# A sammelband of 5 mathematical texts, in Latin, illustrated manuscript on paper, [Italy, late 15th century].

Details

FIBONACCI, Leonardo [c.1170-c.1250]; BOETHIUS, Anicius Manlius Severinus [c.480-524], GROSSETESTE, Robert [1175-1253]; [DE PULCHRO RIVO, Johannes, attrib.]

A sammelband of 5 mathematical texts, in Latin, illustrated manuscript on paper, [Italy, late 15th century].

217 x 158mm. v + 222 leaves + ii, complete, collation: 1-10

(2) Prince Baldassare Boncompagni-Ludovisi (1821-1894), one of the leading figures in 19th-century mathematics, a bibliophile and scholar responsible for the widespread propagation and popularisation of several key mathematical texts of the Middle Ages, including Fibonacci. His vast library consisted of some 650 manuscripts and over 20,000 printed volumes: the manuscripts alone constituting one of the largest private collections of scientific and mathematical texts. The texts in the present manuscript were assembled and bound by Boncompagni: remnants of his shelf label on spine and numbers 176 (see E. Narducci,

(3) Robert B Honeyman (1897-1987), metallurgical engineer and bibliophile. Purchased in 1932: his shelf mark ‘Gen Sci 6 Ms23’. His sale at Sotheby’s, May 2 1979, lot 1109 to Nico Israel. Offered in cat.22,

(4) J.G. Bergart, and loaned to the John Hay Library, Brown University (published in K.P. Harrington, ed.,

(5) Bonhams, 22 June 2011, lot 1009.

This sammelband gathers together some of the essential mathematical texts of the early Middle Ages. Written by the 6th-century Roman philosopher Boethius,

In 1852 Boncompagni listed 12 surviving manuscript copies – partial or fragmentary – of the

Leonardo Pisano, or Fibonacci, is rightly considered one of the greatest mathematicians of the Middle Ages. His most important work, the

The

The impact of Fibonacci on the history of Western mathematics is incalculable: even at the turn of the 16th century, Luca Pacioli would acknowledge his dependence on Fibonacci in his

A sammelband of 5 mathematical texts, in Latin, illustrated manuscript on paper, [Italy, late 15th century].

**A vanishingly rare testament to the foundations of modern mathematics and algebra: a 15****th****-century illustrated sammelband of mathematical texts****,****including the most significant chapters in Fibonacci****’****s revolutionary***Liber Abaci***, owned and bound by the one of the most important figures in the history of 19****th****-century mathematics, Prince Baldassare Boncompagni.**217 x 158mm. v + 222 leaves + ii, complete, collation: 1-10

^{8}, 11^{6}, 12-13^{8}, 14-15^{12}, 16^{10}, 17^{12}, 18^{14}, 19-23^{12}, 19th-century foliation in pen followed here, the first four texts ff.1-102 in two columns of 28-32 lines, ruled space: 173 x 56mm, the watermark a crossbow in a circle, closest to Bricquet 739, in use in Italy from 1468; rubrics and initials in red, capitals touched in red, the Boethius illustrated with 125 diagrams in red and brown, the Grosseteste illustrated with 10 diagrams, the final text by Fibonacci ff.104-221 in a single column of c.26 lines in an Italian humanist cursive hand, ruled space: 141 x 94mm, the watermarks of a cross and a bull’s head similar to Bricquet 11806 and 1455a, both found in the Venetian region in the 1480s (opening leaf with small marginal repair and some soiling, occasional ink erosion to diagrams, some marginal staining and thumbing). Mid-19th century marbled boards (edges scuffed and rubbed). In a chemise and red quarter morocco case.*Provenance*:*(1) Pietro Girometti (1811-1859), Roman gem-engraver and medallist. No 25 in his catalogue of*

*Codici Cartacei e Membranacei**dei secoli XIV**o**e XV**o**[**…**]*, 1856, sold with 33 other manuscripts to:(2) Prince Baldassare Boncompagni-Ludovisi (1821-1894), one of the leading figures in 19th-century mathematics, a bibliophile and scholar responsible for the widespread propagation and popularisation of several key mathematical texts of the Middle Ages, including Fibonacci. His vast library consisted of some 650 manuscripts and over 20,000 printed volumes: the manuscripts alone constituting one of the largest private collections of scientific and mathematical texts. The texts in the present manuscript were assembled and bound by Boncompagni: remnants of his shelf label on spine and numbers 176 (see E. Narducci,

