## Josse. Epitome compendiosaq[ue] introductio in libros arithmeticos divi Severini Boetii [Lefevre], adiecto familiari commentario dilucidata [Clichtove]. Introductio annotationibus explanata, sex libris distincta. Liber de quadratura circuli, liber de cubicatione spherae; perspectivae introductio [Bovelles]. Praxis numerandi certis quibusdam regulis constricta [Clichtove]. Insuper Astronomicon [Lefèvre].

Paris: H. Estienne & W. Hopyl, 27 June 1503.

First edition of this very rare collection of works, in an attractive Roger Payne binding. The individual works are all first editions with the exception of Lefèvre’s *Epitome* of Boethius’ *De arithmetica* (first, 1496) and an unattributed *Opusculum de p[r]axi numerorum quod Algorismum vovant*, actually the *Algorismus* of Sacrobosco (no earlier printing than this one in auction records). This latter text was the first to introduce Hindu-Arabic numerals into the European university curriculum, thereby greatly simplifying the procedures of practical calculation. The geometrical part of the volume comprises several works of Bovelles (ca. 1479-1567), which deal with the classical problems of the quadrature of the circle and duplication of the cube, and contain a highly original study of stellated polygons. Bovelles also gives here the first published account of the cycloid, a curve that was to be of great significance in the seventeenth century development of mathematics leading up to the invention of calculus and for Huygens’ isochronous pendulum clock. The volume concludes with Lefèvre’s treatise on astronomy. This is a very rare book on the market, with no other copies located in auction records.

*Provenance*: Fol. XLVIIIv with two inscriptions in French, by Guillaume Lailo (?) (dated 1520) and Elisabeth Bowland (dated 18 October 1580); the classics scholar and eminent bibliophile Michael Woodhull (1740-1816) (initial blank with his signature dated June 7th 1783 and later pencil inscription indicating that the book was sold in the Woodhull sale, Sotheby’s, 11 January 1886, lot 445); verso of front free endpaper with signature of the Swedish bibliophile Thore Virgin (1886-1957), dated 17 April 1923, and with ink stamp “Bibliotheca Qvarnsforsiana” on verso of initial blank – his library catalogue *Bibliotheca Qvarnforsiana* was published in 1947). *Binding*: Eighteenth-century russia from the workshop of Roger Payne, “the most noted English binder of the eighteenth century” (Andrews, p. 13) – inscription on recto of front blank stating the cost of the ‘R Payne’ binding as £1 1s. Covers with an elegant geometrical design of plain gold fillets forming a lozenge with semicircular lobes at the corners over a rectangular border. Probably bound for Woodhull, who was a regular patron of Payne. A very similar binding can be seen on a copy of Quintillian’s *Declamationes* (1482), also owned by Woodhull, now held by the Bridwell Library at Southern Methodist University – see “A forgotten binding by Roger Payne,” http://www.smu.edu/Bridwell/SpecialCollectionsandArchives/Exhibitions/SixCenturiesofMasterBookBinding/18thCentury/Forgotten%20Binding%20by%20Payne.

Roger Payne (1739-1797), perhaps the most famous of all English bookbinders, was well known both for his exquisite gold tooling and his squalid lifestyle. He worked at Eton beginning in the late 1750s, then at London with the support of the bookseller Thomas Payne (no relation). There he served many illustrious patrons, including Earl Spencer and the Duke of Devonshire. Payne is commemorated with a statue outside the Victoria and Albert Museum in London (in a group of five British craftsmen – with William Morris, Josiah Wedgwood, Thomas Chippendale and Thomas Tompion).

