In this paper, we analyze the astronomical tables in al-Zīj al-Muqtabis by Ibn al-Kammād (early twelfth century, Córdoba), based on the Latin and Hebrew versions of the lost Arabic original, each of which is extant in a unique manuscript. We present excerpts of many tables and pay careful attention to their structure and underlying parameters. The main focus, however, is on the impact al-Muqtabis had on the astronomy that developed in the Iberian Peninsula and the Maghrib and, more generally, on (...) the transmission and diffusion of Indian astronomy in the West after the arrival of al-Khwārizmī’s astronomical tables in al-Andalus (Muslim Spain) in the tenth century. This tradition of Indian origin competed with the Greek tradition represented by al-Battānī’s astronomical tables and was much more alive in the Iberian Peninsula and the Maghrib than previously thought. From Spain, the Indian tradition entered mainstream European astronomy, where we find echoes of it in all versions of the Alfonsine Tables, both in manuscript and in the printed editions (beginning in 1483), as well as in Copernicus’s De Revolutionibus, published in 1543. (shrink)

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)

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 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)

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)

In this article, we report the discovery of a new type of astronomical almanac by Joseph Ibn Waqār (Córdoba, fourteenth century) that begins at second station for each of the planets and may have been intended to serve as a template for planetary positions beginning at any dated second station. For background, we discuss the Ptolemaic tradition of treating stations and retrograde motions as well as two tables in Arabic zijes for the anomalistic cycles of the planets in which the (...) planets stay at first and second stations for a period of time (in contrast to the Ptolemaic tradition). Finally, we consider some medieval astrological texts where stations or retrograde motions are invoked. (shrink)

Bianchini called Tabulae magistrales a set of eight tables he compiled to solve problems in spherical astronomy. This set, which is the object of this paper, consists of auxiliary and trigonometric functions, including the sine and the tangent functions, for radii 10,000 and 60,000, and seems to be the first set of tables in Latin specifically devoted to mathematical tools for computational astronomy. Bianchini presented some of his tables in decimal form, which meant that for the first time one of (...) the oldest astronomical tradition, the sexagesimal base, was abandoned. (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)

: The Alfonsine Tables were compiled during the second half of the 13th century in Toledo, Spain, and were largely diffused throughout Europe, mainly via Paris. They became the basic computing tool for European astronomers during several centuries. The Tabulae resolutae are a particular form of presenting the Alfonsine material which differs in many ways from that in the first printed edition of the Alfonsine Tables (Venice, 1483). This paper focuses on the influence of the 15th century Viennese astronomer John (...) of Gmunden on the genesis of the Tabulae resolutae, and analyses its contents and impact on European astronomy. (shrink)

The Alfonsine Tables were compiled during the second half of the 13th century in Toledo, Spain, and were largely diffused throughout Europe, mainly via Paris. They became the basic computing tool for European astronomers during several centuries. The Tabulae resolutae are a particular form of presenting the Alfonsine material which differs in many ways from that in the first printed edition of the Alfonsine Tables . This paper focuses on the influence of the 15th century Viennese astronomer John of Gmunden (...) on the genesis of the Tabulae resolutae, and analyses its contents and impact on European astronomy. (shrink)

Astronomers have always considered the motion of the Moon as highly complicated, and this motion is decisive in determining the circumstances of such critical celestial phenomena as eclipses. Table-makers devoted much ingenuity in trying to find ways to present it in tabular form. In the late Middle Ages, double argument tables provided a smart and compact solution to address this problem satisfactorily, and many tables of this kind were compiled by both Christian and Jewish astronomers. This paper presents multiple examples (...) of the diversity of approaches adopted by compilers of tables who used this powerful tool, and brings to light intellectual interactions among them that are otherwise hidden from view. (shrink)