*Catalogo di Manoscritti Ora Posseduti D. Baldassarre Boncompagni*, Rome, 1862, pp.74-75, no 176) and 122 (E. Narducci,*Catalogo di Manoscritti Ora Posseduti D. Baldassarre Boncompagni*, Rome, 1892, pp.77-78, no 122). Sold by his heirs in*Catalogo della Biblioteca Boncompagni. I Manoscritti. Facsimili, Edizioni del Secolo XV.**Abbachi Riviste*, Rome, 1898, lot 99.(3) Robert B Honeyman (1897-1987), metallurgical engineer and bibliophile. Purchased in 1932: his shelf mark ‘Gen Sci 6 Ms23’. His sale at Sotheby’s, May 2 1979, lot 1109 to Nico Israel. Offered in cat.22,

*Interesting Books and Manuscripts on Various Subjects [**…**]*, 1980, no 20, and purchased by:(4) J.G. Bergart, and loaned to the John Hay Library, Brown University (published in K.P. Harrington, ed.,

*Medieval Latin*, 1997, p.661 and p.31, where dated c.1390).(5) Bonhams, 22 June 2011, lot 1009.

*Contents*: BOETHIUS, Anicius Manlius Severinus,*De Institutione Arithmetica*, opening*‘*In dandis accipiendisque muneribus […]’, Book I ff.1-25, Book II ff.25-64; GROSSETESTE, Robert,*Compotus*, opening with a list of the twelve chapters on f.65, and the text proper ‘Computus e[st] sci[en]t[i]a num[era]tionis et divisionis t[em]por[um]’ ff.65-93; Tables for the comparison of Christian and Arabic years, tables of conjunction and opposition with explanatory notes, opening ‘Tabula ad inueniendum annos arabum’, ff.93v-96; [DE PULCHRO RIVO, Johannes, attrib.],*Computus Manualis*, opening ‘Inte[n]tio in hoc Capitulo e[st] Artem [...]’, ff.97-101; blank ff.102-3; FIBONACCI, Leonardo,*Liber Radicum*[chapters 14 and 15 from the*Liber Abaci*], opening ‘[Q]uidam numeri habent radices’, ff.104-221, the text largely corresponding with the Boncompagni edition of*Il Liber Abbaci di Leonardo Pisano*, 1857, pp.353-459, with the beginning of chapter 14 in the 1857 edition ‘Liceat mihi in hoc de radicum’ here at the end of the volume on f.220. The 1857 edition ends ‘[…] dragme pro quantitate rei’ (here on f.215v), the text here continues with references to Campanus of Novara [c.1220-1296] beginning: ‘Sum[m]a progressionis […]’ and ending ‘[…] divisus est igitur triang[u]l[u]s a b c in tres partes equales ut proponit. Camp.’, ff.215v-220.This sammelband gathers together some of the essential mathematical texts of the early Middle Ages. Written by the 6th-century Roman philosopher Boethius,

*De institutione Arithmetica*was the principal mathematical textbook of pre-12th century Western Europe, comprising a philosophical discussion of numbers, their relationships and meanings. One of the text’s most influential features was its division of the mathematical sciences into arithmetic, music, geometry, and astronomy, which it together designated as the*quadrivium*. The*Compotus*of the English statesman, scholastic philosopher, theologian and Bishop of Lincoln Robert Grosseteste was innovative in that it incorporated Arabic astronomical influences into computistical theory. In it Grosseteste defines ‘computus’ as a science of counting and dividing time, and his discussion of the solar year is a key contribution to the raging medieval debate around calendar reform. The text survives in 38 manuscripts (for the most recent critical edition see A. Lohr and C.P.E. Nothaft,*Robert Grosseteste**’**s**‘**Compotus**’*, 2019). By the far the rarest of the texts in this sammelband, though, is the extract from Fibonacci’s*Liber Abaci.*In 1852 Boncompagni listed 12 surviving manuscript copies – partial or fragmentary – of the

