The volume starts with a dedication and prologue; the text of canons, which explains the tables and how to use them, with examples; followed by the tables themselves.
A list of the 52 canons (f.1r); the dedication to Leonello d’Este (d. 1450) and prologue: "Johannes Blanchinus Ill(ustri) p(rincipi) domino Leonello Marchioni Esten(si) [salutem] p(lurimam) d(icit). Consideranti michi dive Leonelle et principatum tuum …" (f.4r); the main text of the canons: "[P]tholomeus qui merito illuminator divine artis astronomie vocari potest suo libro Almagesti …" (f.4v), ending "… Et hoc sufficit deo laus. Finiunt Canones tabularum Johannis de Blanchinis" (f.18v); tables (f.20), beginning with tables of precession, headed "Augis communis", including some calculated for Ferrara and Bologna; a second group of tables, beginning with a "Tabula mediorum motuum in annis Christi collectis" (f.144v) (the 122 tables of the 1495 edition are listed and explained by Chabás and Goldstein, 2009, pp.24-132); added near-contemporary notes (f.152v) include a poem to the Virgin Mary by Maffeo Vegio (d.1458): "Virgo decus nostrum cuius se credidit alvo…".
Giovanni Bianchini has been described as the fifteenth century’s "foremost astronomer, not excepting such men as Toscanelli and Regiomontanus" (Thorndike, 1950, p.5). Originally from Bologna, he taught at the University of Ferrara and worked for three successive Dukes of Ferrara: Nicolò (d.1441), Leonello (d.1450), and Borso (d.1471). It is known that he was still alive in 1469, so the present manuscript was probably copied within his lifetime. His tables, completed in 1442, were based largely on the Parisian version of the Alfonsine tables, so-called because they were compiled by astronomers for King Afonso X of Castile (d.1284, see lots 8 and 9); the original tables were soon lost, however, and only the canons survived, from which scholars in Paris in the 1320s compiled new tables.
"The tables of Giovanni Bianchini … are the largest set of astronomical tables produced in the West before modern times … his tables reflect a well defined approach to astronomy, a practical way to present it, and a solid computing ability … his set depends directly on the Alfonsine tradition, but differs from all previous sets in various crucial ways: the tables of the planets and the luminaries have a consistent format based on an internal organising principle different from the other sets of tables" (Chabás and Goldstein, 2009, pp.viii, 8). To give a sense of the scale of his achievement, they record that the tables occupy 633 pages in the 1495 printed edition, and include about 315,000 numbers of one or two digits, of which more than 300,000 have been computed, and about 15,000 are for the arguments.
About twenty-two manuscripts include some or all of the tables, but several of these do not include the prologue and canons, which explain how they were compiled and how they are to be used. For example, "The Introduction closes with some basic information helpful to the reader when using the tables: years are 365;15 days; the beginning of the year is March 1; the epoch is the Incarnation; physical signs of 60° are used, as in the Parisian Alfonsine Tables; computed examples and some tables are for Ferrara whose geographical coordinates are longitude 32° and latitude 45°; and motions are referred to the 9th sphere (i.e., the coordinates are tropical)" (Chabás and Goldstein, 2009, p.16).
There are two main versions of the text: the earlier one, represented by the present manuscript, has a dedication composed in 1442 to Leonello d’Este (d.1450), while the later one has a dedication to Frederick III (d.1493), Holy Roman Emperor, composed in honour of his visit to Ferrara in 1452. Although it was produced in the 1460s (or perhaps the early 1470s), the present manuscript is a copy of the "first edition".
Compared to the usual full set of 51 canons (see Chabás and Goldstein, 2009, pp.16–18; cf. Thorndike, 1950, pp.172-74), the present manuscript has an extra one, no. 36, making a total of 52. In addition, there is a very curious interpolation. At the bottom of f.10v, in the middle of the 27th canon, is a note indicating that the text continues on the next-but-one leaf (rather than on the immediately following page). On the intervening leaf is a text, apparently unpublished, written entirely in red ink, beginning: "Et si equationes dierum sit subtilissime investigationis … Scias itaque quod dies astrologi idest equalis est transitus totius firmamenti …" and ending "… Vale tuus Marcus Sanutus". The text starts in the left column of the verso (f.11v) continues in the right column, then in the lower margin, and then in the lower margin of the facing page (f.12r). We have found no evidence that this text appears in any other manuscript, and it may thus be unique, composed specifically for the present volume. Its author is doubtless the Venetian patrician Marco Sanuto (d.1505), described as "dottissimo in ogni disciplina, ma principalmente negli studii dell’astronomia, dell’aritmetica, della geometria, e in tutti insomma le parti matematiche versatissimo" (Cigogna, 1827, p.111).
