chapter 1 Nicholaus de Heybech and His Table for Finding True Syzygy* Introduction The calculation of eclipses was a major task for medieval astronomers, and the first step in this procedure was the determination of the time from mean to true syzygy (where syzygy means either the conjunction or the opposition of the Sun with the Moon). The basic approach given in Ptolemy’s Almagest was refined by subsequent astronomers in various ways. In the Latin West of the late Middle Ages the corpus of Alfonsine astronomy held a dominant position. Of special interest in this tradition is the solution to this problem in Chap. 22 of John of Saxony’s canons for the Alfonsine Tables (ca. 1327)1 as well as the solution attributed to Nicholaus de Heybech of Erfurt (ca. 1400).2 The text and table of Nicholaus de Heybech (see Appendix 1) have not been discussed previously.3 lt will be shown that the method of Nicholaus de Heybech is much * Historia Mathematica 19 (1992), 265–289. 1 Editio princeps, Ratdolt [1483]; cf. Poulle [1984, 17]. 2 In a short note, Thorndike [1948] collected what little is known about Nicholaus de Heybech of Erfurt. His principal text is the canon and table to find the time of true conjunction and opposition of the Sun and the Moon. The date of composition of this text is uncertain but some of the manuscripts of it were copied in the 1440s. Thorndike adds that most of the manuscripts are of the fifteenth century but one manuscript, dated 1394, was in the Library of Grenville Kane, Tuxedo Park, New York (the present location of that manuscript is in Prince- ton). In addition to listing manuscripts of the text which will be discussed below, Thorndike reports that ms Köln W* 178 (fol. 29v) contains a table of mean conjunctions for the years from 1384 to 1504 computed for the meridian of Paris and ascribed to a certain “Nicholaus,” sug- gesting that it is the same author. In the manuscript we find the author’s name in the phrase given in the heading as “composita per Nycolaum de Er*” where the asterisk represents here a balloon-shaped symbol. However, it is by no means certain that this author is to be iden- tified with our Nicholaus. Moreover, Hartmann [1919, 12–13] refers to a certain “Nicholaus de Heybech” who was registered as a student at Erfurt University in 1421, and he suggests that this might be our Nicholaus. According to Thorndike, in 1392 Nicholaus de Heybech com- pleted a copy of Gerard of Cremona’s Theorica Planetarum, preserved in ms Cues 213. From this meager information we conclude that Nicholaus de Heybech was active circa 1400. 3 A translation of the text of Nicholaus de Heybech appears in Appendix ii. © koninklijke brill nv, leiden, 2015 | doi: 10.1163/9789004281752_003 10 chapter 1 simpler than that of John of Saxony. In the same period another way to solve this problem by means of tables, introduced by Levi ben Gerson (d. 1344) and followed by Jacob ben David Bonjorn (fl. ca. 1361), has recently received extensive treatment.4 Levi ben Gerson’s method requires the use of a set of four tables and calls for many more computations than the method of Nicholaus de Heybech. The Alfonsine tradition is identified with Alfonso x, king of Castile (Spain), who reigned from 1252 to 1284. He sponsored much scientific activity, and a number of astronomical works were written in, or translated into, Castilian at that time. The Alfonsine Tables are a special case because they are only extant in a Latin version produced in Paris in the 1320s, and derivatives from it. lt has even been argued that there never was a Spanish version prior to the Parisian one [see Poulle 1988]. The manuscript tradition of these tables is very complex and has not been adequately examined. For this reason, it has been customary to identify the Alfonsine Tables with those published by E. Ratdolt in 1483 despite the difficulty in deciding which tables were intended to be so designated by the Parisian group in the 1320s, let alone by the astronomers serving under Alfonso x. One of the characteristic features of the Parisian version (and the edition of 1483) is the division of the circle into “physical” signs of 60° rather than “natural” signs of 30° that were prevalent in ancient and medieval astronomy [Poulle 1988, 100]. We refer to the entire manuscript tradition associated with these tables as the corpus of Alfonsine astronomy. We shall first discuss Ptolemy’s method and then the method presented by John of Saxony, neither of which is reduced to specific tables for this purpose. Then we turn to the method of Nicholaus de Heybech, who successfully pre- sented his solution to this problem in a single table. We begin by introducing some definitions and notation. Let λs, λ̄ s, λm, and λ̄ m be the true and mean longitudes of the Sun and the Moon, respectively, at a mean syzygy that occurs at a given time t. The solar correction (cs) and the lunar correction (cm) are defined as cs(κ̄) = λs – λ̄ s and cm(ᾱ) = λm – λ̄ m 4 On Levi ben Gerson’s method, see Goldstein [1974, 136–144, 229–241]; on Jacob ben David Bonjorn see Chabás [1989, 26–39, and 1991]..