Nuremberg: [Johann Petreius], 1537.
First edition, extremely rare, combining two major Arabic works on planetary astronomy: al-Battani’s The Motions of the Stars, printed here for the first time, and al-Farghani’s Elements of Astronomy, here in its second printed edition but the first with the additions and geometrical proofs of Regiomontanus. “The indebtedness of Copernicus to al-Battani is well known. He quotes him fairly often, especially — as does Peurbach — in the chapters dealing with the problems of solar motion and of precession. Much more frequent references to him are found in Tycho Brahe’s writings and in G. B. Riccioli's New Almagest; in addition, Kepler and — only in his earliest writings — Galileo evidence their interest in al-Battani’s observations” (DSB, under al-Battani). The extensive annotations to the Crawford copy of De revolutionibus also clearly show that al-Battani’s observations were much studied by Erasmus Reinhold, Copernican advocate and author of the Prutenic tables (see Gingerich, Census, p. 273, who suggests that Reinhold used the 1537 Nuremberg edition of al-Battani). “In the spring of 1464 at the University of Padua, then under Venetian control, Regiomontanus lectured on the ninth-century Muslim scientist al-Farghani. Although the main body of these lectures has not survived, “Johannes Regiomontanus’ Introductory Discourse on All the Mathematical Disciplines, Delivered at Padua When He was Publicly Expounding al-Farghani” was later published in Continentur in hoc libro Rudimenta astronomica Alfragani …, whose first item was John of Seville’s twelfth-century Latin translation of al-Farghani’s Elements of Astronomy (Nuremberg, 1537). Also included in this volume was Plato of Tivoli’s twelfth-century Latin version, “together with geometrical proofs and additions by Johannes Regiomontanus,” of al-Battani’s The Motions of the Stars. One such addition (to al-Battani’s chapter 11, although the printed edition misplaced it in the middle of chapter 12) may have been the germ from which Regiomontanus subsequently developed the earliest statement of the cosine law for spherical triangles … he was the first to formulate this fundamental proposition of spherical trigonometry” (DSB, under Regiomontanus). The volume begins with Regiomontanus’ oration on al-Farghani, which “deserves to be called the first modern history of mathematics” (Goulding, pp. 8-9), and an introduction to Euclid, both published here for the first time. ABPC/RBH list only a copy sold by Sotheby’s in 1934 and a fragment (al-Farghani only) offered by Goldschmidt in 1952.
“Battani (850-929) was one of the most influential astronomers of the early Islamic period. He was particularly well known for the accuracy of his observations, which he carried out at Raqqa in northern Syria over a period of 40 years ... In Raqqa, Battani devoted considerable financial resources to establish a private observatory at which he regularly conducted observations during the period from 877 to 918. Among the instruments that he is known to have used are a gnomon, horizontal and vertical sundials, a triquetrum, parallactic rulers, an astrolabe, a new type of armillary sphere, and a mural quadrant with an alidade. For several of these instruments, Battani recommended sizes of more than a meter in order to increase the accuracy of the observations. In 901, Battani observed a solar and a lunar eclipse in Antioch.
“The accuracy of Battani’s observations of equinoxes and solstices, as judged from the one existing report and his determination of the lengths of the seasons, is not much inferior to that of Tycho Brahe 700 years later. This remarkable achievement must have been due to a careful construction and alignment of his large instruments, as well as to a clever method of combining multiple observations of the same type of phenomenon (which was certainly not simple averaging). The value obtained by Battani for the Ptolemaic solar eccentricity, expressed sexagesimally as 2;4,45 parts out of 60, is almost exact. In fact, it is clearly better than the values found by Nicolaus Copernicus, who was troubled by refraction because of his high geographical latitude, and Brahe, who incorporated the much too high Ptolemaic value for the solar parallax in the evaluation of his observations.