The arithmetical part of the volume, comprising the first 48 leaves, begins with Lefèvre’s *Epitome* of Boethius’ *De arithmetica*, which was based on the Greek, under the supervision and with the collaboration of Heinrich Lorit. Anicius Manlius Severinus Boetius, commonly known as Boethius (ca. 480-524), was a Roman aristocrat, statesman, and scholar. Literate in Greek, Boethius was a translator and commentator on earlier Greek works and, as such, provided a vital intellectual link between the ancient classical world and the emerging Middle Ages. His *De arithmetica* is largely a translation of Nicomachus of Gerasa’s *De institutione arithmetica libri duo* (ca. 100). Boethius considered mathematics as consisting of four parts: arithmetic, music, geometry, and astronomy – the four subjects that formed the medieval *quadrivium*. Arithmetic, as the foundation of the other three, was the most important of these subjects. His *De arithmetica* consists of rather esoteric number theory involving complex categorizations of numbers. Modern scholarship shows how such number theory was useful in proportions involving music and architecture. The *Epitome* is here supplemented by the commentary of Lefèvre’s student Josse Clichtove (ca. 1473-1543), together with Clichtove’s own *Praxis numerandi*, a more practical work on arithmetic.

Thought to have been written around 1225, Sacrobosco’s *Algorismus* was widely used in the middle ages and reproduced into the early modern period. “Sacrobosco (ca. 1195-1256) … was not only the first but the most widely published of the medieval writers. His *Algorismus* is known to have been printed at Strasbourg in 1488, and again at Vienna in 1517, Cracow in 1521, and Venice in 1523 … Josse Clichtove in 1503 and 1522 published the *Epitome* of Jacques Lefèvre d’Etaples (Jacob Faber Stapulensis) together with his own *Praxis numerandi*. He also included the piece that he described in his 1503 preface as *opusculum de praxi numerorum* (“a small work on the practice of numbers”), an algorism *non inscite (nescio quo authore) compositus* (“not unskillfully written, whose author I do not know”). The piece opens with the words *Omnia quae a primeva rerum origine processerunt* which identify it as Sacrobosco’s *Algorismus*” (Stedall, p. 111).

“The most important mathematical work of Bouelles, who was also known as Charles de Bouvelles, was published in three languages: in Latin, in French and in Dutch as *Boeck aenghaende de Conste en de Practycke van Geometrie*. The *Geometrie* includes chapters on stellated polygons, which had been discussed in Bradwardine’s *De geometria speculative*. It is very likely that Bouvelles knew this tract, for he refers to Bradwardine in his introduction to the section on the quadrature of the circle. Extending the sides of a regular convex polygon results in a stellated polygon of the first order; in the same way the latter can be transformed into a stellated polygon of the second order, and so on. Bouelles started with the stellated pentagon, the first stellated polygon of the first order, and showed that the sum of its angles equals two right angles. For this he used the regularity of the polygon and showed that every angle is 36°, so the sum is 180°. After having shown that the sum of the angles of a stellated hexagon equals four right angles, he went on to the first stellated polygon of the second order, the heptagon; and, referring to his proof for the pentagon, he said that the sum of the angles of the heptagon also equals two right angles” (DSB II: 360-361).“The most original contribution of Bovelles was his study of the cycloid [the curve traced out by a point on the circumference of a circle as it rolls along a straight line]. This curve … he investigated in the *Introductio in geometriam* (written in 1501 but not published until 1503). Prior to the works of Gunther and Cantor the postulation of this curve had been attributed incorrectly to Nicholas of Cusa, but recent research has confirmed Bovelles as its discoverer. Although Bovelles did little more than postulate its existence, later mathematicians drew out its full implications. Galileo, Mersenne, and Roberval all worked with it, but it was Pascal who solved completely the problem of its quadrature in 1659 and found the center of gravity of a segment cut off by a line parallel to the base. By the time of Pascal, more than one hundred and fifty years had passed since Bovelles’s discovery and his claim to credit was ignored …

“Two other traditional problems absorbed Bovelles’s energies in the early years at Paris. These were the quadrature of the circle and the duplication of the cube. Simply stated, the first problem aimed at finding a square whose area was the same as a given circle. Complicating matters was the fact that only straight edges and compasses could be utilized to solve the problem. With only these instruments it was impossible to construct the desired square. This, however, was not known either to the Greek mathematicians or to Renaissance geometers. Thus Bovelles and Oronce Finé among others attempted solutions using only compass and straight edge …

