and a
litle perceiuerance, in Geometrical Figures. But in many other caſes doth Arith-
metike ſtand the Capitaine in great ſede. As in proportionyng of vittayles, for
the Army, either remaining at a ſtay: or ſuddenly to be encreaſed with a certaine
number of Souldiers: and for a certain tyme. Or by good Art to diminifh his com-
pany, to make the victuals, longer to ſerue the remanent, & for a certaine determi-
ned tyme: if nede ſo require. And ſo in ſundry his other accountes, Recke-
ninges, Meaſurynges, and proportionynges, the wife, expert, and Circumſpect Ca-
pitaine will affirme the Science of Arithmetike, to be one of his chief Gounſaylors,
directers and aiders. Which thing (by good meaneſs) was euident to the Noble,
the Couragious, the loyall, and Curteous tohn, late Earl of Warwicke. Who
was a yong Gentleman, throughly knowne to very ſew. Albeit his luſty valiant-
nes, ſorce, and Skill in Chiualrous ſeates and exerciſes: his humblenes, and frende-
lynes to all men, were thinges, openly, of the world perceiued. But what rotes
(fotherwife,) vertue had ſaſtened in his breſt, what Rules of godly and honorable
life

John Dee his Mathematicall Preface.

Rule: Simple and Compound: both forward and backward: How might they
miffie Arithmetical helpe in the Rules of Felowshyp: either without tyme, or with
tymer and betwene the Marchant & his Factor? The Rules of Bartering in wares
only: or part in wares, and part in money, would they gladly want? Our Mar-
chant venturers, and Trauaylers ouer Sea, how could they order their doynges
iustly and without loffe, vnleaft certaine and generall. Rules for Exchaüge of mo-
ney, and Rechaunge, were, for their vſe, deuifed: The Rule of Alligation, in how
fundry caſes, doth it conclude for them, ſuch precife verities, as neither by naturall
witt, nor other experience, they, were hable, els, to know: And (with the Mar-
chant then to make an end) how ample & wonderfull is the Rule of Fafle poſiti-
ons: especially as it is now, by two excellent Mathematiciens (of my familier ac-
quayntance in their life time) enlarged: I meane Gemma Frisius, and Simon Iacob.
Who can either in brief conclude, the generall and Capitall Rules? or who can I-
imagine the Myriades of fundry Caſes, and particular examples, in Act and earneſt,
continually wrought, tried and concluded by the forenamed Rules, onely: How
fundry other Arithmetical praeſifes, are commonly in Marchantes handes, and
knowledge: They them ſelues, can, at large, teſtifie.

The Mintmaſter, and Goldsmith, in their Mixture of Metals, either of diuerſe
kinde, or diuerſe values: how are they, or may they, exacely be directed, and met-
ualloſly pleafured, if Arithmetike be their guide?-- And the honorable Philiſiās,
will gladly confefſe them ſelues, much beholding to the Science of Arithmetike,
and that fundry wayes: But chiefly in their Art of Graduation, and compounde
Medicines. And though Galenus, Auerrois, Arnoldus, Lullus, and other haue pu-
blifhed their poſitions, aſwell in the quantities of the Degrees about Tempera-
ment, as in the Rules, concluding the new Forme reſulting: yet a more precife,
commodious, and eafy Method, is extan: by a Countreyman of ours (aboue 200.
yeares ago) inuented. And foraſmuch as I am, vncertaine, who hath the ſaue:
or when that little Latin treatife, (as the Author writ it,) ſhall come to be Printed:
(Both to declare the deſire I haue to pleafure my Countrey, wherin I may: and al-
ſo, for very good prote of Numbers vſe, in this moſt ſubtile and frutefull, Philoſo-
phicall Conſclusion,) I intend in the meane while, moſt briefly, and with my far-
der helpe, to communicate the pith thereof vnto you.

First describe a circle : whole diameter let be an inch. Diuide the Circumſe-
rence into ſoure equall partes. Frò the Center, by thate 4. ſections, extend 4. right
lines : eche of 4. inches and a halſe long : or of as many as you life, aboue 4. with-
out the circumference of the circle : So that they ſhall be of 4. inches long (at the
leaſt) without the Circle. Make good euident marks, at euery inches end. If you
lie, you may ſubdivide the inches againe into 10. or 12. ſinaller partes, equall. At
the ends of the lines, write the names of the 4. principall elementall Qualities.
Hore and Colde, one againſt the other. And likewife Mayſt and Dry, one againſt
the other. And in the Circle write Temperate. Which Temperature hath a good La-
titude : as appeareth by the Complexion of man. And therefore we haue allow-
ed vnto it, the foreſayd Circle : and not a point Mathematicall or Phyſicall.

Now, when you haue two things Mifcible, whole degrees are * truely
kauen : Of neceſſitie, either they are of one Quantitie and waight, or of diuerſe.
If they be of one Quantitie and waight: whether their formes, be Contrary Qua-
lities, or of one kinde (but of diuerſe inſtentions and degrees) or a Temperate, and a
Contrary, The forme reſulting of their Mixture, is in the Middle betwene the degrees of

*in the

*Take some part of Lullus counſayle in his booke de Q.Eſſentia.

R. B.