“Battani also made accurate measurements of the obliquity of the ecliptic, which he found as 23° 35' (the actual value in the year 880 was 23° 35' 6"), and the geographical latitude of Raqqa (36° 1', modern value 35° 57'). Furthermore, he determined all planetary mean motions anew. He found the parameters of the lunar model to be in agreement with Ptolemy and the eccentricity of Venus the same as derived by the astronomers working under Ma’mun. Battani also confirmed the discovery of Ma’mun’s astronomers that the solar apogee moves by 1' in 66 Julian years, and found the precession of the equinoxes to be equal to the motion of the solar apogee. He accurately measured the apparent diameters of the Sun and the Moon and investigated the variation in these diameters, concluding that annular solar eclipses are possible. In the 18th century, Battani’s observations of eclipses were used by Richard Dunthorne to determine the secular acceleration of the motion of the Moon.
“Battani’s most important work was a zji, an astronomical handbook with tables in the tradition of Ptolemy’s Almagest and Handy Tables, later called al-Zij al-Sabi … The Sabi’ Zij is the earliest extant zij written completely in the Ptolemaic tradition with hardly any Indian or Sasanian-Iranian influences. As with many Islamic zijes, its purpose was much more practical than theoretical. Although the planetary models and the determination of the solar parameters are explained in some detail, … most of the text in the Zij consists of instructions for carrying out practical calculations by means of the tables, which constitute a third of the book … Although Battani copied some of the planetary tables directly from the Handy Tables, he also computed many tables anew … The Sabi' Ztj enjoyed a high reputation in the Islamic world and was very influential in medieval and Renaissance Europe. Biruni wrote a treatise entitled Jala’ al-adhhan fi zij al-Battani (Elucidation of genius in al-Battani’s Zij), which is unfortunately lost. Later zijes such as those of Kushyar ibn Labban, Nasawi, and Tabari were based on Battani’s mean motion parameters. In Spain, the Sabi’ Zij exerted a large influence on the earliest astronomical developments and left many traces in the Toledan Tables. Two Latin translations of the canons of the Zij were prepared in the 12th century. The one by Robert of Chester has not survived, but the translation by Plato of Tivoli, made in Barcelona, was printed in Nuremberg in 1537 (together with Farghani’s introduction to Ptolemaic astronomy) and again in Bologna in 1645 under the title Mahometis Albatenii de scientia stellarum liber, cum aliquot additionibus Ioannis Regiomontani ex Bibliotheca Vaticana transcriptus” (Biographical Encyclopedia of Astronomers).
“The Arabs were, according to Carra de Vaux, unquestionably the inventors of plane and spherical trigonometry, which did not, strictly speaking, exist among the Greeks … With the Arabs, the trigonometrical functions of sine, tangent, cosine and cotangent became explicit. They adopted for ‘sine’ the name jayb which signifies an opening, bay, curve of a garment, especially the opening of an angle. The Latin term ‘sinus’ is a mere translation of the Arabic jayb. It appears in the twelfth century in the translation of the De motu stellarum of al-Battani. The definition of the cotangent expressed as a function of the sine and of the cosine appears there for the first time, and in ch. III trigonometry begins to assume the appearance of a distinct and independent science. In spherical trigonometry also al-Battani presented an important formula (uniting the three sides and one angle of a spherical triangle), which has no equivalent in Ptolemy:
cos a = cos b cos c – sin b sin c cos A”
(Holt et al, p. 714).
Al-Farghani (cs. 800-870), an Arab or Persian Sunni Muslim, was one of the most famous astronomers of the ninth century. He was one of a group of astronomers who worked at Baghdad under the patronage of al-Ma’mun. His textbook Kitāb fī Jawāmiʿ ʿIlm al-Nujūm, or Elements of astronomy on the celestial motions, written about 833, was a non-mathematical summary of Ptolemy’s Almagest taking into account the findings and observational data of earlier Islamic astronomers. “The influence of the Elements on mediaeval Europe is clearly attested by the existence of numerous Latin manuscripts in European libraries. References to it in mediaeval writers are many, and there is no doubt that it was generally responsible for spreading knowledge of Ptolemaic astronomy, at least until this role was taken over by Sacrobosco’s Sphere. But even then, the Elements of al-Farghani continued to be used, and Sacrobosco’s Sphere was clearly indebted to it. It was from the Elements that Dante derived the astronomical knowledge displayed in the Vita nuova and in the Convivio” (DSB).
