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Showing papers in "Transactions of The American Philosophical Society in 2014"


Journal Article
TL;DR: The influence of foreign ideas on Indian gayakas is discussed in this article, where the authors make clear the creative use they made of their borrowings in devising the yuga-system of astronomy, pointing out their almost complete lack of originality.
Abstract: (ProQuest: ... denotes non-USASCII text omitted.)(ProQuest: ... denotes formulae omitted.)ONLY in recent years have the interrelationships of Babylonian, Greek, and Indian astronomy and astrology become a subject which can be studied meaningfully. This development is due to several factors: our greatly increased understanding of cuneiform material made possible by the scholarship of Professor O. Neugebauer; 1 the discovery of Babylonian parameters and techniques not only in the standard Greek astronomical texts,2 but in papyri and astrological treatises as well; and the finding of Mesopotamian material in Sanskrit works and in the traditions of South India. Unfortunately, a lack of familiarity with the Sanskrit sources and a failure to consider the transmission of scientific ideas in the context of a broad historical perspective have recently led one scholar to the erroneous conclusion that Sasanian Iran played a crucial role in the introduction of Greek and Babylonian astronomy and astrology to India and in the development of Indian planetary theory.4 It is my purpose in this paper to survey briefly the influence of foreign ideas on Indian gayakas so as to make clear the creative use they made of their borrowings in devising the yuga-system of astronomy; and then to examine the character of Sasanian astronomy and astrology, pointing out their almost complete lack of originality.The earliest Indian texts which are known - the Vedas, the Brâhmaijas, and the Upanicads - are seldom concerned with any but the most obvious of astronomical phenomena; and when they are so concerned, they speak with an obscurity of language and thought that renders impossible an adequate exposition of the notions regarding celestial matters to which their authors subscribed. One may point to the statement that the year consists of 360 days as a possible trace of Babylonian influence in the Kgveda,4 but there is little else which lends itself to a similar interpretation. It has often been proposed, of course, that the list of the twenty-eight naksatras which is given for the first time at the beginning of the last millennium before Christ in the Atharvaveda and in various Brâhmanas is borrowed from Mesopotamia.8 But no cuneiform tablet yet deciphered presents a parallel; the hypothesis cannot be accepted in the total absence of corroborative evidence.However, the naksatras are useful in the tracing of Indian influence on other cultures. The oldest lists0 associate each constellation with a presiding deity who is to be suitably propitiated at the appointed times. It became important to perform certain sacrifices only under the benign influence of particularly auspicious naksatras.7 The roster of activities for which each was considered auspicious or not was rapidly expanded,6 and, in particular, the naksatras came to be closely connected with the twelve or sixteen samskâras or purificatory rites. Thereby they gave rise to the most substantial part of muhurtasâstra, or Indian catarrhic astrology,® traces of which are to be found in Arabic, Byzantine, and medieval Latin texts.10 The Indians also combined the twenty-eight naksatras with the Babylonian arts of brontology and seismology 11 in a form which, for some unknown reason, became immensely popular among the followers of Buddha.'2 Their works spread these superstitions throughout Central Asia and the Far East.18The relative seclusion from the West which the Aryans had enjoyed in northern India for centuries alter their invasions was broken shortly before 51.3 b. c., when Darius the Great conquered the Indus Valley. In the ensuing six centuries, save for a century and a half of security under the Mauryan emperors, North India was subjected to the successive incursions of the Greeks, the eakas, the Pah lavas, and the Kuyânas. An important aspect of this turbulent period was the opportunity it afforded of contact between the intellectuals of the West and India. This opportunity was not missed. …

110 citations


Journal Article
TL;DR: In this article, the authors present evidence in support of an hypothesis concerning the dependence of the mathematical astronomy of the Jyotifavedâftga on Mesopotamian science of the Achaemenid period.
Abstract: (ProQuest: ... denotes formulae omitted.)In this paper I intend to advance and offer evidence in support of an hypothesis concerning the dependence of the mathematical astronomy of the Jyotifavedâftga on Mesopotamian science of the Achaemenid period.1 I believe that the evidence in support of the theory that some elements of early Indian astronomy are derived from Mesopotamia is overwhelming, and that the evidence for the rest of my hypothetical reconstruction is persuasive. But I must enter a cautionary note with regard to that portion which relates to the Indian intercalation-cycle: the evidence in both the cuneiform and the Sanskrit sources is so fragmentary that no hypothetical reconstruction of the development or of the interrelation of their respective intercalation-cycles is more than a reasonable guess. I hope that the reader will find my guess more plausible than those of my predecessors.Though the Vedas and Brahmanas provide us with some crude elements of observational astronomy, such as the standard list of 27 or 28 nakcatras or constellations associated with the Moon's course through the sky, and some rough parameters, such as the twelve months and 360 nychthemera of a year, mathematical astronomy begins in India with a group of related texts which I intend to explain in this paper. The basic text of this group is the Jyotifavedâftga * one of the six angas or "limbs" studied by Vedic priests; its purpose was to provide them with a means of computing the times for which the performances of sacrifices are prescribed, primarily new and full moons. This brief work has come down to us in two recensions: a shorter one of 36 verses associated with the Rgveda, and a longer one of 43 verses associated with the Yajurveda, which latter incorporates 29 verses of the Rk-recension. That Rk-recension was composed by one Lagadha, who is otherwise unknown, or, according to another interpretation, by Suci on the basis of Lagadha's teachings; the Yajur-recension names no author, but has the dubious benefit of a bhâcya or commentary by one Somakara. It is the Yajur-recension that has generally been used by modem scholars also, as it, in two of its additional verses, attempts to adjust the older system of the Rk-recension to the familiar terms of medieval Indian astronomy. In this paper the shorter and surely older Rk-recension will be used.We are justified in asserting the originality of the Rk-recension not only by its shortness, but also by its parallelism to other pre-medieval Sanskrit texts. In particular we must discuss here the following seven works in addition to the two recensions of the Jyotifavedâftga:1. The Arthasâstra of Kautilya3 is an ancient work on political science. Many scholars have identified the author with the minister of Candragupta Maurya, who established the Mauryan Empire in northern India shortly before 300 b.c., though it seems fairly secure that our recension of Book Two of the Arthaiâstra does not antedate the second century a.d.4 The twentieth chapter of the second book of the Arthasâstra prescribes the duties of the Mânâdhyakca or Super- intendant of Measurements, among which is included the duty of supervising the measurements of time. These time-measurements are closely related to those of the Jyotisavedanga.2. The Sardulakarnavadana5 is now the thirty-third story in a Buddhist collection of tales about Bodhisattvas, the Divyavadana. Originally it was an anticaste tract in which a king of the Matangas (that is, Candâlas), Trisafiku, asks a Brâhmana, Puckarasârin, to give his daughter, Prakfti, to the outcaste's son, aardulakarna. Upon the Brahmana's refusal of this unorthodox request, Trisafiku proves his status as a Brâhmana by displaying his knowledge of astral divination and astronomy. Our present Sanskrit version is full of interpolations, both in prose and in poetry; but the history of the basic core of the text can be traced back to translations into Chinese by the Parthian prince An Shih-kao, who settled in Loyang in a. …

