In this paper, we analyze the astronomical tables for 1340 by Immanuel ben Jacob Bonfils who flourished 1340–1365, based on four Hebrew manuscripts. We discuss the relation of these tables principally with those of al-Battānī, Abraham Bar Ḥiyya, and Levi ben Gerson, as well as with Bonfils’s better known tables, called Six Wings. An unusual feature of this set of tables is that there are two kinds of mean motion tables, one arranged for Julian (...) years from 1340 to 1380, months, days, hours, and minutes of an hour, and the other arranged in the Hebrew calendar for the times of conjunctions and oppositions of the Sun and the Moon only, with subtables for 19-year cycles, single years in a 19-year cycle, and months. The latter arrangement is found in Bonfils’s Six Wings for solar and lunar motions only, whereas in his Tables for 1340, this arrangement applies to all planets. Notably absent are tables for the trigonometric functions, etc., that are generally found in such sets of astronomical tables. (shrink)

ABSTRACTThe known works of the medieval astronomer/astrologer Henry Bate include a set of planetary mean motion tables for the meridian of his Flemish hometown Mechelen. These tables survive in three manuscripts representing two significantly different recensions, but have never been examined for their principles of construction or underlying parameters. Such analysis reveals that Bate employed an unusual value for the length of the tropical year, which was probably derived by comparing ancient and contemporary observations of the vernal equinox. (...) In addition, there are clear signs that Bate kept revising his parameters for the mean motions of Venus and the three superior planets, none of which can be traced back to earlier sources. Together with some of Bate’s preserved statements, these findings support the conclusion that the Tabule Machlinenses were unique among the astronomical tables produced in medieval Latin Christendom for using independently derived parameters that were the result of new observations. Bate’s achievement connects him to a wider milieu of astronomers operating in late-thirteenth-century Paris, who put an increased emphasis on observation and the critical examination of received data. (shrink)

In astronomy Abraham Zacut is best known for the Latin version of his tables, the Almanach Perpetuum, first published in 1496, based on the original Hebrew version that he composed in 1478. These tables for Salamanca, Spain, were analyzed by the authors of this paper in 2000. We now present Zacut’s tables preserved in Latin and Hebrew manuscripts that have not been studied previously, with a concordance of his tables in different sources. Based on a hitherto (...) unnoticed text in a Latin manuscript, we argue that Zacut is the author of the Tabule verificate which, in our publication of 2000, we took to be anonymous. We also discuss in detail Zacut’s tables for epoch 1513 for Jerusalem that are arranged for the Hebrew calendar, rather than the Julian calendar that he used elsewhere. We then consider a number of fragmentary texts that were found in the Cairo Geniza, now scattered in various European and American libraries. The new evidence is consistent with our earlier finding that Zacut depended both on the medieval Hebrew tradition in astronomy and on the Parisian Alfonsine Tables. (shrink)

Ptolemaic Tradition and Islamic Innovation: The Astronomical Tables of Kūshyār ibn Labbān. By Benno Van Dalen. Ptolemaeus Arabus et Latinus, Texts, vol. 2. Turnhout, Belgium: Brepols, 2021. Pp. xviii + 595, 16 color pls. €120; https://ptolemaeus.badw.de/publications.

The anonymous set of astronomical tables preserved in Paris, Bibliothèque nationale de France, MS lat. 10262, is the first set of displaced tables to be found in a medieval Latin text. These tables are a reworking of the standard Alfonsine tables and yield the same results. However, the mean motions are defined differently, the presentation of the tables is unprecedented, and some new functions are introduced for computing true planetary longitudes. The absence of any (...) instructions as well as unusual technical terms in the headings make it difficult to appreciate the cleverness that went into the construction of these tables that are extant in a unique copy. In this article we provide a detailed analysis of these tables and their underlying parameters. The displaced tables are typical of a pervasive tendency in Islamic science to provide extensive and elegant numerical tables for the convenience of practitioners. The underlying astronomical theory is neither questioned nor affected.Edward S. Kennedy. (shrink)

An Andalusian tradition of zījes seems to have been predominant in the Maghrib due to the popularity of the zīj of Ibn Is[hdotu]āq al-Tūnisī and derived texts compiled in the fourteenth century. This tradition computed sidereal planetary longitudes and allowed the calculation of tropical longitudes by using trepidation tables based on models designed in al-Andalus by Abū Is[hdotu]āq ibn al-Zarqālluh. This tradition also used Ibn al-Zarqālluh's model to calculate the obliquity of the ecliptic, which implied that this angle had (...) a cyclical period of oscillation between a maximum of 23;53° and a minimum of 23;33°: after reaching this minimum value the obliquity of the ecliptic was bound to increase. This paper argues that some new Maghribi sources give information on observations made in the Maghrib in the fourteenth and beginning of the fifteenth centuries that imply that precession had increased beyond the limits allowed by the Zarqāllian trepidation theory, while the obliquity of the ecliptic had diminished below the level accepted by astronomers who followed Ibn al-Zarqālluh. This explains the introduction in the Maghrib of Eastern zījes, which computed directly tropical longitudes and did not accept the cyclical variation of the obliquity. Information about observations of dawn and twilight made both in Egypt and in the Maghrib in the fourteenth and fifteenth centuries is also presented. (shrink)