The Elements has thirty chapters, of which the first describes the Egyptian, Greek, Roman, Russian and Arab calendars and their differences. The remainder of the book covers the principal topics of the Almagest: the inclination of the ecliptic (Al-Farghani finds 23°33' for 829 AD at Baghdad compared with Ptolemy’s 23°51'); the circumference and the diameter of the earth as measured by al-Mamun’s astronomers (approximately 20,400 miles and 6,500 miles); the ascension of the signs of the zodiac in the direct and oblique spheres and equal and unequal hours; description of the planets, their motions and distances from the earth, movements of the sun, moon and fixed stars, retrograde motions of the wandering planets; magnitudes, eccentricities and epicycles, lunar mansions, comparative sizes of the planets and the earth; parallax and eclipses. It “thus gives a comprehensive account of the elements of Ptolemaic astronomy that is entirely descriptive and non-mathematical. These features, together with the admirably clear and well-organized manner of presentation, must have been responsible for the popularity the book enjoyed” (DSB)
The Elements was written after the death of the Caliph al-Mamun in 833 but before 857. Two Latin translations were made in the twelfth century, one by John of Spain (John of Seville) in 1135 and the other by Gerard of Cremona in 1175. Printed editions of the first translation appeared in 1493, 1537, 1546, 1556, 1564 and 1618 (Gerard’s translation was not published until 1910). Jacob Anatoli made a Hebrew translation of the book that served as the basis for a third Latin version published in 1590, and Jacob Golius published a new Latin text together with the Arabic original in 1669.
“In 1464, the great German mathematician Johannes Regiomontanus delivered a set of astronomical lectures to the faculty of the university of Padua, based on al-Farghani’s elementary handbook of astronomy in its medieval Latin translation. He began his course with a historical survey, quite brief (11 pages printed, or about 4000 words), but covering the history of the discipline from antiquity to his own day. This small tract deserves to be called the first modern history of mathematics … Regiomontanus, a highly original and creative mathematician who had dedicated himself to a program of translation and publication, intended to convince his audience not just of the antiquity of the sciences, but also of their current vitality. He began his history promising not just to reveal the origins of the arts and their passage from nation to nation, but to tell “how they were at also translated from various foreign tongues into Latin, which of our ancestors were famed in these disciplines, and to which modern recognition should be granted” ([alpha]4r)” (Goulding, pp. 8-9). “He repeats the notion, common in his time, that geometry had been discovered by the Egyptians as a consequence of the division of the land after the inundation by the Nile; Euclid had collected the geometrical knowledge and written it down in 13 books; Hypsicles had added two more books … In his Padua lecture Regiomontanus particularly praises the writings of Archimedes; he also mentions the new translation of about 1450 by Jacobus Cremonensis. He says that Apollonius’ Conica, when once translated into Latin, would excite the admiration of all mathematicians. As authors on spherics he mentions Theodosius and Menelaus. Under arithmetic – algebra is silently included – Jordanus Nemorarius is particularly praised. Of this author Regiomontanus cites here the Arithmetica in 10 books and the De numeris datis. Since, as he says, the 13 books of Diophantus have not yet been translated from Greek into Latin, the flowering of the higher arithmetic, the ars rei et census, still lies hidden. The subject is known by the Arabic name “algebra.” We know from Regiomontanus’ correspondence that one year earlier, in 1463, he had discovered in Venice a Greek manuscript containing the first six books of Diophantus. Before this discovery the work was apparently unknown in the West. Regiomontanus recognized immediately the importance of what he had found. In his Padua lecture he also mentioned Bianchini as learned in this art. Other important treatises on arithmetic are Johannes de Muris’ Quadripartitum numerorum, the Algorithmus demonstratus, the Arithmetica of Boethius and the practical arithmetic of the monk Barlaam in Greek” (Ragep et al, pp. 92-3).