52 citations


Journal Article
TL;DR: In this paper, Zij al-Sindhind (Kalpa; Caturyuga; mean motions; year-length; sidereal zodiac; trepidation; longitudes of apogees and nodes; ahargarca; mean longitude of planets; longitudinal difference; accumulated epact; trigonometric functions; equation of center; obliquity of ecliptic and method of declinations; combined effect of equations; time to first or second station; ascensional difference; terrestrial latitude; gnomon-shadows; apparent diam
Abstract: (ProQuest: ... denotes formulae omitted.)(ProQuest: ... denotes non-USASCII text omitted.)ContentsI. IntroductionII. Kalyana (parapegma)III. Curtius Rufus (new moon months; paksas)IV. Philostratus (planetary weekdays)V. lAbd al-Bari'VI. Sasanians (naksatras; planetary chords; decans; Zik i Shahriyaran).VII. Severus Sebokht (lunar nodes)VIII. Theophilus of Edessa (military astrology; zodiacal topothesia)IX. Mâshâ'allâh ("Era of the Flood"; planetary chords; cosmic magnet; navams'as)X. Zij al-Sindhind (Kalpa; Caturyuga; mean motions; year-length; sidereal zodiac; trepidation; longitudes of apogees and nodes; ahargarca; mean longitudes of planets; longitudinal difference; accumulated epact; trigonometric functions; equation of center; obliquity of ecliptic and method of declinations; equation of anomaly; combined effect of equations; time to first or second station; ascensional difference; terrestrial latitude; gnomon-shadows; lunar latitude; apparent diameters of sun, moon, and earth's shadow; eclipse-limit; totality of eclipse; duration of eclipse and of totality; color of eclipse; longitudinal parallax; latitudinal parallax; latitudes of planets; value of rr)XI. R$i (interrogations)XII. Bhuridasa and Buzuijmihr (Jovian dodecaeteris; theft)XIII. Abu Ma'shar (nativity of Ceylonese prince; childbirth; ketu; lunar nodes; terms; decans; revolution of years of nativities; place of sun in nativity; astrological places; fulfillment of interrogations)XIV. Ja'far al-Hindl (order of orbits of planets and fixed stars; benefic and malefic planets; quarters of a month; naksatras)XV. Al-QabTsI (karanas)XVI. Simeon Seth (precession; star-catalog)XVII. Vaticanus graecus 1056 (interrogations)XVIII. Parisinus graecus 2506 (lordships of months of pregnancy)XIX. Picatrix (names of planets)XX. Shams al-Din al-Bukhâri (year-beginning; adhimasas; Sin ri; s'ankutala and bâhu)XXI. ConclusionsI. IntroductionAstronomy and astrology in India1 are not indigenous sciences, but are local adaptations and developments of Mesopotamian,2 Greco-Babylonian,3 and Greek 4 texts; and, at an early stage of their developments, parts of the Indian traditions had influenced Sasanian5 and Syriac science before the rise of Islam. There existed, therefore, a more or less common understanding of astronomy and astrology in those regions of the world where Latin, Greek, Syriac, Pahlavi, and Sanskrit were used, though each culture had its particular idiosyncrasies and its special areas of sophistication. Islam was the heir to all of these traditions,6 which it was able to synthesize precisely because of their common features. The object of this paper is to attempt to isolate as many as possible of those elements of the Islamic adaptations of Indian astronomy and astrology that were included in the massive influx of translations of Arabic science into Byzantine Greek and into Latin, as well as in the subsequent translations of this material from Greek into Latin and from Latin into Greek; 1 omit the immense quantity of Hebrew and vernacular texts, and also those Greek and Latin works whose information concerning Indian science is secondary within each culture. Though I have utilized as many printed and manuscript sources as could reasonably be obtained, I am aware that much that is relevant must have escaped my notice, and can only hope that others more versed especially in the Latin sources will continue this work. I have tried, where possible, to add to the citation of the Greek or Latin text one of a Sanskrit passage of appropriate antiquity expressing the same or a similar idea; but, in the interest of avoiding excessive length, I have refrained from citing the Arabic intermediaries and from translating any passage.The period within which Arabic scientific texts were translated into Greek extended from the ninth to the fourteenth century, into Latin from the twelfth to the thirteenth only, though many more Latin translations were made in two centuries than Greek in six. …

51 citations


Journal Article
TL;DR: In the early 13th century, Blemmydes and his pupil George Acropolites as discussed by the authors used the Handy Tables of Theon to study the motions of the celestial spheres.
Abstract: (ProQuest: ... denotes non-USASCII text omitted.)(ProQuest: ... denotes formulae omitted.)FOR almost seven centuries following the publication of the commentary on the Handy Tables of Theon by Stephanus of Alexandria1 little interest was shown in mathematical astronomy in Byzantium. It is tme that, in the ninth century, under the leadership of Leo the Mathematician,3 the text of Ptolemy's Almagest was studied and copied,3 and that scholars in the eleventh and twelfth centuries had learned something of Arabic science. But it seems improbable that many, save perhaps the astrologers, had the motivation or the training necessary for an attempt to understand more than the most elementary principles of the motions of the celestial spheres; and even the astrologers really needed nothing beyond an ability to manipulate tables.This neglect continued into the thirteenth century, both at Nicaea and in Constantinople after it had been recovered from the Latins. But the beginnings of a revival of astronomical studies can be traced to the early decades of this century when a few scholars sought to sustain Greek learning under the patronage of John III Vatatzes (1222-1254) and Theodore II Lascaris (1254-1258).Nicephorus Blemmydes,4 who taught at the Imperial court from 1238 to 1248 and whose pupils included George Acropolites,5 reawakened an interest in ancient Greek science which had been virtually dead since the time of Michael Psellos8 in the eleventh century. His Epitome physica7 is a completely unoriginal book, and its treatment of astronomy (chapters 25-30) is pitifully inadequate. He has very little that is sensible to say about planetary theory ; but he does demonstrate that he has read Aristotle, Cleomedes, and Euclid with some comprehension, and he observed at least one lunar eclipse, that of 18 May 1258.8An account9 of an observation of a solar eclipse by his pupil George Acropolites in the company of the Imperial court on 3 June 1239 reveals the intellectual atmosphere in which Nicephorus was working. The Empress Irene asked Acropolites, then only twenty-one years old, what had caused this phenomenon. He, though he had just begun his studies under Blemmydes, was able to reply correctly that the Moon was interposed between the Earth and the Sun. The court physician, Nicolaus, scoffed at this ridiculous response, and the Empress, trusting her doctor, called Acropolites a fool. She quickly regretted her use of this derogatory term, not because she realized the correctness of Acropolites' explanation, but because she considered it improper to insult one engaged in philosophical studies. Two years later the Empress died; the philosopher seriously suggests that the eclipse was a portent of that unfortunate event, as was also the appearance of a bearded comet. It was Acropolites who, after the capture of Constantinople by Michael VIII Palaeologus in 1261, restored mathematics to the capital; he taught Euclid and Nicomachus to George (later Gregory) of Cyprus and others.10Among his pupils was, apparently, George Pachymeres,11 a man who progressed much further in astronomical studies than had his teacher. Pachymeres' knowledge of this subject is, naturally, set forth in the fourth book of his Quadrivium.12 To a large extent this consists of elaborate instructions for the multiplication of sexagesimal numbers, a procedure he regarded as incredibly difficult, a discussion of the risings, settings, and culminations of various constellations, and a number of the fundamental doctrines of astrology, many of which are also found in the Epitome physica of his mentor's mentor. He is capable of such improbable statements as: "They say that a yearly revolution of the Sun takes place in 365 degrees (poipais for finipcuc), 14 minutes, and 48 seconds" ; but his planetary theory is far more complete than that of his predecessor, and he himself is far from being confused about everything.George of Cyprus' friend John Pediasimus13 continued Blemmydes' study of Cleomedes' KvkAiki) eecopia pmcbpcov, on which he wrote a commentary ; and other mathematicians of this period were Maximus Planudes,14 who composed one of the first treatises on Indian numerals in Byzantium15 and an exegesis of the first two books of Diophantus,16 and his pupil Manuel Moschopulus, who wrote the first Western treatise on the construction of magic squares. …