A table in five columns for the radii of the Sun, the Moon, and the shadow is included in sets of astronomical tables from the fifteenth to the early seventeenth century, specifically in those by John of Gmunden (d. 1442), Peurbach (d. 1461), the second edition of the Alfonsine Tables (1492), Copernicus (d. 1543), Brahe (d. 1601), and Longomontanus (d. 1647). The arrangement is the same and the entries did not change much, despite many innovations in (...) class='Hi'>astronomical theories in this time period. In other words, there is continuity in presentation and, from the point of view of the user of these tables, changes in the theory played no role. In general, the methods for computing the entries are not described and have to be reconstructed. In this paper, we focus on the users of these tables rather than on their compilers, but we refer to modern reconstructions where appropriate. A key issue is the treatment of the size of the Moon during a solar eclipse which was not properly understood by Tycho Brahe. Kepler’s solution and that of his predecessor, Levi ben Gerson (d. 1344), are discussed. (shrink)

ArgumentThe Astronomical Book of Enoch describes the passage of the moon through the gates of heaven, which stand at the edges of the earth. In doing so, the book describes the position of the rising and setting of the moon on the horizon. Otto Neugebauer, the historian of ancient science, suggested using the detailed tables found in later Ethiopic texts in order to reconstruct the path of the moon through the gates. This paper offers a new examination of (...) earlier versions of the Astronomical Book, using a mathematical analysis of the figures and astronomical theories presented throughout the Aramaic Astronomical Book; the results fit both the data preserved in the scrolls and the mathematical approach and religious ideology of the scroll's authors better than the details found in the late Ethiopic texts. Among other new insights, this alternate theory also teaches about the process of the composition of the Astronomical Book in the first centuries of its composition. (shrink)

In the century between the creation of the first large, European astronomical observatory by Tycho Brahe in the 1580s and the national observatories of France and England in the 1660–1670s, astronomers constructed ever more sets of tables, derived from various geometrical and physical models, to compute planetary positions. But how were these tables to be evaluated? What level of precision or accuracy should be expected from mathematical astronomy? In 1644, the Stetin astronomer and calendar-maker Lorenz Eichstadt published (...) a new set of tables, mostly cobbled together from earlier tables, which include a running commentary on how his tables might be expected to match ‘observed’ planetary positions. His earlier works also often display a rhetoric of ‘exactitude’ and ‘error’. Eichstadt thus offers a case study of explicit discussions of ‘precision’ in mid-seventeenth astronomy. Although some tables could generate positions to arcseconds, Eichstadt argued that a regime of five arcminutes should be enough for most table users who were, presumably, computing horoscopes. (shrink)

This article examines an unstudied set of astronomical tables for the meridian of Cambridge, also known as the Opus secundum, which the English theologian and astronomer John Holbroke, Master of Peterhouse, composed in 1433. These tables stand out from other late medieval adaptations of the Alfonsine Tables in using a different set of parameters for planetary mean motions, which Holbroke can be shown to have derived from a tropical year of $$365\frac{1}{4} - \frac{1}{132}$$ 36514-1132 or $$365.\overline{24}$$ (...) 365.24¯ days. Implicit in this year length was a 33-year cycle of repeating solar longitudes and equinox times, which has left traces in other astronomical tables from fifteenth-century England. An analysis of the manuscript evidence suggests that Holbroke owed his value for the “true length of the year” to a certain Richard Monke, capellanus de Anglia, who employed this parameter and the corresponding 33-year cycle in an attempt to construct a perfect and perpetual solar calendar, leading to his Kalendarium verum anni mundi of 1434. (shrink)

The ArgumentLevi ben Gerson, also known as Gersonides or Leo de Balneolis, was one of the most original Jewish thinkers of the Middle Ages, and he wrote on logic, philosophy, biblical exegesis, mathematics, and astronomy. During the last years of his life he maintained relations with the papal court of Clement VI (1342–52) at Avignon, and collaborated in the translation into Latin of hisSefer Tekhuna(Book of Astronomy). The object of this paper is to establish the main stages of the redaction (...) of the Hebrew and Latin extant versions of his astronomical work. Although Levi declares that the work was finished in 1328,1 argue that this text was the preliminary draft of the preserved one, most of which was composed after 1338. A thorough revision of the work was undertaken at an indeterminate date before 1344. It is also argued that the final form of the work was probably due to the request of solar and lunar tables made to Levi by “great and noble Christians” around 1332. (shrink)

Some variants in the materials related to the planetary latitudes, including computational procedures, underlying parameters, numerical tables, and so on, may be addressed in the corpus of the astronomical tables preserved from the medieval Islamic period, which have already been classified comprehensively by Van Dalen. Of these, the new values obtained for the planetary inclinations and the longitude of their ascending nodes might have something to do with actual observations in the period in question, which are the (...) main concern of this paper. The paper is in the following sections. In the first section, Ptolemy’s latitude models and their reception in Islamic astronomy are briefly reviewed. In the next section, the medieval non-Ptolemaic values for the inclinations and the longitudes of the nodal lines are introduced. The paper ends with the discussion and some concluding remarks. The derivation of the underlying inclination values from the medieval planetary latitude tables and determining the accuracy of the tables are postponed to “Appendix” in the end of the paper. (shrink)

SUMMARYIn 1803, the most prominent Japanese astronomer of his time, Takahashi Yoshitoki, received a newly imported Dutch translation of J. J. Lalande's ‘Astronomie’. He could not read Dutch, yet he dedicated almost a year to a close examination of this massive work, taking notes and contemplating his own astronomical practices. How did he read a book he could not read? Following the clues Yoshitoki left in his notes, we discover that he found meanings not only in words, but also (...) in what are often taken for granted or considered to be auxiliary tools for data manipulation, such as symbols, units, tables, and diagrams. His rendering of these non-verbal textual elements into a familiar format was crucial for Yoshitoki's reading, and constituted the initial step in the process of integrating Lalande's astronomy into Japanese astronomical practices, and the subsequent translation of the text into Japanese. (shrink)