Highlights from the De Morgan Library

The books featured below encompass eight main, overlapping subject areas of De Morgan’s library

De Morgan’s books were not limited to his major subject interest of the history of mathematics, and a flavour of its wider contents appears in the smaller selection of books features:

De Morgan was interested in the origin of his books, sometimes recording in his books his source of acquisition, drawing attention to previous owners, and going to some length to verify ownership inscriptions. De Morgan also owned contemporary publications given to him by other significant  mathematicians and scientists of his time, being part of a wide scientific and mathematical circle including George Biddell Airy, Francis Baily, J.W. Lubbock and John Couch Adams, whose authors frequently presented each other with inscribed copies of their books and articles. Examples of provenance are also displayed:

Arithmetic

Rechnung auf allen Kaufmannschaft
Johannes Widmann von Ege
Leipzig: C. Kachelofen, 1489
Incunabula 2

Johannes Widmann (c.1460-c.1500), a Leipzig lecturer, wrote about both arithmetic and algebra. His Behende und hubsche Rechenung auf fallen Kauffmanschafft is the first important German textbook on commercial arithmetic. As De Morgan notes in manuscript on a front flyleaf of his copy, it is the first book to use the signs “+” and “-“: not as symbols of operation, but to express excess and deficiency in packages of merchandise.

This copy is rubricated. De Morgan acquired it some time after 1847, when he listed it in his Arithmetical Books from the Invention of Printing to the Present Time as “among books of the fifteenth century which I have had no opportunity of seeing”. He was fortunate to acquire it: this is the one of only two copies recorded by the ISTC as being in the British Isles.

Arithmetica integra
Michael Stifel
Nuremberg: J. Petreius, 1544
[DeM] L.1 [Stifel] SSR

This is the second of five mathematical works by the noteworthy German mathematician Michael Stifel (c.1487-1567). Arithmetica Integra, a more scholarly work of its kind than any of its German predecessors and Stifel’s greatest work, contains algebra (including radicals) and geometry as well as arithmetic, such that De Morgan’s note on the front free endpaper reads: “The first German writer on algebra”. The text uses the signs + and -, supposed by De Morgan to have been invented by him to denote addition and subtraction, and also the sign √ for radicals. Stifel’s treatment of exponents includes a discovery of logarithms, predating Napier and using a different method. The early pages of this copy contain extensive annotations in a contemporary hand.

De arte supputandi libri quattuor
Cuthbert Tunstall
London: R. Pynson, 1522
[DeM] L.1 [Tunstall] SSR

De Morgan in his Arithmetical Books was laudatory about Tunstall: “This book is decidedly the most classical which was ever written on the subject in Latin, both in purity of style and goodness of matter. The author had read every thing on the subject, in every language which he knew … and had spent much time, he says, ad ursi exemplum, in licking what he found into shape. … For plain common sense, well expressed, and learning most visible in the habits it had formed, Tonstall’s book has been rarely surpassed, and never in the subject of which it treats”. As hinted by De Morgan, Tunstall’s work is not original, but a confessed compilation. Tunstall‘s motivation for writing it was a suspicion that that the accounts goldsmiths with whom he was dealing were incorrect; he renewed his study of arithmetic in order to check their figures. His work was the first printed in Great Britain to be devoted wholly to mathematics.

This is the first of three 16th-century editions in De Morgan’s library. De Morgan’s designation of it on the title page as “very rare” has since been disproved: nineteen other copies are recorded in Britain on ESTC, chiefly held in Oxford and Cambridge libraries, with another five in North America.

Cocker’s Arithmetick
Edward Cocker
33rd edn
London: E. Tracy, 1715
[DeM] L.1 [Cocker] SSR

Cocker’s Arithmetick was first published in 1678. It was exceedingly popular, running through over 100 editions, influencing British textbooks for over a century, and generating a fixed expression, “according to Cocker”. A popular play of 1757 described it as “the best Book that ever was wrote”. The work’s success may derive from the fact that it is aimed at the requirements of trade rather than the gentry and their tutors; its importance lies in the fact that it represents the popular view of elementary mathematics at the time. This is one of six editions published between 1685 and 1771 in De Morgan’s library.