35 citations


Journal Article
TL;DR: The more secular examples of children's books produced by Thomas Hardy have been credited by scholars with having "lifted the gloom from the nursery," and blending amusement with instruction in a form that was both appealing and marketable.
Abstract: For some scholars, the most enduring books published by Thomas are the works meant to appeal to children, including alphabet books, riddle books, poems, stories, songs, and hymnals, for which he had a total of 1,500 cuts in stock.1 Based on "the English plan" of British printer John Newbery, these little volumes embodied the aims and methods of John Locke, who recommended the use of picture books as a study aid, and endorsed works, such as Aesop's Fables, as both pleasurable and desirable reading for children. Although virtue, according to Locke, was still the first aim of juvenile reading, he sought to give moral instruction with "innocent amusement," laying down rules for making children healthy, virtuous, and happy.2A work that combines the new principle of amusement for children with the old Puritan concern for spiritual preparation is A Curious Hieroglyphic Bible, published by Thomas in 1788 with nearly five hundred cuts. Advertised as "an easy way of leading them I children] on in Reading" and as an effective, playful means of teaching Scripture to the young, each page contains a Biblical quotation in which key words are replaced by pictures of the objects that the words signify. For example, the picture of a sturdy vessel replaces the word "ark" in the passage concerning Noah related in Genesis 8:10-11 (Figure 4.1). The task of deciphering the puzzle was made easy for the reader, if necessary, by referring to the key below. Sentences that explain the figures are placed at the bottom of each page, and the words represented by the figures are identified in italic print. Thomas based his edition on the English hieroglyphic version published in London by T. Hodgson in 1780. The hieroglyphic Bible encompasses a tradition of image and text that flourished on the continent and in England for over a century, the first known example of which was published in Augsburg by Melchior Mattsperger in 1687.3The more secular examples of children's books produced by Thomas have been credited by scholars with having "lifted the gloom from the nursery," and blending amusement with instruction in a form that was both appealing and marketable. Instead of directing children to read godly books and be mindful of the last judgment, children were increasingly counseled to be virtuous because such conduct led to a successful life on earth. The Little Pretty Pocket Book, based on the Newbery edition, issued by Thomas in 1787, is typical of the new attempt to amuse children and put Locke's theories into practice by means of special books. Tiny in format and printed in small type, the size was convenient for children to handle. Although the illustrations at the top of the page were highly simplified and lacked depth, they were numerous and a distinct novelty. A page with "Rules for "Behavior" offers a diminutive illustration in the horizontal oval usually associated with the work by English engraver Thomas Bewick. By depicting boys sharing toys, the image gives the viewer a glimpse into the world of order and amusement recommended for young readers.However, the entertainment in this type of book is only occasional, often obscured by the maxims or morals attached to the tale. For example, in an illustration for Mary Jane Kilner's The Adventures of a Pincushion: Designed Chiefly for the Use of Young Ladies, a mother is admonishing one of her daughters for selfish behavior (Figure 4.2). The emphasis on manners, and the inclusion of an ornate mirror in the room, signals the middle-class preoccupation with refinement, success, and moral certainties. Moreover, the subject of the cut, a woman and two children grouped together, is generic and might be brought into service in similar books, because its lack of individuality was a way of depicting any child's world in simple and uncomplicated terms that could be easily understood. …

20 citations


Journal Article
TL;DR: Al-Fazâri is the name of the person most directly connected with the transmission of a Sanskrit work on astronomy-the Mahasiddhanta belonging to what later became known as the Brahmapakfa-to the Arabs in the early part of the eighth decade of the seventh century of the Christian era.
Abstract: (ProQuest: ... denotes formulae omitted.).Al-Fazâri is the name of the person most directly connected with the transmission of a Sanskrit work on astronomy-the Mahasiddhanta(l) belonging to what later became known as the Brahmapakfa-to the Arabs in the early part of the eighth decade of the eighth century of the Christian era. This was not the first infusion of Indian astronomical theories into Islam; prior to it was the mediating influence of the Zij al-Shâh in the versions of Khusrau Anushirwan and of Yazdijird III, the composition of the Zij al-Arkand and its derivatives at Qandahr Nallino is followed by Brockelmann (Suppl. I, 391) and Kennedy (No. 2). Suter, on the other hand, speaks of two personalities: an Ibrâhim ibn Habib (p. 3) who wrote various works and constructed an astrolabe, and his son Muhammad (pp. 4-5) who was involved in the translation of the Sindhind. The confusion is due to the inaccuracies of the Islamic biographers and bibliographers and to the existence of several contemporaries bearing the name al-Fazârl. There is, for instance, an Abu cAbdallah Muhammad ibn Ibrâhim ibn Hftblb ibn Sulayman ibn Samura ibn Jundab al-Fazarl (Fihrist, p. 79), who was reputed as an authority on geomancy, and a Muhammad ibn Ibrâhim al-Fazarl (Fihrist, p. 164), who was a "slave poet"; but elsewhere (Fihrist, p. 273; cf. al-Mas'udl, Muruj al-dhahab, 8, 290-91, and Ibn al-Qifyi, p. 57) Ibn al-Nadlm writes of an Abu Ishaq Ibrâhim ibn Habib al-Fazârl of the family of Samura ibn Jundab, who was the first in Islâm to make a plane astrolabe and who wrote a Kitab al-qafida fi cilm al-nujum (Poem on the Science of the Stars), a Kitab al-miqyas Wl-zawal (Measurement of Noon), a Kitab al-zij 'old sini al-cArab (Astronomical Tables According to the Years of the Arabs), a Kitab al-camal bi5l-asfurldb tea huwa dhdt al-halaq (Use of the Armillary Sphere), and a Kitab al-camal bi'l-asturlab al-musattah (Use of the Plane Astrolabe). These seem to be son and father respectively.But Ibn al-Qifti (p. 270) says of Muhammad ibn Ibrâhim al-Fazarl that he was outstanding in the science of the stars, a speaker about future events, experienced in the tasyir of the planets, and the first in the Islamic religion, at the beginning of the 'Abbâsid dynasty, who was concerned with this subject; al-Fazarl's work on tasyir is referred to by Abu Macshar as cited by Shâdhftn in his Mudhakarat (see CCAO, 5,1 ;148). And the astronomer whose fragments are here collected is called Muhammad ibn Ibrâhim al-Fazarl by Ibn al-Adaml (Frag. Z 1), by Câ'id al-AndalusI (ed. p. 13, trans. p. 46, and ed. p. 60, trans. p. 117), and by al-Blrunl (Frag. Z 15, 18, and 25 and Frag. Q 2). A reasonable solution to this problem of al-Fazâri's name would perhaps be to assume with Nallino that only one person is referred to in the passages cited above but that, in the entry on the astronomer al-Fazâri, Ibn al-Nadlm or his manuscript tradition has omitted the "Muhammad ibn" with which the entry should have begun.This suggestion is strengthened by the fact that the later biographical tradition refers to him as Muhammad. Thus Yaqut (Irshad, p. 268) gives a long genealogy of twentyseven generations beginning with Muhammad ibn Ibrâhim ibn Habib ibn Samura ibn Jundab. Yaqut further quotes al-Marzubani to the effect that Muhammad ibn Ibrâhim al-Fazari al-Kufi was an expert on the stars; and Yahya ibn Khalid al-Barmaki's saying that four men were without equal in their specialties: al-Khalil ibn Ahmad, Ibn alMuqaffa', Abu Hanifa, and al-Fazari; and Jacfar ibn Yahya's saying that he did not see more exceptional men in their fields than al-Kisa^i in grammar, al-AsmacI in poetry, al-Fazari in the stars, and Zulzul in playing the lute. …