“Bovelles was interested also in the duplication of a cube. This involved finding the edge of a cube whose volume was twice that of a given cube. The solution of this problem had been attempted many times in classical antiquity, notably by Eudoxus (370 B.C.), Apollonius (225 B.C.), and by Diocles (180 B.C.), who used a curve known as the cissoid. During the Middle Ages, when the advanced Greek mathematicians were largely neglected, there wasn’t much interest in this problem. Italian mathematicians of the fifteenth century were aware of it but made no important contributions toward solving it. In 1503 Bovelles published his *De Cubicatione Spherae* which dealt with the problem through an extended use of the cissoid curve” (Victor, pp. 42-3).

Lefèvre’s treatise to astronomy “is not so much a commentary as a rational reconstruction of Peurbach’s ideas” (Boner, p. 14), namely those presented in the latter’s *Theoricae novae planetarum* (first published in 1474). Lefèvre’s treatise presents a modified Ptolemaic system based on Regiomontanus and Peurbach, but with the infusion of doctrines of planetary harmony and mystical numerology which derive from Lefèvre’s study of natural magic under Pico della Mirandola.

The *Epitome*, with Clichtove’s commentary and his *Praxis numerandi*, was reprinted in 1510 and 1522, but neither of these editions contained the works of Bovelles, and only the first contained the *Astronomicon*. The latter work was included with a 1515 printing of Peurbach’s *Theoricae novae planetarum*, and was also printed separately in 1517. Bovelles’ geometrical works were translated into French (1547, 1551, 1555 and 1566), and also into Dutch (1547).

Lefèvre (ca. 1455-1536) was an outstanding humanist, theologian and translator. Ordained a priest, Lefèvre taught philosophy at the Collège du Cardinal Lemoine in Paris from about 1490 to 1507, where he was instrumental in introducing a new curriculum of studies, with an emphasis on science and mathematics. His first contribution was an edition of Sacrobosco’s *Sphera* (1495), which went through several editions, but more important for mathematical studies was the publication in 1496 of his edition of the arithmetic of the mediaeval French mathematician Jordanus Nemorarius; this work also included the first printing of his *Epitome* of Boethius’ *De arithmetica*. Bovelles studied under Lefèvre at Paris, sharing with him a high regard for the Christian Neoplatonic philosophy of Nicholas of Cusa. Albert Rivaud considers him “perhaps the most remarkable French thinker of the fifteenth and early sixteenth century.” Writing in 1507 on the famous men of France, Symphorien Champier acknowledged Bovelles as a disciple of Lefèvre and termed him “mathematicae deditissimus.” Born in Nieuport (Flanders), Clichtove also studied under Lefèvre at Paris. A champion of reform in philosophical and theological studies during the earlier part of his life, he devoted himself later almost exclusively to combating the doctrines of Luther.

Adams F 18; Moreau-Renouard I, 374, 140; Renouard VIII, 8; Smith, Rara, pp. 29-30; Houzeau-Lancaster 2290; Macclesfield 1225 (1522 edition); Schreiber 9. Boner (ed.), Change and Continuity in Early Modern Cosmology, 2011. Stedall, ‘Of Our Own Nation: John Wallis’s Account of Mathematical Learning in Medieval England,’ *Historia Mathematica* 28 (2001), 73–122. Victor, *Charles de Bovelles, 1479-1553: An Intellectual Biography, 1978. Andrews, Roger Payne and his art. A short account of his life and work as a binder*, 1892.

Folio (278 x 200 mm), ff. cxii, with numerous marginal woodcut diagrams. Title page ruled in red, with arms of the University of Paris and initials of Henri Estienne (without historiated border found in later editions). Eighteenth-century russia from the workshop of Roger Payne, spine and hinges with very well done restoration.

Item #3866

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Price:
$20,000.00
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