Algebra

General Trattato di Numeri et Misure
Niccolò Tartaglia
Vinegia: C.T. dei Nauò, 1556-1560
[DeM] L [Tartaglia] fol. SSR

“Of this enormous book I may say … that it wants a volume to describe it”, wrote De Morgan (Arithmetical Books, p. 21). Niccolò Tartaglia (“Stammerer”) was one of Italy’s greatest sixteenth-century mathematicians, known partly for his discovery (published by Cardan) of the solution of cubic equations. The General Trattato is his most extensive work. It covers arithmetic, geometry and mensuration as well as algebra as far as quadratic equations. De Morgan’s copy is one of several volumes he possessed previously owned by the French statesman, bibliophile and historiographer Jacques-Auguste de Thou (1553-1617), as shown by the gilt coat of arms stamped on the centre of the upper and lower boards.

The Whetstone of Witte
Robert Record
London: J. Kyngstone, 1557
[DeM] L.2 [B.P.1] SSR

Robert Record (1510-1558) was England’s most influential sixteenth-century mathematician. The Whetstone of Witte is the fourth of four books he wrote on mathematics, all in the form of dialogue, and all in the English language to promote accessibility and readability. The Whetstone of Witte is the first noteworthy attempt to write an algebra in England. It supplements his more elementary Grounde of Artes (1543). Based on German writers of algebra, such as Johann Scheubel and Michael Stifel, it introduces the “+” and “-“ signs into England and contains Record’s own innovation to mathematics, the equals sign (=).

Clavis Mathematicae Denuo Limata
William Oughtred
5th edn
Oxford: T. Leigh, 1698
[DeM] L0 [Oughtred] SSR

This brief treatise on algebra and arithmetic was composed in about 1628 and first published in 1631 to instruct the Earl of Arundel’s son, whom Oughtred tutored. The best work of one of the most influential seventeenth-century English mathematical writers, its popularity is evident from its translation into English (1647), from its generation of an explanatory volume, comparable in length with the original, by Gilbert Clerke (Oughtredus explicatus, 1682), and from the number of editions.published. In the Clavis Mathematicae, Oughtred uses various mathematical symbols, some already known, others of his own devising, such as the multiplication sign (X),:: for proportion, and ~ for the absolute value of a difference. This copy is inscribed on the title page: “J.O. Halliwell”, i.e. the Shakespearean scholar James Orchard Halliwell, later Halliwell-Phillipps (1820-1889), from whose sale of mathematical books at Sotheby’s in 1840 De Morgan bought copiously.

Invention Nouvelle en l’Algebre
Albert Girard
Amsterdam: G.J. Blaeuw, 1629
[DeM] L.2 [Girard] SSR

Albert Girard (1595-1632) was a French mathematician. In this book, he is one of the first to attack the problem of the treatment of the numerical cubic equation by trigonometry scientifically, and states for the first time the fundamental theorem of algebra that all algebraic equations receive as many solutions as the denomination of the highest term shows.

Geometry

Elementa Geometriae
Euclid
Venice: L. Achates and Guilielmus de Papia, 1491

Euclid’s Elements is the most successful and most long-lasting geometrical textbook of all time, with use extending over 2,000 years and over 1,000 editions having been published since its first appearance in print in 1482. It incorporates all the essential mathematical knowledge of Euclid’s time.  De Morgan’s 70-odd editions include both those of the incunabula period, from 1482 and 1492. While the 1482 edition is more significant because the edition princeps, and as a printing phenomenon for being the first printed book to include mathematical diagrams, the second edition, shown here, is considerably rarer: 38 copies of the first edition are recorded in the ISTC, but only 11 of the second edition. Of the two printers, Guilielmus de Papia was involved in only one other book, also from 1491, while Leonardus Achates printed 46 books between 1472 and 1491, on various subjects.

Quadratura Circuli, tandem Inuenta & Clarissimè Demonstrata
Oronce Finé
Paris: S. de Colines, 1544
[DeM] L [Finé] fol. SSR

The quadrature of the circle – i.e. finding a square whose area is the same as that of a given circle – was one of the three famous problems of solid geometry to occupy ancient Greek mathematicians. The Frenchman Oronce  Finé (1494-1555) was one of numerous later mathematicians to take up the challenge, others including Montucla, Huygens, James Gregory and Johann Bernouilli. Shortly after Finé produced his proof, Pedro Nunes (1502-1578) demonstrated it to be incorrect. Finé’s works were soon forgotten. Their inclusion in the De Morgan library helps to show De Morgan’s desire of having as many works as possible in his library, good and bad, important and insignificant, to document the entire history of the subject.