20 citations


Journal Article
TL;DR: Ya'qub ibn Tariq, one of the earliest 'Abbasid astronomers, was identified by Kennedy as mentioned in this paper, who presented a collection of fragments and the succeeding article by E. S.H. Kennedy.
Abstract: (ProQuest: ... denotes formulae omitted.)Ihe following collection of fragments and the succeeding article by E. S. Kennedy present all the material so far discovered relevant to one of the earliest of 'Abbasid astronomers and attempt to interpret that material historically and scientifically. Many absurd assertions have been made concerning early Islamic science by historians who have not had the time or ambition to read the original sources but who are content to continue the historiographic tradition begun in Spain in the twelfth century. These two articles and similar collections of other early Muslim astronomers and astrologers will attempt to provide a different basis for assessing the formative period of science in Baghdad.The Fihrist of Ibn al-Nadim (p. 278), which is copied in a rather inaccurate manner by Ibn al-Qifti (p. 378), tells us of Ya'qub very little indeed.Ya'qub ibn Tariq, one of the best astronomers. Among his books are: Kitdb taqti kardajdt al-jayb; Kitdb miI irtafaca min qaws nisf al-nahdr; and Kitdb al-zij rnahlul fi al-Sindhind li-daraja daraja, which is in two books; the first is on the science of the sphere, and tho second on the science of the dynasty (duwal ).The first of these works must have described the method of converting a table of sines whose argument is expressed in intervals of 3;45° (a normal Indian table of kramajya'8, from which, apparently through Pahlavi, comes the Arabic kardaja) to one whose argument is expressed in intervals of Io. It was either a part of, or was used in writing, the Kitdb al-zij. The second work apparently deals with the problem of determining the altitude of the Sun from the day-circle. It may have been extracted from the zij, or from the Kitdb al-cilal which Ibn al-Nadlm neglects to mention. The fragments of the third work are discussed below. The subject of the second book of this zij. Him al-duwal, seems extremely peculiar; perhaps one should amend the text of both Ibn al-Nadlm and Ibn al-QiftI(!) to Him al-dawr, "science of revolution(s)."The Sindhind upon which Ya'qub's zij was based was, of course, that translated by al-Fazârl2 from a Sanskrit work allied to the Paitamahasiddhdnta of the Visnudharmottarapurdna3 and the Brdhmasphutasiddhdnta of Brahmagupta.4 The Sanskrit work was brought to Baghdad by a member of an embassy sent from Sind to the court of alMansur (754-775);5 the date is variously reported as being a.H. 154 (24 Dec, 770-12 Dec. 771)8 and a.h. 156 (2 Dec. 772-20 Nov. 773).7 Al-Biruni8 gives another date for the embassy, a.h. 161 (9 Oct. 777-27 Sept. 778) which, falling outside of al-Mansur's reign, is probably instead the date of Ya'qub ibn Tariq's Tarkib al-aflak. A fourth date, 1,972,947,868 years from the beginning of the lcalpa (a.d. 767), can be discerned in alHâshimi,8 but it is not clear to what it refers. The member of the embassy from Sind who is associated with the Sindhind was later identified, mainly by Andalusian scholars,10 with Kanaka, the astrologer of Hârun al-Rashid;11 this identification has no basis.Besides the three works mentioned by Ibn al-Nadlm, which are probably really one (the zij), we know from a number of sources that Ya'qub wrote a book entitled Tarkib al-aflak. This was a treatise, as its title indicates, on the arrangement of the heavens; as was indicated above, it was probably composed in 777/8. A third work was his Kitab al-Hlal, which explained the rationale for the mathematical procedures followed by astronomers; a long series of books of this sort was written by subsequent writers.12 Below are given the fragments with some brief comments of Ya'qub's Z(ij), T(arkib al-aflak), and K{itab al-cilal).ZIJZ 1. Al-HashimI, Kitab Hlal al-zijat, 95 v: 12-17.As for Ya'qub ibn Tariq, he composed his zij for Barah, and its revolutions are in agreement with (those of) the Sindhind as to the four hundredth part, but he made its collected (years) (majmnc) ten years according to years of the Persians and their months, up to noon of the day after your day. …

16 citations


Journal Article
TL;DR: In this article, the authors present an investigation into the process by which the ideas both of the precession and of the trepidation of the equinoxes were introduced into India and there interpreted in terms of an older Indian tradition of the position of the solstices relative to the naksatras and in other ways.
Abstract: (ProQuest: ... denotes formulae omitted.)The process by which various non-Ptolemaic elements of the Greek astronomical tradition were transmitted to India and were there transformed into the astronomy of the siddhantas is a subject of complexity and of obscurity. Its elucidation, however, is of great historical importance, both for the understanding it will afford us of the motivation for particular Indian solutions of problems in mathematical astronomy, and for the insight we will obtain from it into those areas of Hellenistic astronomy that, being almost totally eclipsed in Greek by the brilliance of Ptolemy's Almagest, can be discerned, though dimly, in the poetry of jyofihsastra. The present paper contains an investigation into one aspect of this process, that in which the ideas both of the precession and of the trepidation of the equinoxes were introduced into India and there interpreted in terms of an older Indian tradition of the position of the solstices relative to the naksatras and in other ways. This example, like that of the planetary model previously discussed in this journal (ii (1971), 80-85), beautifully illustrates the failure of the Greeks to communicate and of the Indians to grasp the full significance of the concepts transmitted.The Jyotisavedanga1 of Lagadha (5/4th century B.c.?) states (Arca 6 = Yâjuca 7): "The Sun and the Moon begin their northern [course] at the beginning of aravicthâ [Dhanictha]; the southern [course] of the Sun [begins] in the middle of Sarpa [Aslecâ]. [The beginnings of these two courses occur] always in [the months] Mâgha and aravana [respectively]." One also finds this scheme in, for example, the Parasaratantra cited by Utpala (a.d. 966) on the Brhatsarphita2 of Varahamihira (ca a.d. 550).By the time of Varahamihira a fixed sidereal zodiac was in use in India.3 In this zodiac the beginning of Aries was identified with the beginning of the nakcatra Asvini; in the fifth and sixth centuries the beginning of Aries was further said to be the point of the vernal equinox. Varahamihira recognized the discrepancy with the statement of Lagadha (Brhatsatyhita 3, 1-2):Once, according to what is said in ancient treatises, the southern ayana of the Sun was from the middle of Âelecâ, and the northern began with Dhanicthâ. Now [one] ayana of the Sun begins at the beginning of Cancer, the other at the beginning of Capricorn. This is a negation of what was said; the difference is made manifest by direct observations.In his Pancasiddhantika* (3, 20-2) Varahamihira explains this change by a theory of trepidation over an arc of 46;40°-23;20° (identified with the Sun's maximum declination) to either side of the equinox:When the sum [of the longitudes] of the Sun and Moon is a revolution, it is called Vaidhrta [yoga]; but if it is a revolution plus 10 nakcatras [133 ;20c]. Vyatipata. The time is to be ascertained by means of the degrees attained [by the luminaries]. When the return of the Sun was from the middle of Ââlecâ [at 113;20°], then the ayana [-correction] was positive; now the ayana is from Punarvasu [at 90°]. When the falling away [from the mean position] of the ayana is reversed, then the correction [kcepa] for the Sun and Moon [equals] the degrees of the maximum declination [kâcthâ] of the Sun [23;20°]. There is Vyatipata if the sum [of the longitudes] of the Sun and the Moon is 180°.This is the earliest datable reference to a theory of trepidation or precession in India ; unfortunately no rate is given. A theory of trepidation was known to Theon of Alexandria (a.d. 361) and to Proclus (a.d. 410-485), and a theory of precession to Hipparchus (ca -126); Hipparchus's length for a tropical year was used by Sphujidhvaja (a.d. 269/70) in his Yavanajdtaka (79, 34) and in the Romakasiddhanta summarized by VaTahamihira in his Paiicasiddhântikâ (1, 15 and 8, 1). It is not unreasonable to suppose that the idea of trepidation or precession was introduced into India by the Greeks, though the parameters chosen by the Indians are their own, and that the arguments presented in favour of the hypothesis of a motion of the colures are derived from a particular interpretation of the Vedangajyotisa. …