Regiomontanus possessed manuscripts of at least two Latin versions of Euclid’s Elements: the Campanus redaction made shortly before 1260, and an earlier version compiled by Robert of Chester about 1140. The latter was copied by Regiomontanus himself from a manuscript bought by Cardinal Bessarion in Vienna in 1461 (Bessarion’s manuscript is now in the Marciana, but Regiomontanus’ copy is lost). This manuscript is of particular importance because it contains two versions of Euclid – version II, which is ascribed to “Adelhardus”, i.e., Adelhard of Bath, and version III, ascribed to Boethius. The introduction to version III was published in the present volume, where it is erroneously ascribed to Regiomontanus himself. The same introduction is present in Regiomontanus’ own autograph copy of Euclid (now in Nuremberg), which he compiled using the two manuscripts in his possession.
Bound at the end of the volume is a copy of the second edition of the following work of Agostino Ricci (fl. 16th century), first published in 1513:
De motu octavae sphaerae, opus mathematica, atque philosophia plenum. Ubi tam antiquorum, quam iuniorum errores, luce clarius demonstrantur in quo & quamplurima Platonicorum, & antiquae magiae (quam Cabalam Hebraei dicunt) dogmata videre licet intellectu suavissima. Eiusdem de astronomiae autoribus epistola [edited by Oronce Fine]. Paris: Simon de Colines, 1521.
“Agostino Ricci, a converted Jew, had written a book titled De motu octavae sphaerae (1513), which dealt with “the movements of the eighth sphere in a philosophical manner, together with the teachings of the Platonists and ancient magic (which the Hebrews call Kabbalah).” Ricci, with whom Agrippa corresponded and from whom he sought advice on the publication of his Dialogus de homine, was the astrologer of the Marquis of Monferrato and seems to have been Agrippa’s intermediary in winning the favour of the ruler. Agostino Ricci had been a pupil of the famous Abraham Zacuto at Salamanca and continued to study under him at Carthage. Many years later he served as physician to Pope Paul III” (Goodrick-Clarke, The Western Esoteric Traditions, p. 58). Ricci’s Almanach Perpetuum was used for all navigational tables (including those of Vasco da Gama) from its publication in 1496 until Nuñez's tables of 1537. No complete copy of either the 1513 or 1521 edition located in auction records.
[AL-FARGHANI:] Adams A740; Lalande p. 36; Houzeau & Lancaster 764 (‘fort rare’); RAS I, p. 8; Roller and Goodman I, p. 28 (9 preliminary leaves only); VD 16 A1202; Zinner 1655 (stating that the second part was obtainable separately, although we have been unable to locate a copy); not in Crawford. Goulding, Defending Hypatia: Ramus, Savile, and the Renaissance Rediscovery of Mathematical History, 2010; Holt et al, The Cambridge History of Islam: Volume 2B, Islamic Society and Civilisation, 1977; Ragep et al, Tradition, Transmission, Transformation: Proceedings of Two Conferences on Pre-Modern Science Held at the University of Oklahoma, 1996. On Regiomontanus’ Oratio, see Rose, The Italian Renaissance of Mathematics, pp. 95-9. OCLC locates copies in US at Brown University, Providence, New York University Libraries, New York Public Library, Harvard and Smithsonian (apparently part I only). [RICCI:] Renouard, Colines 22; Houzeau & Lancaster 2355; this edition not in Riccardi.
[AL-FARGHANI:] Two parts in one vol., 4to (200 x 144), ff. [x], 26; 90, with woodcut initials and several woodcut diagrams in text. [RICCI:] 4to (200 x 144), ff. 51, . Contemporary blind-tooled calf, spine strengthened with paper, very worn, chords and sewings still holding but outer material of binding almost completley worn away. Old inscription watered out on title page.