Geometria
René Descartes
Amsterdam: L. & D. Elzevir, 1659-1661
[DeM] L6 [Descartes] SSR

René Descartes (1596-1650) helped to revolutionise mathematics in the seventeenth century, establishing a universal mathematics in which algebra, geometry and arithmetic were closely related. His La Géometrie began life as a 100-page appendix to Discours de la methode pour bien conduire sa raison et chercher la verité dans les sciences (1637). In its present form it is divided into three books, the first relating fundamental operations of arithmetic to geometry, the second classifying curves, and the third dealing with the nature of roots of equations. Geometria was the first appearance of analytical geometry. It was, according to John Stuart Mill, “the greatest single step ever made in the progress of the exact sciences”. De Morgan’s copy bears the ownership inscription of the Devonian mathematician and astronomer John Hellins (d. 1827).

De Linearum Curvarum cum Lineis Rectis Comparatione Dissertatio Geometrica
Pierre de Fermat
Toulouse: A. Colomiez, 1660
[DeM] L6 [Lalovera] SSR

Fermat’s De Linearum Curvarum is a small treatise of just 39 pages. Pierre Fermat (1601-1665) was a lawyer who practised mathematics as a hobby. Yet his contribution to the subject renders him one of the great seventeenth-century mathematicians: in his studies of curves and equations developed the idea of analytic geometry before Descartes, although he did not publish, and Lagrange considered him the first inventor of the new calculus, by the method of maxima and minima. De Morgan in 1852 recorded the item as “scarce”, and indeed in late 2007 this was the only copy on COPAC.

Calculus

Exercitationes Geometricae Sex
Bonaventura Cavalieri
Bologna: G. Monti, 1647
[DeM] L6 [Cavalieri] SSR

The Italian mathematician Bonaventura Cavalieri (1598-1647) is best known for having invented the principle of indivisibles, first published in 1635 and presented in its final form here. His theory was based on the assertion that a line is made up of an infinite number of points, a plane of an infinite number of lines, and a soli of an infinite number of planes. Indivisibles were a forerunner of calculus, an intuitive step in the development of the integral calculus which superseded them. De Morgan’s comment, written in 1852 and pasted on the back of the title page of his copy, states his role clearly: “This work must not be confounded with the Geometria of Cavalieri published in 1635, and reprinted after his death. But of the two, this is the work which most established his claim to have ushered in the dawn of the integral calculus”.

Commercium Epistolicum
John Collins
London: J. Tonson and J. Watts, 1722
[DeM] L.3 [Collins] SSR

De Morgan owned all four edition of the Commercium Epistolicum, a work which he thoroughly disliked. The text, originally published by the Royal Society, is a collection of correspondence concerning the priority dispute between Newton and Leibniz as to who first invented infinitesimal calculus. It is a partisan account in Newton’s favour; Newton in fact both put the volume together and wrote an extensive review of it. It was De Morgan who in 1846 revisited the case and who wrote several articles in what De Morgan’s wife terms “justice to Leibnitz”, exposing dishonesty in Newton’s arguments of Leibniz having plagiarised him in the invention.

La Methode des Fluxions et des Suites Infinies
Isaac Newton
Paris: De Bure l’aîné, 1740
[DeM] L.3 [Newton]

Although Newton began work on fluxions, as he called calculus, in 1664 or 1665, and wrote hisMethod of Fluxions and Infinite Series in Latin in 1671, the work was not published until 1736, in John Colson’s English translation. According to the thirty-page introduction to this edition, Newton himself forgot the work until 1704. Buffon’s French translation is from the English, minus Colson’s commentary. De Morgan notes on the title page: “Saw this book for the first time May 7, 1852. Led to it by Dr Jas Watson’s answer to part of the preface. A. De Morgan”. De Morgan regarded Buffon’s comments superior to Colson’s, as indicated by his marginal comments at the beginning of the introduction.