9 citations


Journal Article
TL;DR: In the Paitâmahasiddhânta of the Visnudharmottarapurâria, the authors, the authors investigate the Greek background of the common Indian model for the star-planets which involves two concentric epicycles.
Abstract: The development of geometric models to explain the inequalities of planetary motion in terms of combinations of circular motions is characteristic of Greek astronomy, and derives its initial bias from statements of the Pythagoreans, Plato, and Aristotle regarding the structure of the universe and, in the case of Aristotle, the difference between the mechanics of the sublunar centre of the cosmos and that of the celestial spheres. It is hardly necessary to point out here that among the devices invented to account for these inequalities are the eccentric circle and the epicycle, whose properties were investigated by Apollonius of Perge in about 200 b.c.1 The occurrence of these devices in Sanskrit astronomical texts of the fifth century a.d. immediately suggests some Greek influence. And the supposition of such an influence is greatly strengthened by the fact that Greek adaptations of Babylonian linear astronomy2 and Greek treatises on genethlialogy3 were translated into Sanskrit between the second and fourth centuries a.d.; it is virtually confirmed by the fact that the earliest Sanskrit siddhânias to employ epicyclic models, the older Romaka (for the luminaries only4) and Paulisa (for the Sun only5), are largely of Greek or GrecoBabylonian origin. It is my intention here to investigate the Greek background of the common Indian model for the star-planets which involves two concentric epicycles.In the Paitâmahasiddhânta of the Visnudharmottarapurâria,6 which is our earliest extant exponent of the Indian double-epicycle planetary model (it was probably composed in the first half of the fifth century a.d.), the pattern was set for all later texts except for those belonging to or aware of the auduyaka System of the Âryapakca. The orbits of the planets are concentric with the centre of the Earth. The single inequalities recognized in the cases of the two luminaries are explained by manda-cpicycles (corresponding functionally to the Ptolemaic eccentricity of the Sun and lunar epicycle respectively), the two inequalities recognized in the case of each of the five star-planets by a mandaepicycle (corresponding to the Ptolemaic eccentricity) and a .%Arn-epicycle (corresponding to the Ptolemaic epicycle). The further refinements of the Ptolemaic models are unknown to the Indian astronomers.If one tries to imagine the geometric model utilized by the Paitâmahasiddhânta, one immediately realizes that it cannot be cinematic ; the planet cannot ride simultaneously on the circumferences of two epicycles. These two epicycles must be regarded simply as devices for calculating the amounts of the equations by which the mean planet on its concentric orbit is displaced to its true position. This interpretation is confirmed by the explanation offered in early texts of the mechanics of the unequal motions of the planets : demons stationed at the manda and ftghra points on their respective epicycles pull at the planets with chords of wind.7 The computation of the total effect of these two independent forces upon the mean planet varies somewhat from one school (pak$a) of astronomers to another, or even from astronomer to astronomer within a paksa. But the fundamental concept remains clear: the planet is always situated on the ciicumference of a deferent circle concentric with' the centre of the Earth, while two epicycles (one each for the Sun and Moon) revolve about it. As the planet progresses with its mean velocity about this deferent circle, at each instant it is pulled by the two epicycles away from its mean to its true longitude. These instantaneous true longitudes are subject to computation, but a true course of the planet over a period of time can only be conceived of as a series of such instantaneous true longitudes.This is not to deny that the equivalence of an eccentric to an epicyclic model had also been transmitted from Greece to India, though it would seem that the transmission was effected by a different text from that from which the doubleepicycje theory is derived. …

8 citations


Journal Article
TL;DR: In this paper, the authors compare the use of magic in the second half of the twelfth century to what was known by William of Auvergne and Albertus Magnus, both of whom had access, in the region of Paris, to the new magic of Arabic origin that was coming into France and England from Spain.
Abstract: When one thinks of magic in the period of Frederick II, one's thoughts naturally turn to his astrologus, Michael Scot1. For Dante, some seventy-five or eighty years after Michael's death, had Virgil point out in the fourth bolgia of the eighth circle of Hell1:Quell' altro che ne' fianchi e cosi poco,Michele Scotto fu, che veramenteDelle magiche frode seppe il gioco.But neither Henry of Avranches}, Michael's contemporary, nor Salimbene4, the chronicler of Frederick's reign, mention this proclivity for magic. Yet a reading of the manuscripts of Michael's Liber introductorius5 and Liber particularise qUick]y reVeal that, while often stating that the use of magic is against the teachings of the Roman church1, Michael firmly believed in the efficacy of magic and was familiar, in embarrassingly intimate detail, with the modes of operating magically. In this paper I intend to relate his magic to what was known by his contemporary, William of Auvergne2, and by the somewhat later Albertus Magnus3, both of whom had access, in the region of Paris, to the new magic of Arabic origin that was coming into France and England from Spain4 - traditionally from Toledo5; and then to describe in some detail a fifteenth-century manuscript now in the Biblioteca Nazionale in Firenze - II. iii. 2146 - that turns out to be one of our most complete extant copies of these new magical texts, texts which are the foundation also for most of what Michael knew about learned magic.Let us begin with William of Auvergne, who, in his De universo, divides magic into three types7: sleight of hand, optical illusions, and the employment of demons. The first two are obviously not unnatural, though they may be fraudulent. Nor are the marvelous powers inherent in certain stones, plants, or animals unnatural; they are simply virtues that we are incapable of understanding. Indeed, one of the innate powers possessed by some natural objects is that of hindering magicians or putting evil spirits to flight. Those evil spirits or demons are real for William and for his contemporaries, and they are permitted by God to deceive man and to entice him into error and sin. The magus who falsely believes that he can obtain control of these demons by means of his invocations, suffumigations, prayers, and sacrifices is led not only into the error of heresy but into self-delusion as well. The demons do evil out of their own malignancy, the necromancer who attempts to direct them becomes their instrument.This may appear to be the attitude towards magic that one ought to expect from a Bishop of Paris. What William brings in to the discussion are references, both direct and oblique, to a number of Latin translations of Arabic works on black magic. Thus he refers to the Idea and Almanda! of Salomon1; to the seven books of the seven planets written by Mercurius - that is, by Hermes2; to the De stationibus ad cultum Veneris of Toz the Greek* a name variously distorted in the printed edition of William's works; to Artefius on eharacteres or magical writing4 and to Plato's Liber Neu mich5 or Book of the Cow. We shall have more to say of most of these works later; for now it must suffice to report that William is the first Westerner to record the names of these works, save for that of Toz. For already, in 1143, Hermann of Carinthia, writing in Beziers on the border of France and Spain, cited the thelesmatici - makers or operators of talismans - Iorma the Babylonian and Tuz the Ionian as employing the planetary spirits in their magical arts6 and Daniel of Morley, reporting in the last quarter of the twelfth century to John, Bishop of Norwich, concerning his studies in Toledo, speaks approvingly of «the science of images, which the great and universal Book of Venus, edited by Thoz the Greek, has handed down»7. Indeed, I suspect that all of the translations accessible to William, and others that I shall discuss later, were made in Spain toward the middle and end of the twelfth century. …

