Fibonacci manuscript: Boethius Arithmetica; Grosseteste Computus; Johannes de Pulchro Rivo Computus Manualis; Fibonacci Liber Flos i.e. Liber Abbaci chapters 14 and 15
Lot 1009
Sold for US$ 338,000 inc. premium
Auction Details
Fibonacci manuscript: Boethius Arithmetica; Grosseteste Computus; Johannes de Pulchro Rivo Computus Manualis; Fibonacci Liber Flos i.e. Liber Abbaci chapters 14 and 15 Fibonacci manuscript: Boethius Arithmetica; Grosseteste Computus; Johannes de Pulchro Rivo Computus Manualis; Fibonacci Liber Flos i.e. Liber Abbaci chapters 14 and 15 Fibonacci manuscript: Boethius Arithmetica; Grosseteste Computus; Johannes de Pulchro Rivo Computus Manualis; Fibonacci Liber Flos i.e. Liber Abbaci chapters 14 and 15
Lot Details
5 mathematical manuscript texts in Latin, [Italy or Northern Italy: late 14th century – late 15th century], all on paper, bound into a single volume. The first four texts in one codex, written out in an Italian gothic hand [watermarks of crossbow in a circle, cf. Bricquet 743-750]; leaves 1-102 (final leaf 102 blank), a-k8, l6, m-n8, in double column, with headings, some underlining, capital strokes and rubricated initials, the text by Boethius illustrated by 125 diagrams in red and brown, the text by Grosseteste illustrated with 10 diagrams.
The final text of the volume comprises a rare work by Fibonacci, written out in an Italian humanist cursive hand of the late 15th century [watermarks of a cross and a bulls head cf. Bricquet 11806 and 1455a, both found in the Venetian region in the 1480's], leaves 103-221 (leaves 103 and 222 blank) single column, a-b12,c10, d12, e14, f-k12. Initials and chapter headings left blank for rubrication.
Together 222 leaves (foliated in a 19th century hand probably at the time of binding). Mid-19th century marbled boards. Custom chemise and red quarter morocco case. First leaf with a small marginal repair and light soiling, pale narrow staining to the top edge of about 40 leaves, a few ink-burns to the diagrams, binding lightly rubbed with joints and corners showing.

1. BOETHIUS, Anicius Manlius Severinus [c 480-524] De Arithmetica.
Opening "Incipit arismetice dandies accipiendisque." TK 669. Books I and II. Fol 1r-24v; Fol II 25r-64r.
2. GROSSETESTE, Robert [1175-1253]. Computus. Opening "Incipit compotus magistri R nichomensis epsicopi ... Computus est Scientia numerationis et divisionis temporum." TK 243. Fol 65r-93r.
3. [Various tables for the comparison of Christian and Arabic years, tables of conjunction and opposition etc with explanatory notes.] Fol 93v-96r.
4. [DE PULCHRO RIVO, Johannes, attrib.] Computus Manualis.
Opening "Incipit computus manualis. Intentio in hoc capitulo est artem." TK 764. Fol 97r-101r, 102 blank.
5. FIBONACCI, Leonardo of Pisa [c 1175-1250]. Liber Flos [chapters 14 and 15 from the Liber Abaci]. Opening "Incipit: liceat mihi in hoc de radicum." Chapter 14. TK 1245, the text corresponding with the version published by Boncompagni in 1857 pp 353-459. Fol 215r-220r comprise an unidentified continuation of the text not published by Boncompagni.

The Boncompagni-Honeyman copy. An important surviving sammelband of medieval and ancient mathematical texts including a rare example of the Liber Flos by Fibonacci, one of the most influential mathematical works from the early centuries of the second millennium. The first four texts were copied out by a scribe in the late 14th century and including several astronomical tables of the 13th century and Boethius's mathematical magnum opus De Arithmetica. The most important of the texts in this sammelband is the Fibonacci text for Liber Flos, copied out separately from the Liber Abaci in the late 15th century. THIS MANUSCRIPT IS ONE OF ONLY FOUR SURVIVING EXAMPLES of the advanced mathematics of chapters 14 and 15.