Logarithms

Mirifici Logarithmorum Canonis Descriptio
John Napier
Edinburghi: A. Hart, 1614
[DeM] L.5 [Napier] SSR

The invention of logarithms came as a bolt from the blue. Logarithms depend upon the difference between arithmetical and geometrical progression, and enable the solution of complex multiplication and division problems by simple addition and subtraction. This was not only John Napier’s greatest achievement, but rendered him, in the opinion of his compatriot David Hume, “the person to whom the title of ‘great man’ is more justly due than to any other whom his country has ever produced”. This is the first edition of Napier’s first work on logarithms.

Arithmetica Logarithmica
Adriaan Vlacq
2nd edn
Gouda: P. Rammasenius, 1628
[DeM] L.8 [Briggs] fol. SSR

Adriaan Vlacq (1600-1667) was a Dutch mathematician, noted for his ability when printing scientific works. Henry Briggs (1561-1630) had already computed logarithms up to 20,000. Vlacq’sArithmetica Logarithmica reprints Briggs’s tables and adds 70,000 new logarithms calculated by himself, from 20,000 to 90.000. Vlacq’s tables, including his errors, were copied by many others in later years.

Probability

The Doctrine of Chances
Abraham de Moivre
London: A. de Moivre, 1718
[DeM] L.2.1 [Moivre]

The French-born, London-based mathematician Abraham de Moivre (1667-1754) was a pioneer of probability theory. This is the second book devoted entirely to the subject of chance, following Jakob Bernoulli’s Ars Conjectandi (1713). It develops an argument which De Moivre presented to the Royal Society and published in Latin in its Transactions as De Mensura Sortis in 1711, bound in at the back of De Morgan’s copy. A benefit of the book, as described in the preface, is “to be a help to cure a Kind of Superstition, which has been of long standing in the World, viz. that there is in Play such a thing as Luck, good or bad” (p. iv). Revised editions followed in 1738 and 1756, both also held by De Morgan.

Essai Philosophique sur les Probabilités
Pierre Simon Laplace
Paris: Mme Ve Courcier, 1814
[DeM] L.2.1 [Laplace]

Most of the work of Simon Laplace (1749-1827) was concerned with astronomy and celestial mechanics. Yet he also established the theory of probability, initially in Théorie Analytique des Probabilités (1812); the Essai Philosophique sur les Probabilités develops and applies his earlier text in a second edition. A popular work for the general reader, its contents include Laplace’s definition of probability, remarks on moral and mathematical expectation, and application of the theory to ordinary problems of chance, vital statistics, and future events. He stressed its importance for physics and astronomy.

This is one of twelve books by Laplace in De Morgan’s library. It is distinguished by the inscription on the verso of the half-title: “pour Monsieur Woodhouse de la part de l’autheur”, with De Morgan’s note above it: “Laplace’s Autograph”.

Astronomy

Sphaera Mundi
Joannes de Sacro Bosco
Venice: Octavius Scotus, 9 Oct 1490

Sacro Bosco’s Sphaera Mundi (c.1220) was the most popular geography and cosmology of the Middle Ages and through to the end of the sixteenth century. It is extant in hundreds of manuscripts and in at least 160 printed versions produced between 1482 and 1673. The work is based on Ptolemy and his Arabic commentators. A comprehensive account of the earth as a sphere in the centre of the universe, it is divided into four books, which describe (1) the general structure of the universe; (2) the circles of the celestial sphere; (3) the phenomena caused by the diurnal rotation of the heavens; and (4) planetary motions and eclipses. This is the earliest of five editions in De Morgan’s library.

Astronomic[o]n lib. VIII

Julius Firmicus Maternus
Basel: J. Herwagen, Mar. 1533
[DeM] Mo [Firmicus] fol. SSR

Julius Firmicus Maternus was a Roman astrologer, writing in about 340 A.D., who wrote about judicial astrology according to the precepts of the Babylonians and Egyptians. De Morgan wrote in his copy: “This is the last edition published of Julius Firmicus, and perhaps there will never be another”; in fact, there was one more, in 1551. This copy stands out for its elaborate blind-stamped binding, showing Christ on the front and Luther on the back.