6 citations


Journal Article
TL;DR: In the early second millennium B.C. as discussed by the authors, Neugebauer et al. developed a concrete symbol indicating that there was no number occupying a place in a place-value system, but the scribes often assumed that the structure of the table would guide the reader to the correct interpretation of an ambiguous number.
Abstract: (ProQuest: ... denotes non-USASCII text omitted.)(ProQuest: ... denotes formulae omitted.)In the early second millennium B.C. Mesopotamian mathematicians used a place-value system of notation with base sixty. Using two wedges impressed on clay - a vertial Y for one and a sideways...for ten, they could express by the addition of symbols every number from one to nine and from ten (plus one to nine) to fifty (plus one to nine); after fifty-nine -...they returned again to... meaning now 1 x 60. Since these numerical forms could be extended infinitely both as integers and as fractions, the symbol Y could mean, depending on context, 1, 1 x 60,1 x 602, 1 x 603____1 x 60", or 1/60,1/602,1/603____1/60^. In the earliest usage of this system, there was no expressed symbol corresponding to an empty sexagesimal place; instead, the Babylonians often avoided confusion by simply leaving an emtpy space between two symbols: e.g.,4 ...would be read 12, but 4 YY10, 2 = 602. There was no way to write the equivalent of 10, 0, 2 = 36,002; such a number could only be recognized from context.In the period between the late eighth and the late sixth centuries B.C., some scribes began to use a punctuation mark, ..., that d indicated a stop or separation as the separator of fen or any multiple of ten and of one or any other number up to nine when they were in two sexagesimal places; thus, 10, 2 would be written. ...But they also began to use this same symbol to change, for example,...which was either 2, 10 = 130 or 2, 0, 10 = 7210, etc. into the unambiguous ...10. Here was first developed a concrete symbol indicating that there was no number occupying a place in a place-value system (see Neugebauer, 1934-1935, vol. 1, pp. 72-73 (no. 27], and NeugebauerSachs, 1945, pp. 34-35 [no. 33]).This symbol was widely though not universally employed in Babylonian astronomical tables of the last three centuries B.C., in both meanings (see Neugebauer, 1941 and 1955), but the scribes often assumed that the arithmetical structure of the table would guide the reader to the correct interpretation of an ambiguous number. When it was necessary to name an empty sexagesimal place, the Akkadian words used were nu tuk, meaning "nothing", the exact equivalent of the Greek ... which translates it, and of the Latin nihil, but not of the Sanskrit eunya and its Arabic derivative, sifr, both of which signify "empty".Beginning in the second century B.C. Babylonian astronomical tables and parameters written in this fashion began to be translated into Greek. The Greeks used the letters of their alphabet to indicate numbers, with one letter corresponding to each number from one to nine, one letter for each number from ten in multiples of ten to ninety, and one letter for each number from one hundred in multiplies of a hundred to nine hundred, so that twenty-seven letters expressed all numbers up to 999, after which the sequence repeated itself. Thus, the three letters ... (300 + 60 + 5) meant 365, for which the Babylonians wrotey'Y Y yy (6,5). The Greeks continued to use their traditional system to write integers in astronomical tables, but for the sexagesimal fractions they wrote the number in each sexagesimal place in their alphabetical notation; thus for 365 + 14/60 + 48/602, which modem historians write in the form 365; 14, 48. Greek papyri of the period immediately preceding and following the beginning of the common era demonstrate that, by using vertical dividing lines such as are also used in Sanskrit manuscripts to separate the sexagesimal places, they removed all ambiguities...But they did not leave an empty sexagesimal place blank; rather, they filled it with an adaptation of the Akkadian symbol for zero, ^ ; this adaptation looks like a circle with a bar over it: o or ^ (see Jones, forthcoming). This, then, is the origin of the form of the symbol for zero as a circle. It is necessary to note that this form of zero was known, through a translation of Greek astronomical tables into Latin, in Western Europe before the introduction of the Arabic adaptation of the Indian numerals (see Pingree, forthcoming). …

Journal Article
TL;DR: The earliest documented attempt to discuss critically any portion of the Almagest was written by an otherwise totally obscure Artemidorus in the latter half of the second century or at the beginning of the third.
Abstract: (ProQuest: ... denotes non-USASCII text omitted.)My objectives in this paper are two: to reveal the richness of the tradition of the study of the Almagest1 between the date of its composition in the middle of the second century AD2 and its appearance simultaneously in Byzantium3 and Baghdad4 in the late eighth century, and to hypothesise about the origins of one of several commentaries on the Almagest that were composed during this period.The earliest documented attempt to discuss critically any portion of the Almagest was written by an otherwise totally obscure Artemidorus in the latter half of the second century or at the beginning of the third. A passage regarding the lunar theory of Books IV and V of the Almagest is quoted from this Artemidorus in the anonymous commentary on the Handy Tables edited by Jones and shown by him to contain an example that can be dated 24 April 213.5 Artemidorus established a tradition - fortunately not followed universally - of failing to understand or of misrepresenting Ptolemy's statements in the Almagest.6It is clear that Artemidorus, however deficient his understanding, approached the Almagest as an astronomer interested in the way in which Ptolemy's solutions to problems work mathematically. The same can be said of the two Alexandrian scholars who commented on the Almagest during the course of the fourth century. Pappus composed his ...7 after 18 October 320, the date for which, in his commentary on Almagest VI4, he computed the time of a mean conjunction of the sun and the moon.8 Of Pappus's Scholion there survive in their entirety only Books V and VI; as we shall see, some fragments of other books - it is not yet clear how many - can be recovered from other sources. Rome conjectured that Pappus followed a tradition established by some earlier commentator of dividing each of the thirteen books of the Almagest (excluding, presumably, the Star Catalogue in VII and VIII) into sections called ... echoes of this practice survive in the commentary of Theon9 and in the later scholia.10 These divisions may have been more useful in the teaching of the Almagest, which was strongly directed toward the students' acquiring computational skills, than were Ptolemy's chapter divisions, which reflect his concern with the logical development of astronomical theory. Despite his emphasis on computations, Pappus makes in Books V and VI about a dozen errors in calculation, and in eight cases seems to have deliberately falsified his results in order to make them agree with the Almagest.11 His students could not have been very alert since they seem to have let him get away with his slipshod habits.Theon composed his ...12 on the Almagest most probably in the 360s and 370s. Now that Professor Tihon has discovered most of Theon's commentary on Book V in the margins of Vaticanus Graecus 198,13 we have all of the ... except for Book XI. Of the eighteen manuscripts of the commentary known to Rome the oldest is Laurentianus 28.18, copied in the ninth century and at present preserving only Books I to IV and VI. In fact, ten of the manuscripts contain nothing beyond Book VI, and they, without the Laurentianus, form Rome's Class II. So there existed an edition of Theon that broke the text at the end of Ptolemy's discussion of spherical trigonometry, and the theories of the sun, the moon, and eclipses. This is also the dividing point between the two volumes of Heiberg's critical edition. One wonders if the survival of Books V and VI of Pappus's ... may not be due to their being the end of a first volume of an edition of which the second volume in its entirety, the first in its beginning have been lost.Theon assumes a fairly low level of mathematical ability and accomplishment in his students. They need, for instance, to be instructed at great length on the multiplication and division of sexagesimal fractions and on a variety of geometrical theories, while in general Theon teaches them nothing beyond the replication of Ptolemy's calculations. …

