Tabule Ioan. Blanchini Bononiensis, cum plerisque additionibus ac novis tabellis nuper impresse, per L. Gauricum neapolit. castigate.

Venice: Giunta Lucantonio, 1526.

First edition edited by Luca Gaurico, second edition overall (first, 1495), of “the largest set of astronomical tables produced in the West before modern times” (Chabas & Goldstein, p. viii). “Bianchini set out to achieve a correction of the Alfonsine Tables – the standard in Europe for a couple of centuries by the time he wrote – with those of Ptolemy. He was a great admirer of Ptolemy and critical of the corrupted Ptolemaic and Alfonsine texts then in current use” (Tomash, p. 141). This second edition contains almost twice as much astronomical data as the first. “Bianchini’s set of auxiliary tables for computing planetary latitudes in the edition of 1526 was not included in the editio princeps of 1495, despite the fact that these tables appear in manuscript copies … they appear in a manuscript copied by Copernicus” (Goldstein & Chabas, p. 458). Bianchini was “the first mathematician in the West to use purely decimal tables” (Feingold, p. 20), at the same time as Al-Kashi in Samarkand, and he also used negative numbers and the rule of signs. Bianchini (d. 1469), an astronomer attached to the Ferrara court of the Este, was considered by his disciple Regiomontanus to be the greatest astronomer of his time, and his Tabulae was one of the most sophisticated and widely-disseminated fifteenth-century attempts to correct the Alfonsine Tables, the thirteenth-century planetary tables that were relied upon by all astronomers and navigators well into the sixteenth century. His rigorous mathematical approach made the Alfonsine Tables available in a form that could be used by Renaissance astronomy. Among the known manuscripts of Bianchini’s Tabulae in European public collections is one copied by Regiomontanus at Vienna in 1460 (Nuremberg Stadtbibliothek MS Cent V 57), and another copied later in the century by Copernicus himself at Padua (Uppsala MS Copernicana 4, ff. 276-81), underlining the influence of the Tabulae on the two greatest astronomers of the early modern period. “There can be little doubt that early in his career Copernicus depended on Bianchini’s tables for planetary latitude which, in turn, are based on Ptolemy’s models for the Almagest. Hence, Bianchini’s tables can be considered as a source for Copernicus’s knowledge of astronomy” (Goldstein & Chabas, p. 470). Georg Peurbach and his student Regiomontanus visited Bianchini in Ferrara and corresponded with him, and they “were both calculating ephemerides from Bianchini’s tables around 1456. Of their contemporaries (Regiomontanus’ and Peurbach’s), only Bianchini … possessed a comparable proficiency and originality” (DSB XV, pp. 474-5). ABPC/RBH list only one copy of this edition, and that defective, and none of the first edition. OCLC lists five copies in US (Brown, Burndy, Columbia, Huntington, Michigan).

“As an exact science astronomy makes extensive use of numerical computations. In early astronomy, this is best exemplified by astronomical tables in the tradition of Ptolemy’s Almagest that dates to the 2nd century AD. Throughout the Middle Ages, astronomers compiled a great variety of astronomical tables to help computers determine the positions and other circumstances of the heavenly bodies and to help them solve astronomical problems related to the daily rotation, the determination of the times of eclipses, etc. … Astronomers addressing a variety of problems put together different tables and compiled ‘sets of tables,’ that is, consistent collections of astronomical tables embracing all or some aspect of mathematical astronomy and usually accompanied by a text, called ‘canons’, explaining their use. Most sets of tables compiled in Europe in the Middle Ages followed the structure of those composed in Arabic, that is, handbooks called zijes.

“In the Renaissance the mathematical sciences played an important role in humanistic culture, and they were highly appreciated at various social levels. Mathematical astronomy was regarded as especially valuable, for it was associated with cosmology and philosophy, as well as with astrology and astrological medicine. In other words, there was a considerable market for publications that included almanacs, ephemerides, and lunaria, several of them ranking among the best sellers in scientific publications, as well as sets of astronomical tables. The investment of time and money by the printer in producing these sets of tables was significant, and the fact that more than one edition of the same set appeared is an indication of the popularity of this genre. In particular, Bianchini’s tables were printed three times between 1495 and 1553.