De Revolutionibus Orbium Caelestium Libri VI
Nicolaus Copernicus
Nuremberg: J. Petreius, 1543
[DeM] M1 [Copernicus] fol. SSR

This is the first edition of Copernicus’s famous, trailblazing work postulating that the earth moves around the sun rather than vice versa. Copernicus probably had his main idea between 1508 and 1514, when he wrote his “Commentariolis” (“Little Commentary”), which he distributed privately in 1514, and completed his theory of the universe by 1530. The effect of De Revolutionibus was at first muted by the well-meaning preface of its editor, Andreas Osiander, who wrote pacifically that Copernicus was not really advocating the sun as the centre of the universe; it was merely a convenient hypothesis on which to base efficient mathematical models of planetary motions.

De Morgan’s copy is one of several De Morgan books from the library of Frederick North, fifth Earl of Guilford (1766–1827). Unusually among De Morgan’s books, it contains light Latin annotations by De Morgan in the text, explained by De Morgan on the title page: “Aug. 4, 1864. I have this day entered all the corrections required by the Congregation of the Index (1620) so that any Roman Xtian may read the book with a good conscience”.

Astronomiae Instauratae Progymnasmata
Tycho Brahe
Uranienborg: G. Tambach, 1610
[DeM] M [Brahe] SSR

Tycho Brahe (1546-1601) was a Danish astronomer and nobleman who designed and built new instruments and observed the positions of the moon and planets with unprecedented accuracy.Astronomiae Instauratae Progymnasmata is his fifth and final work, finished and issued posthumously. It discusses the motions of the sun, moon, and stars. In addition, it returns to the supernova of 1572, the subject of Brahe’s first book (De nova stella, 1573), analysing this phenomenon in more detail than the earlier work had done.

De Morgan’s copy is from the library of Frederick North, fifth Earl of Guilford (1766–1827).

Philosophy

Sum[m]ule Totius Logice
Jodocus Trutvetter
Erfurt: Heirs of L. Schenck, 15 Sept. 1501
[DeM] G3 [Trutvetter] SSR

Jodocus Trutvetter, of Eisenach, was a pre-eminent German philosopher who followed William of Occam’s “new way”. While rector of the University of Erfurt he taught Martin Luther, who addressed him in a letter of 1518 as “the first theologian and philosopher” and the first of contemporary dialecticians. De Morgan bought this copy in July 1861 at one of the sales at Sotheby’s of Guillaume Libri’s books. His comments, pasted on the front flyleaves, include the remarks that the work is so rare that the Scottish philosopher William Hamilton never saw a copy, and that Thomas Spencer Baynes (editor of the Encyclopaedia Britannica) revived the work’s quantification of the predicate (on the basis of its epitome, for he had not seen the book) in hisNew Analytic of Logical Forms (1850). This is one of only two copies on COPAC; the second is in the British Library.

Dialectica
Petrus Ramus
Cologne: T. Baum, 1573
[DeM] Ge [Ramus] SSR

The French philosopher Pierre Ramus (1515-1572) influenced methods of teaching logic through the seventeenth century. His Dialectica was first published in 1543. Its French translation (1555) was the first book to be published on dialectics in the French language. The work attacks Aristotle and the university curriculum as confused and disorganised. A key work in the Ramist canon, it was reprinted many times. De Morgan noted of this German edition: “This edition, 1573, was published in the year following the slaughter of Ramus in the massacre of St Bartholomew, and was no doubt a consequence of the interest excited by the manner of Ramus’s death”.

Elements of Philosophy
Thomas Hobbes
London: A. Crooke, 1656
[DeM] Go [Hobbes] SSR

Thomas Hobbes (1588-1679) is generally regarded as the founder of English moral and political philosophy. He had already conceived a large-scale exposition of the elements of philosophy as a whole, when he published De Cive in 1642. Elements of Philosophy begins with De Corpore (the body), which deals with metaphysics and physics. It progresses to De Homine (man) on epistemology, including optics, and psychology. De Cive (citizen) discusses ethics and politics. This is the first edition.

Bibliography

Bibliographia Mathematica et Artificiosa Novissima Perpetuò Continuanda
Cornelis à Beughem
Amsterdam: Janssonio-Waesbergi, 1688
[DeM] 016.51 [Beughem] SSR

Cornelis à Beughem (fl. 1678-1710), a bookseller and city councellor in Emmerich, was the seventeenth century’s foremost bibliographer. He published a series of bibliographies with the firm with which he worked, Janssonius van Waesberghe, listing books published in the relevant subject area in all Europe during the second half the seventeenth century in any language, whether first or revised editions. His bibliographies were distinguished from earlier ones by being arranged by author, and by their limited chronological coverage to the present and the immediate past. The Bibliographia Mathematica follows bibliographies of law and politics (1680) and medicine and physics (1681). De Morgan’s comment on it, written on a front flyleaf in April 1863, is “Scarce, and useful”.