*Liber Abaci*(B. Boncompagni,*Della Vita e delle Opere di Leonardo Pisano, matematico del secolo decimoterzo*, Rome, 1852, pp.25-69). A more recent 2017 survey by the Italian mathematician Enrico Giusti lists eight complete, or near-complete manuscripts: one in Siena (Biblioteca Comunale L.IV.20, 13th century); one in Rome (Biblioteca Apostolica Vaticana, Pal.lat.1343, 13th/ 14th century); one in Milan, (Biblioteca Ambrosiana, ms. I.72 sup, 13th century); one in Naples (Biblioteca Nazionale, ms. VIII.C.18, 17th century); and five in Florence (Biblioteca Nazionale Centrale, Conv. Soppr. C.I.2616, 14th century; Magl. XI.21, 14th century; Fond. Princ. II.III.25, 16th century; Biblioteca Riccardiana, ms. 783, 15th century). In addition to these are extracts, such as the present manuscript, containing the final and most significant chapters of*Liber Abaci*. Eight of these manuscripts survive in public institutions. Three are in Paris: Bibliothèque Mazarine, ms. 1256, 14th century; Bibliothèque Nationale, Paris, Lat. 7367, 15th century; and Lat. 7225A, 16th century; three are in Florence: Biblioteca Riccardiana, ms. 2252, 14th century; Biblioteca Medicea Laurenziana, Firenze, Gaddi 36, 14th century; and Biblioteca Nazionale Centrale, Magl. XI.38, 16th century; one is in Perugia, Biblioteca Augusta, ms. D 68; and one is at the Vatican, Biblioteca Apostolica Vaticana, Vat. Lat. 4606, 14th century. The present Fibonacci text belongs to the Parisian trio of manuscripts, of which the one at the Mazarine is the primary exemplar: all three begin ‘Quidam numeri habent radices’, end with ‘Liceat mihi in hoc de radicum’ and contain the extra text with references to Campanus of Novara.Leonardo Pisano, or Fibonacci, is rightly considered one of the greatest mathematicians of the Middle Ages. His most important work, the

*Liber Abaci*, is the first complete and systematic explanation of Hindu-Arabic numerals by a European writer. Little is known of Leonardo’s life, and most biographical details are drawn from his introduction to his*Liber Abaci*. When he was young, his father was employed as a ‘publicus scriba’ in Bugia, modern-day Algeria, and it was apparently there that Leonardo learned how to use the abacus and became familiar with Hindu-Arabic numeration. He travelled widely through Egypt, Syria, Greece, Sicily, and Constantinople, where he developed his skills as a mathematician, became involved in academic debates, and fell into the court circles of Frederick II, Holy Roman Emperor.The

*Liber Abaci*is divided into 15 chapters. The first section introduces the Hindu-Arabic number system, including methods for converting between different representation systems. This section also includes the first known description of trial division for testing whether a number is composite and, if so, factoring it. The second section deals with commerce, conversions of currency and calculations of profit and interest. The third and largest section deals with a number of mathematical problems, including the Chinese remainder theorem, perfect numbers and Mersenne primes as well as formulas for arithmetic series and for square pyramidal numbers. The final and most important section, which includes chapters 14 and 15, and was in a small group of distinct manuscripts (see above) – as in this one – extracted as a stand-alone text, deals with approximations, both numerical and geometrical, of irrational numbers such as square roots, and introduces Fibonacci’s algebraic method, drawing on Euclid’s*Elements*and introducing Arabic sources into European mathematics for the very first time.The impact of Fibonacci on the history of Western mathematics is incalculable: even at the turn of the 16th century, Luca Pacioli would acknowledge his dependence on Fibonacci in his

*Summa*. According to William Goetzman: ‘The five-hundred-year period following Leonardo saw the development in Europe of virtually all the tools of financial capitalism that we know today: share ownership of limited-liability corporations, long-term government and corporate loans, liquid and active international financial markets, life insurance, life annuities, mutual funds, derivative securities, and deposit banking. Many of these developments have their roots in contracts first mathematically analyzed by Fibonacci'. (W. Goetzmann, ‘Fibonacci and the Financial Revolution’,*The Origins of Value: The Financial Innovations that Created Modern Capital Markets*, 2005, p.125).Special Notice

No VAT on hammer price or buyer's premium.

## Brought to you by

Eugenio Donadoni
Senior Specialist, Medieval & Renaissance Manuscripts