“By the time Bianchini compiled his tables (c. 1442), European astronomers has access to several variants of the Parisian Alfonsine Tables, that is, a set of tables which was recast beginning in the 1320s by a group of notable scholars working in Paris, and based on the work done by the astronomers in the service of King Alfonso X of Castile in the second half of the 13th century. Unfortunately, only the canons of the original Castilian Alfonsine Tables are extant, not the tables themselves.

“All these sets of astronomical tables are in the tradition of Arabic zijes: they contain a great many tables and, at their core, are those for the determination of the positions and motions of the five planets and the luminaries. The position of a planet in longitude (along the ecliptic), as well as the Sun and the Moon, is computed from tabulated values for mean motions and equations … in addition to tables for planetary longitude, there are tables for eclipses, planetary latitudes (the distance of a planet north or south of the ecliptic at any given time), etc. …

“The Alfonsine tradition lies within the Ptolemaic tradition, having a set of parameters in common as well as the same underlying model. Nevertheless, we find a great variety of tables in this tradition, and among them are those of Bianchini … his set depends directly on the Alfonsine tradition, but differs from all previous sets in various critical ways: the tables for the planets and the luminaries have a consistent format based on an internal organizing principle different from other sets of tables, and his tables contain the largest number of entries ever computed in the Alfonsine tradition …

“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. And so they were published in 1495 in Venice for the first time …

“The editio princeps (1483) of the Parisian Alfonsine Tables devoted 120 pages to numerical tables, excluding the star catalogue. In these pages we have counted more than 51,000 numbers of one or two digits, of which 41,000 have been computed, and about 10,000 are for the arguments in the tables (i.e., belonging to sets of consecutive numbers). The tables authored by Bianchini fill 633 pages in the edition of 1495 and contain about 315,000 numbers of one or two digits, that is, more than 6 times the amount in the Parisian Alfonsine Tables. Of these, 300,000 have been computed (more than 7 times the amount in the Parisian Alfonsine Tables), and about 15,000 are for the arguments. It should be noted that the second edition of Bianchini’s tables (1526) enlarged the number of tables from 68 to 111, thus considerably increasing the undertaking of printing numbers” (Chabas & Goldstein, pp. 1-11).

Many of Bianchini’s tables are ‘double argument tables’. “The simplest astronomical table consists of two columns of numbers, such that for each value in the first column there corresponds one and only one entry, representing what nowadays is called a function. The first column gives the successive values of the argument, currently called the independent variable. The information contained in such a table can be represented as a two-dimensional graph, although it was not done so at the time. Astronomical tables in the Almagest were not all of the simplest kind, for many of them had more than two columns, such that the entries in each column depended on a single argument. In the Latin West a special form of astronomical tables, introduced in the 14th century, is called a ‘double argument table’, that is, a table with two arguments, one set at the head of each column and another set at the head of each row, corresponding (in modern terms) to a function of two variables. This ingenious type of table can be represented as a three-dimensional graph. The advantage of double argument tables is that they reduce the number of steps in the computation of a planetary position, etc. But this meant that the table maker had to produce many more entries in the tables, which required him to perform a larger number of computations” (Chabas & Goldstein, p. 1).

“The book has two dedications, one to Leonello d’Este (d. 1450), … and a later one addressed to Frederick III, Holy Roman Emperor … the dedication to Emperor Frederick was suggested by Bianchini’s patron at the time, Borso, and was presented to the Emperor on the occasion of his visit to Ferrara in January 1452 …Prior to the dedications in the first two printed editions, we find an encomium in praise of Bianchini’s book that was written by Augustinus Moravus in January 1495 at Padua. In these editions the tables are preceded by canons consisting of an Introduction and 51 chapters …