Typographical Antiquities
Joseph Ames
London: W. Faden, 1749
[DeM] CC7 [Ames] fol.

Joseph Ames’s Typographical Antiquities constitutes a landmark in printing history, which has formed the basis of later histories of English printing, including augmented editions by William Herbert and Thomas Frognall Dibdin. Ames began it in 1732, as a correction to George Psalmanazar’s inaccurate and inadequate history of printing published in that year, and finished it seventeen years later. Ames gave accurate transcriptions of title pages, based on the books themselves rather than early catalogues (a task facilitated by his own collection of title pages), and was the first person to attempt to use type identification to date early books. De Morgan refers to Ames in the note he pasted in the front of John of Garland’s Liber Synonymorum, also shown here.

Miscellaneous

Liber Synonymorum
John of Garland
Parisi: J. Antoine, 8 Nov. 1502
[DeM] A5 [Garlandia] SSR

John of Garland (c.1195-c.1258) was an English grammarian, lexicographer and poet who lived in Paris, and whose works were copied widely until entering the market of printed books in the fifteenth century. His Liber Synonymorum is a lexicographical treatise in verse and is one of a group of word books for mediaeval pupils which helps boys learn Latin vocabulary by grouping words topographically rather than alphabetically. De Morgan showed his interest in the work as a piece of early printing (a post-incunable) through the notes he made about John of Garland and the printed history of the work in 1845 and attached to the front flyleaf. The copy shown is the only copy of this particular edition recorded on COPAC.

Commentarii de Scriptoribus Britannicis
John Leland; ed. by Anthony Hall
Oxford: Sheldonian Theatre, 1709
[DeM] Foc [Leland] SSR

The poet and antiquary John Leland (c.1503-1552) planned to compile a dictionary of British writers which, with 593 entries, arranged chronologically, was nearing completion when he became insane in about 1547. Leland’s unpublished writings were integral to the work of other historians and antiquaries, including William Dugdale and John Aubrey, before being published, in what remains the sole printed edition, by the antiquary Anthony Hall (1679-1723). De Morgan’s note, written in 1857 and tipped in at the front, details something of its reception: “This book has always had a bad name: I never could tell why.  Hall was a man of learning and industry and had nothing to do but to see Leland’s MSS properly printed. But when it was printed, Tanner [i.e. antiquary Thomas Tanner] was meditating what he afterwards performed in his Bibliotheca, and was topped by this publication, at which he was naturally rather sore. Now nothing gives a book so bad a name as the world knowing that such a publication has arrested a better performance: and such a man as Tanner speaking against such a work as this was enough to damage it seriously.”

Provenance

Calendarium
Jacob Pflaum
Ulm: J. Zainer, 1478

Johann Zainer, Ulm’s first printer, was one of the most notable exponents of the art of using wood-blocks for book ornamentation.  He issued several calendars and almanacs, many of which comprise a single folio.  This one was about his twentieth dated work.

This copy contains the label of the Frankfurt citizen Georg Kloss (1787-1854), who an historian of freemasonry, medical practitioner (from 1810) and book collector.  As a student, Kloss had already collected 10,000 medical dissertations, which he sold to the University of Bonn for 560 taler in 1820.  He next set out to collect works printed in Germany to 1550, a task assisted by the dissolution of several old German monastery libraries and by the fact that relatively few German collectors of his time desired such books.  The rich collection of manuscripts and early printed books which he built up between 1817 and 1835 was based on the collections of Johannes von Dalberg, bishop of Worms (d. 1503), Adelmann von Adelmannsted and the Church library of Esslingen. Other sources included the collections of Christoph Scheurl (d. 1542) and Johann Fichard (d. 1581), the abbey library of Ochsenhausen and the libraries of various contemporary collections. In 1833 Kloss offered his library to various large libraries in Germany for 17,000 taler. They declined, whereupon the library was sold at Sotheby’s in 1835, for the minimal sum of £2,261 for 4,682 lots.  This book, sold on 22 May 1835, was purchased by Longmans for 14 shillings.