In addition to the present canons and tables, Bianchini composed five other shorter works between 1440 and 1460: (i) Compositio instrumenti discusses an instrument used to determine the altitude of stars; (ii) Canones tabularum super primo mobile is about spherical trigonometry; (iii) Flores Almagesti is a collection of 8-10 treatises on arithmetic, algebra, astronomy, etc.; (iv) Canones tabularum de eclipsibus luminarum reports observations of eclipses in 1440, 1448, 1451, and 1455, and computations for a future eclipse in 1460; while (v) Tabulas magistrales includes high precision tables for tangents and cosecants, "where Bianchini abandons sexagesimal notation, replacing it with decimal notation … [he] was the first mathematician in the West to use purely decimal tables of trigonometric functions, soon followed by Regiomontanus" (Chabás and Goldstein 2009, p.20).
RARITY AND IMPORTANCE FOR THE HISTORY OF SCIENCE
"Probably due to their substantial size and complexity, the tables of Bianchini were not copied very often in manuscript, but frequently enough to suggest to the printer that there was a market for them" (Chabás and Goldstein, 2009, p.9). There were three printed editions, in 1495, 1526, and 1553, the first two published in Venice, the third in Basel. Chabás and Goldstein knew of twenty-one manuscripts that include some or all of the tables, of which none are in the USA, and none in private hands; the present manuscript and a copy formerly in the Honeyman collection (which belongs to the later post-1452 "second" edition) were apparently unknown to them. Based on published descriptions of the other copies, it appears that at least five are incomplete, at least seven more contain the second edition of the text, and at least four more are later in date than the present manuscript. In other words, it seems that a maximum of five other complete copies of the first edition exist that are as early as the present copy, and all of them are in European institutional libraries (two in Cracow and one each in Florence, Milan, and Vienna).
Bianchini famously corresponded in the 1460s with Johannes Müller, alias Regiomontanus (d.1476), and in a letter dated 1456 Georg Peurbach (d.1461) describes how he and Regiomontanus had used Bianchini’s tables when calculating ephemerides. In fact, Regiomontanus made his own copy of the tables in 1460, a manuscript now in Nuremberg (Stadtbibliothek, MS Cent V 57). Likewise Nicolaus Copernicus (d.1453) copied parts of the tables (Uppsala, MS Copernicana 4): "there can be little doubt that early in his career Copernicus depended on Bianchini’s tables for planetary latitude … hence, Bianchini’s tables can be considered a source for Copernicus’s knowledge of astronomy" (Chabás and Goldstein, 2004, repr. 2014).
Probably no two of the manuscripts or printed editions are entirely alike in their contents; "as a living text, each copy was personal for some astronomer and differs from copies in the possession of other astronomers" (Chabás and Goldstein, 2009, p. 23). It has not been possible for the present catalogue to tabulate the present volume with others in the manner of Chabás and Goldstein (pp.24-27; cf. Thorndike, 1950, pp.174-75), but it is probable that future research on the present manuscript would throw considerable light on the dissemination, circulation, emendation, and influence of Bianchini’s work.
E.A. Cigogna, Delle inscrizioni Veneziane, II, 1827
Thorndike, ‘Giovanni Bianchini in Paris Manuscripts’, Scripta Mathematica, 16, 1950, pp.5-12, 169-80
Chabás and B. Goldstein, ‘Ptolemy, Bianchini and Copernicus: Tables for Planetary Latitudes’, Archive for the History of Exact Sciences, 58, 2004, pp.553-73; reprinted in their Essays on Medieval Computational Astronomy, 2014
Chabás and B. Goldstein, The Astronomical Tables of Giovanni Bianchini, 2009
Chabás and B. Goldstein, A Survey of European Astronomical Tables in the Late Middle Ages, 2012
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