“The Introduction begins with references to Ptolemy and the Almagest: ‘Ptholomeus qui merito illuminator divine astrologie vocari potest, in suo libri Almagesti.’ Several scholars other than Ptolemy are mentioned (Hipparchus, Thabit ibn Qurra, al-Battani, the compilers of the Toledan Tables, and Alfonso X, among others), but we note that none of them are later than Alfonso (d. 1284). The Introduction focuses on two astronomical matters, precession/trepidation and the latitude of the planets. Bianchini praises the work of Alfonso and in the first table of the treatise he addresses the problem of precession/trepidation strictly in accordance with the Alfonsine corpus. As for the planetary latitudes, Bianchini indicates that he compiled tables following the instructions given by Ptolemy in Book XIII of the Almagest, which is indeed the case, to overcome ‘significant discrepancy from the truth, especially for Venus and Mercury’, found in other sets of tables. The Introduction closes with some basic information helpful to the reader when using his tables …

“In the edition of 1526 the editor, Luca Gaurico, added 8 short paragraphs after Chapter 51. The title of the first is ‘Verum ascendentis gradum per earum seminis rectificare secundum Jacobum Dundum patavinum’, apparently based on a previous work by the astronomer Jacopo de Dondi of Padua (1298-1359), and that of the eighth, ‘Latitudinem 5 errantum supputare,’ On the other hand, the edition of 1553 has only the first 18 chapters” (Chabas & Goldstein, pp. 15-19).

“Giovanni Bianchini was appointed by Nicolo d’Este to a position in the Ferrara accounting office in 1427, and was made director in 1430. He became Fattor generale in 1433, ambassador to Milan in 1446, was sent to Rome in 1450 because of some business involving coinage, and spent three months in Venice in 1454. He had achieved this high standing despite his lacking a formal education and his never having been to the university. Nothing is known about his birth and death dates; he probably died in 1466 or shortly thereafter, at an advanced age.

“Bianchini had published several large tables. One of these, on the motions of the planets, he dedicated to Leonello de Ferrara in 1442. The sixty-fold division of the signs (after the Alfonsine Tables) was continued in these tables; an innovation that he introduced was a set of tables from which the synodic revolution could be deduced from the true position of the planets for each day. Regiomontanus had made himself a copy in Vienna of these tables and an abbreviated commentary, albeit first in 1460 …

“When Frederick III was in Italy in 1452, he took Bianchini into his service as an advisor and elevated him to the nobility. According to the heraldic letter of May 18, 1452, his coat-of-arms showed the Imperial Eagle and an armillary sphere. In gratitude Bianchini dedicated an annotated table to him … This work is supposed to give the foundations of astrology, but instead is a miscellaneous collection of unrelated tables without any of Bianchini’s own input …

“Later, Bianchini published another collection of tables, Tabulae primi mobilis, to which he repeatedly referred in his letters. These tables made it possible to correct celestial events to the Ferrara horizon … Part of this table and those of the first work were printed in Venice in 1495, and were edited by Gauricus later (1526 and 1553)” (Zinner, pp. 37-8).

Bianchini wrote five other treatises, which survive only in manuscript: Compositio instrumenti, on the construction and use of an instrument to determine the altitude of the stars; Canones tabularum super primo mobile, on spherical trigonometry; Flores Almagesti, his largest work, dealing with arithmetic, algebra, proportion, and various astronomical matters; Canones tabularum de eclipsibus luminarium, which reports observations he had made on several lunar and solar eclipses; and Tabulas magistrales, a set of decimal tables including tangents and cosecants.

Houzeau & Lancaster 12595. Tomash B150 (manuscript). Chabas & Goldstein (eds.), The Astronomical Tables of Giovanni Bianchini, 2009. Goldstein & Chabas, ‘Ptolemy, Bianchini, and Copernicus: Tables for Planetary Latitudes,’ Archive for History of Exact Science 58 (2004), pp. 453-73. Zinner, Regiomontanus, 1990.



4to (215 x 151 mm), ff. [xxviii], 398, title and some of the tables printed in red and black, lily device printed in red on title and in black on final leaf, woodcut initials (numerous errors in pagination). Contemporary vellum, remains of ties, a fine and attractive copy.

Item #4502

Price: $9,500.00

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