Leonardo of Pisa, called Fibonacci, is often considered the greatest mathematician of the Middle Ages, and the mathematical Renaissance may be dated to him. His most important and largest work [the Liber Abaci] is the first complete and systematic explanation of the Hindu numerals by a Christian writer (Sarton, Introduction to the History of Science II: 611). Leonardo was born around 1175, the son of a Pisan merchant, and in his early life travelled widely around Italy to Genoa and Venice, but also to Barbary, Egypt, Syria, Greece and France. On these trips he seems to have learned the Arabic ways of arithmetic and computation. From 1200 he settled back in Pisa and started on his mathematical writings, the first and most important work was the Liber Abaci (The Book of Calculation) written in 1202. Unfortunately no copy of this first version has survived. Around 1228 a second version of the text was completed, with additional chapters including the last two chapters 14 and 15, the fourth section of the work, also found separately transcribed as Liber Flos. In the Dictionary of Scientific Biography Kurt Vogel analysed the Liber Abaci in its four sections. The first section introduces and explains the Indian number system [Hindu-arabic numerals], the second section explains mercantile calculations, the third and largest section answers many mathematical problems, and the fourth section chapters 14 and 15, which Vogel describes as the most advanced mathematically. "Leonardo here shows himself to be a master in the application of the algebraic methods and an outstanding student of Euclid. Chapter 14 is devoted to Calculus with radicals ... at the end of Chapter 15 ... one sees particularly clearly what complete control Leonardo had over the geometrical as well as the algebraic methods for solving quadratic equations and with what skill he could use in applied problems."
After 1228 very little is known of Fibonacci's life but his influence was significant for another 500 years. Even in 1500 in Pacioli's Summa, Pacioli acknowledges his complete dependence on Fibonacci. Fibonacci's original work and the copies of it are locked away in a small number of manuscripts, most of which are in Italy in the Vatican Library. It is said that there are 12 surviving mss texts of the Liber Abaci, and 4 copies of selected chapters 14 and 15, two in the Vatican library (Vatican Urb Lat 291, 14th century in Italian) called Fiore dei Fiori and another (Vatican Latin 4606, 14th century in Latin) called Flos. The two known examples outside Italy, the present one and another in the Bibliotheque Nationale (BN 7367- probably Flos), both conform with the published text in 1857.
It was not until Boncompagni published the text in 1857 that Fibonacci's important work was exposed to a wider "modern" mathematical community. Since then, the modern world's debt to Fibonacci has become increasingly apparent. The Liber Abaci was the first mathematical guide to achieve popularity in the fields of commerce and industry, with its practical applications in book-keeping, weights and measures, and the calculation of interest, and it was also the first text to suggest that a negative number could be used to represent a loss. The Golden Ratio found in Fibonacci's sequence has been observed in plant life, brain waves, architecture, aircraft, and music. In the 20th century his calculations have been adapted for new uses such as investment practices, where technical traders use ratios derived from the sequence to establish levels of support and resistance in stock prices ("Fibonacci retracement"). Recently Fibonacci has achieved wider popular recognition still as a key plot element in Dan Brown's Da Vinci Code.

Narducci, Enrico. Catalogo di Manuscritti ora posseduti da Baldasarre Boncompagni. Rome, 1892. Present MS is no 122 pp 77-78.
Faye, C.U. & W.H. Bond. Supplement to the census of Medieval and Renaissance Manuscripts in the United States and Canada, 1962, p 20 no 6.
Harrington, K.P. & Joseph Pucci. Medieval Latin 1997, plates 5, 30, 31.

1. Prince Baldassare Boncompagni-Ludovisi (1821-1894). These texts were assembled and bound by Boncompagni, with the remnants of his shelf label on spine and number 122, and his number 176 beneath (listed in his catalogue as ms122). The famous Aristocratic collector of mathematical texts in Italy in the 19th century and a historian of Science. This volume sold at auction in 1898.
2. Purchased by Robert B Honeyman in 1932 (his shelf mark Gen Sci 6 Ms23).
3. Honeyman sale Sothebys London, May 2 1979, lot 1109 to Nico Israel.
4. Purchased by J.G. Bergart in 1980, since on loan to the John Hay Library, Brown University.
See illustrations.
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