Journal Article
TL;DR: In this paper, it has been claimed that Sergius of Rtsh'alnA, the early sixth century translator, was responsible for the Syriac version,1' and In any case, he did write on astronomy and on spherical trigonometry.
Abstract: Some concepts of Greek mathematical astronomy reached Islam in the eighth century through translations and adaptations of Sanskrit and Pahiavi texts. These represented largely non-Ptolemaic ideas and methods which had been altered in one way or another in accordance with the traditions of India and Iran. When to this mingling of Greco-Indian and Greco-Iranian astronomy was added the more Ptolemaic Greco-Syrian in the late eighth and early ninth centuries, and the completely Ptolemaic Byzantine tradition during the course of the ninth, the attention of Islamic astronomers was turned to those areas where these several astronomical systems were in conflict. This led to the development in Islam of a mathematical astronomy that was essentially Ptolemaic, but in which new parameters were introduced and new solutions to problems in spherical trigonometry derived from India tended to replace those of the Almagest.THE PROBLEM OF THE INFLUENCE of Greek mathematical astronomy upon the Arabs (and in the following I have generally excluded from consideration the related problems of astronomical instruments and star-catalogues) is immensely complicated by the fact that the Hellenistic astronomical tradition had, together with Mesopotamian linear astronomy of the Achaemenld and Seleucld periods and its Greek adaptations, already Influenced Use other cultural traditions that contributed to the development of the science of astronomy within the area In which the Arabic language became the dominant means of scientific communication in and after the seventh century a.d. An Investigation of this probelm, then, must begin with a review of those centers of astronomical studies in the seventh and eighth centuries which can be demonstrated to have influenced astronomers who wrote in Arabic. This limitation by means of the criterion of demonstrable influence will effectively exclude Armenia, where Ananias of Shirak worked in the seventh century,1 and China, where older astronomical techniques,* some apparently derived ultimately from Mesopotamian sources,* were partially replaced by Indian adaptations of Greek and Greco-Babylonian techniques rendered into Chinese at the T'ang court in the early eighth century.4 But it leaves Byzantium, Syria, Sasanian Iran, and India.While astronomy had been studied at Athens by Proclus* and observations had been made by members of the Neoplatonic Academy In the fifth and early sixth centuries,* and while Ammonius, Eutoclus, Philoponus, and Simplicius had written about astronomical problems at Alexandria in the early sixth century,7 a hundred years later the tradition was transferred to Constantinople, where Stephanus of Alexandria-perhaps in imitation of the Sasanian Zlk-i Shahriyârân-prepared in 617/618 a set of instructions with examples illustrating the use of the Handy Tables of Theon for the Emperor Ileraclius.8 Such studies, however, were soon abandoned, not to be revived in Byzantium till the ninth century, when their restoration seems to have been due to the stimulus of the desire to emulate the achievements of the Arabs. Except for the texts of the Little Astronomy* and some passages reflecting Greco-Babylonian astronomy in pseudo-Heliodorus10 and Rhe- torlus of Egypt," Byzantine astronomy !n this period was solidly Ptolemaic.The history of astronomical writings In Syriac before the rise of Islam Is difficult to trace. The works of Bar Dal?an," hls pupil Philip," and of George, the Bishop of the Arabs," indicate that sufficient knowledge of the subject must have existed to permit the casting of horoscopes; for this all that Is really needed, of course, are tables, and It Is certain that a Syriac version of the Handy Tables existed.14 There may also have been a Syriac translation of Ptolemy's Syntaxis since some of the Arabic versions arc said to have been made from that language.1* In fact, It has been claimed that Sergius of Rtsh'alnA, the early sixth century translator, was responsible for the Syriac version,1' and In any case he did write on astrology and on the motion of the Sun. …

Journal Article
TL;DR: The authors examines the origins of the puranic and jyotisa cosmologies, showing which of the elements in each were influenced by Babylonian and Greek ideas, and how the jyotsis adapted to their own system what puranic ideas they could while rejecting all others.
Abstract: This article examines the origins of the puranic and jyotisa cosmologies, showing which of the elements in each were influenced by Babylonian and Greek ideas, and how the jyotisis adapted to their own system what puranic ideas they could while rejecting all others. The key jyotisa text, the Paitamahasiddhania, is paradoxically preserved in an upapurana. the Visnudharmottarapurana. It is further shown that a movement to reconcile the cosmology of the astronomers with that of the puranas began in the late seventeenth century, perhaps in an attempt among Indian intellectuals to close ranks against the perceived threat to their traditions posed by Islamic and European astronomy.THERE EXIST IN A NUMBER of puranas. as Kirfel' has demonstrated, two descriptions of the universe having a common source. In this common source the earth, prihivl, with its seven concentric pairs of continents and oceans,2 is a horizontal disk in the center of a vertical universe enclosed in the brahnmnda. That universe contains seven iokas above' and seven potalas below/ The first three of the upper seven constitute the Vedic triad the bhurloka being the surface of the earth, the bhuvarloka the region between the earth and the sun, and the svarloka the region between the Sun and Dhruva, the pole-star. From the center of the earth rises mount Meru/ which acts somewhat as does the Vedic ak$a or axle that connects heaven and earth (which occurs only as a simile for Visnu!)/ though the name Meru (or rather, Mahameru) appears first in Vedic literature only in the Tait tiriyarany aka (1.7.1.2); for Meru in the purSnic text is the axle around which the wheels carrying the celestial bodies rotate. It also serves the function, as do Anaximenes' "higher parts of the earth," of explaining the disappearances of the Sun. the Moon, and the nakfatras. Above these circle the Saptareis7-Ursa Maior presumably because that constellation, as was noted in the Babylonian omen series. Enfima Ann Enlil, never disappears from the night sky. The cakras of these jyotlrpfi arc rotated by chords of wind that bind them to Dhruva, which is located on the tail of the starry Steumâru or Dolphin/ Dhruva is also a late concept; it first appears in the prescriptions for the marriage ceremony given in the grhyasfltras/ though there only as an unmoved star, not as one pole ol the axis about which the other celestial bodies revolve.The concepts of Merit and Dhruva serve to date this cosmology to the middle of the last millennium B.

Journal Article
TL;DR: In the early 8th century, the earliest Arabic zfjes were composed on the basis of Indian methods: the Zfj al-Jumic and the Zft al-Hazur at Qandahar as discussed by the authors.
Abstract: Indian astronomy entered early Islam through several routes1. The urdharutrikapaksa that had been initiated by Aryabhata of Kusumapura in about 500 influenced the Zlk-i Shuhriyurun composed in PahlavT at the Sasanian court in Ctesiphon under Khusro Anushirwan in 556. This is known to us now through the astrological computations made by Masha'allah ibn AtharT, a Persian Jew from Basra, for the several astrological histories that he wrote in the decades before and after 800:. From the works of Masha'allah extant in Arabic, Greek, and Latin, and from the discussions of them by al-Hashiml in his Kitub cilal al-zfjut and by al-Blruni in his Kitub tamhfd al-mustaqirr li-macnu al-mamarry we know that Khusro's zfk utilized the urdharutrika's apogees of Saturn, Jupiter, and the Sun; and its equations of the center of Jupiter and, within one minute, Mars and the Sun. This Zfk-i Shuhriyurun already employed the Persian calendar, and was probably influenced by Ptolemy4.The zfk of Khusro strongly influenced that produced under the last of the Sasanian Shah~i Shahs, Yazdijird III, which was translated into Arabic as the Zfj al-Shuh by al-Tamimi in about 800. This also is now lost, but much concerning it may be learned from the Zfj al-mumtahan (Tabulae Probatae), the zfjts of Habash al-Hasib, and again, al-Hashimi and al-BTruni5. While some modifications were made in the parameters - e.g., in Mars' equation of the center - the structure and calendar of Khusro's ztk were retained, and the influence of Ptolemy may even have been expanded.In the early eighth century the earliest Arabic zfjes were composed on the basis of Indian methods: the Zfj al-Jumic and the Zfj al-Hazur at Qandahar, the Zfj ai-Arkand at Sind in 735 largely on the basis of the urdharutrikapaksa as expounded in Brahmagupta's Khandakhudyaka, and the Zfj al-Harqan on the basis of the uryapaksa of Aryabhata's Âryabhatfya in 7426. None of these was wildly popular outside of Sind and Afghanistan; we know of them only through al-Hashiml and al-Biruni. More significant for the transmission of Indian astronomy to the Islamic world was the translation of a Sanskrit text, apparently entitled Mahusiddhunta, into Arabic at the court of al-Mansur in Baghdad in the early 770's7. Two of those involved in the popularization of this translation, the Zfj al-Sindhind, were Muhammad ibn Ibrâhim al-Fazarl8, who, according to one story, was involved in the translation itself, and Ya'qub ibn Tariq9.Al-Fazarl, in about 775, wrote on the basis of the Zfj al-Sindhind, the Zfj al-Shuh, and the Ptolemaic tradition (probably as represented by the Handy Tables in their Pahlavi version)10, a Zfj al-Sindhind al-kabfr. Basically, al-Fazâri's mean motions of the planets (including the Sun and the Moon), their nodes, and their apogees were derived from the bruhmapaksa through Brahmagupta's Brâhmasphutasiddhunta, the equations of the center and of the anomaly from the Zfj al-Shuh, and the table of declinations of the Sun from the Handy Tables; other computations, involving three different values for the radius, R, in a sine-table - 150 from the KhandakhOdyaka, 3270 from the Bruhmasphutasiddhunta, and 3438 from the Paitumahasiddhanta and the Aryabhatfya - were derived from various Indian and Sasanian sources. Al-Fazâri in some instances - e.g.y in the mean motions of Saturn and of the lunar node, and in some of the equations - differs from his identifiable sources. Some of his tables, as had been Ptolemy's for Chords and declinations, were entered with arguments of 0;30°, while the equation tables imitated the Indian practice of intervals of 90724 or 3;45° (and its multiples 7;30° and 15°). Though the bruhmapaksa does not allow for precession, al-Fazâri used Ptolemy's value of Io per 100 years. It appears that al-Fazâri's Zfj al-Sindhind al-kabfr followed the Zfj al-Shah in using the epoch of Yazdijird III (16 June 632) and the Persian calendar, though in about 788 he published a Zfj calu sintal-cArab which utilized the epoch of the Hijra (16 July 622) and the Muslim calendar. …