Théorie de la Lune
M. Clairaut
2nd edn
Paris: Dessaint & Saillant, 1765
[DeM] M [Clairaut]

De Morgan’s note, pasted on the verso of the front flyleaf, facing the title page, explains the provenance of this volume: “Sept. 30, 1852. This book was bought by me many years ago long before any sale of M. Libri’s books. It must have been stolen at some time from the library of the Observatory at Paris. I removed the above stamp from over the red one, and find that it was one of La Condamine’s books, all of which ought to be at the observatory. This is an instance not only of the usual thefts from French libraries, but of the indecorous manner in which even those libraries place one stamp over another, caring nothing for the popular suspicion that they themselves may have received books which but for their own concealment would prove themselves stolen”. The reference to Libri’s books pertains to the accusation of Guillaume Libri in 1848 of stealing books from various French libraries. “The above stamp” mentioned by De Morgan is that of the astronomical division of Académie royale des sciences (1782). The red stamp is that of the mathematician and explorer Charles Marie de La Condamine (1701-1774), member of the Académie royale des sciences from 1730.

A Dissertation on the Use of the Negative Sign in Algebra
Francis Maseres
London: S. Richardson, 1758
[DeM] L.2 [Maseres]

Francis Maseres (1731-1824) was a colonial administrator (1766-9) and writer. This is one of four books of his in De Morgan’s library; De Morgan also owned a further two edited by Maseres. This book argues that the negative sign should be used exclusively as a symbol for subtraction. It is inscribed on the first front flyleaf: “F. Maseres, Sept. 1, 1770”. Under this, De Morgan has written: “From whom it came into the hands of Wm Frend and from him to A. De Morgan”. The said William Frend (1757-1841) was a religious writer and actuary, an intellectual leader of the reformist London Corresponding Society and a close associate of leading radicals of his day. He taught mathematics to the children of aristocratic families and was influential in reorganising the Rock Life Assurance Company. From 1831 Frend was De Morgan’s neighbour, and from 1837 his father-in-law, De Morgan marrying Frend’s oldest daughter, Sophia Elizabeth, in August of this year.

De Morgan’s Contemporaries

On a Remarkable Phenomenon that Occurs in Total and Annual Eclipses of the Sun
Francis Baily
[London: J. Moyes?, 1837?]
[DeM] M (B.P.6)

Leading astronomer and stockbroker Francis Baily (1744-1844) and Augustus De Morgan were long-term friends: Baily co-founded and was President of the Royal Astronomical Society, of which De Morgan was from 1831 Secretary.

This is one of three items in De Morgan’s library inscribed to De Morgan by Baily; De Morgan also possessed 33 items identified as having previously been owned by Baily, at least some of which he purchased at the sale of Baily’s library at Sotheby’s in 1845.

On Sound and Atmospheric Vibrations
George Biddell Airy
London: Macmillan, 1868
[DeM] N.2 [Airy]

George Biddell Airy (1801-1892) was Astronomer Royal of England and contributed to lunar and planetary theory. As Plumian Professor of Astronomy at Cambridge for 46 years, he taught De Morgan as an undergraduate and, in 1827, recommended him for the first Chair of Mathematics at University College London. The two men served together for many years as officers of the Royal Astronomical Society. De Morgan described Airy as an intimate friend, and the two men corresponded regularly over decades. This is one of 37 items by Airy in De Morgan’s library, of which eleven are inscribed as a gift to De Morgan from Airy.

Spherical Trigonometry for the Use of Colleges and Schools
Isaac Todhunter
Cambridge: Macmillan, 1859
[DeM] L.4 [Todhunter]

The textbooks of Isaac Todhunter (1820-1884) render him the most widely-known mathematician of his period to elementary students and teachers. Whereas Baily and Airy were De Morgan’s seniors, Todhunter was his junior. De Morgan taught Todhunter at evening classes at University College London, and it was on De Morgan’s recommendation that Todhunter subsequently went to St John’s College, Cambridge. While Todhunter respected all his London teachers, De Morgan was the one whom he venerated most highly, describing his admiration as unbounded. This is one of seventeen items by Todhunter in De Morgan’s library, of which eight are inscribed as being from the author.