Journal Article
Abstract: (ProQuest: ... denotes non-USASCII text omitted.)Near the beginning of his Disputationes advenus astrologiam divinatricem Pico della Mirandola mentions (') «the books of Plato concerning the Cow (which) the magi cause to circulate [...] filled with execrable dreams and figments». This paper presents an attempt to define the origins - in part Neoplatonic - of the execrable dreams contained in the Book of the Cow, to explain how its magic works in tandem with its gemellus, the celestial magic of the Picatrix generally so much more familiar to historians of Renaissance Neoplatonism, and finally to examine what little evidence there is for the popularity of this text during the Renaissance.The Syrian city of Harran has long been associated with occult events (2) - if not from the time that Abraham was brought there from Ur of the Chaldaeans as recorded in Genesis (5), at least from about 550 B.C. when the last of the Chaldaean kings, Nabonidus, dreamed that Marduk ordered him to rebuild Ehulhul, the temple of Sin, the god of the Moon, at Harran. In order to make this restoration possible, Marduk employed Cyrus the Persian - the eventual obliterator of Nabonidus' feeble power and of the ancient kingdom of Babylon - as his instrument to destroy the army of Medes who were besieging the city (*).A millennium and a half after the jubilant re-installation of the Moon in his temple liarran was still in ferment with the occult sciences, with some elements derived from Babylon, some from Sasanian Iran, and some from Western and Southern India, while others came from the Greeks, and especially the Neoplatonists (5). In the ninth, tenth, and eleventh centuries the planets and the noetic hierarchy of Neoplatonism were still being worshipped in Harran with rituals of mixed Mesopotamian, Zoroastrian, Indian, and Hermetic origins. The $abians' study of the xocjxoc, of the vouc, of the and of «Komata, however, was based not only on Plato's Republic, Timaeus, and Laws, but as well on an Aristotelian corpus familiar to students of the Neoplatonic schools at Alexandria and at Athens; Ibn al-Nadlm in his Fihrist (6) quotes al-SarakhsI V), a pupil of al-Kindl, as citing their use of the Physics, the De Caelo, the De generatione et corruptione, the Meteorology, the De anima, the De sensu et sensato, and the Metaphysics. We shall see that other Platonic and Aristotelian works as well as some of those already mentioned provided the intellectual background to the Book of the Cow. The Harrânians investigated the relations between the heavens and the sub-lunar world through the medium of astrology, for the correct practise of which they, like Proclus, plunged into the intricacies of Ptolemy's Euvtccfo and 'AiroTeXtapoiTixa among many other texts, including Hermetic, Sasanian, and Indian.Out of this rich mixture of intellectual traditions, the Harrânians in the latter half of the ninth century - by then calling themselves $abians and proclaiming Hermes to be their prophet in order to gain the approval of the Islamic authorities (8) - created the astral magic that is summarized in such confusion in the Ghayat al-hakim (9) and in its Latin translation, the Picatrix (,0). This astral magic is based on Neoplatonic cosmology, astrology, and Harranian worship of the planets. It seeks, through rituals in part suggestive of the Hermetic art of the vivification of statues (n), performed at astrologically propitious times, to persuade the souls of the planets whom God has placed in charge of his material creation to send their subordinate spirits to occupy talismans. These latter are thereby empowered to effect changes in this sublunar world. This is a non-demonic form of magic that relies for its effectiveness on the powers granted by God to the planets and on those inherent by nature in corporeal substances and in the magician's rational soul.But at the same time the Harrânians invented another form of magic based on quite different principles. …

Journal Article
TL;DR: In this paper, the authors presented a translation of the Envina Anu Enlil Table of 360 days from a fragment K.2077-f 3771 to a fragment of K. 11044.
Abstract: K. 2077 -f 3771 is described in Bezold'a Catalogue as «part of an astrological text* and was consequently studied for possible inclusion in Erica Reiner's forthcoming edition of Envina Anu Enlil. Bezold had already drawn attention to the «squares» with figures, eight on the reverse, hut only two preserved on the obverse, and these «squares with figures* ijointed to a text more astronomical than astrological in character.David Pingree. when Erica Reiner showed him her transliteration of the text, recognized that the text deals with the lengths of seasonal hours, and that the «squares* represent a table of the lengths of seasonal hours for every fifteenth day of an «ideal» solar year of 360 days. The missing portions of the table could therefore lie reconstructed. When suljsequently the fragment K. 11044 was joined to K. 2077+, the newly gained portions confirmed Pingree's reconstruction not only of the table, but also of its description in the first four lines of the reverse. The difficulties presented by the remaining ten lines of the reverse, however, remain substantial.The text is here presented in transliteration anti translation. The astronomical commentary is by David Pingree. Moreover, the presentation and the philological commentary have greatly benefited from discussions with David Pingree.This edition is dedicated to the memory of Professor Ernst Weidner, whose pioneer work on the series Envina A nu Enlil had aided and inspired us in our undertaking.While the astronomical interpretation of the tables of the text, and their usefulness in attaining one of tho stated purposes, tho determination of intercalations, is clear (see Astronomical Commentary), the text contains a number of difficulties, and its format is without parallel.The tablet is written in Neo-Babylonian script and dialect, except for the subscript and colophon on the lower edge, which are written in Assyrian script According to the colophon, it was written in the eponymy of Bel-Sadua; if this eponym is identical to Bel-Carrân-eadua, the date ib 649 B. C. *.Tho tablet lias the oblong shape associated with the reports of scholars to Esarhaddon and Assurbanipal * ; almost the entire left half is missing, as can be calculated from the disposition of tho table on tho bottom of the obverse. The reverse is divided by a vertical ruling into two columns. The right half is almost complote, but of tho loft, only a few ends of lines, seemingly all ending in gar, are visible; it seems likely that those lines contained tables or computations.On the obverse, the linos run across the entire width of the tablet, and can be only partially restored. The first two lines state the length of daylight on the longest day of the year, and the next four lines seem to give the explanation of the table (see Astronomical Commentary). From linos 7 to 17 the surface of the tablet is worn off, and therefore the introduction to the table in obv. [16]-20 is not preserved.Tho almost completely preserved right column of the reverse contains, as do the reports, a communication to the king. It states, first, that the text deals with the (yearly) course of the Sun from the Path of Enlil to the Path of Ea and bock, and that from sunrise to sunset and from sunset to sunrise the day (a nychthemeron) contains 12 beru (lines 1-4). The writer goes on to say that ho has made certain computations, and gives instructions for further computations to be mode, presumably in view of finding intercalations (lines 5-6). There follow claims about the novelty of tho subject matter or procedure: the writer informs the king that these mattere had not been written on a tablet but had been preserved in the oral tradition (lines 7 - 8). The remainder (linos 8-12) is unclear in its details. The writer ends with the statement that in the text may be found not only intercalations, but also «giving of signs», and refers not only to the course of the Sun but also to those of the Moon and the planets, which do not otherwise appear in the preserved part of the tablot. …

Journal Article
TL;DR: The history of astronomy, as of all other aspects of human thought, is extraordinarily complex. Much of that complexity is reflected in the subject I am about to address as discussed by the authors, and it can be traced back to Indian adaptations in the fifth century of Greek models and parameters altered to fit existing Indian theories expressed in the Puranas.
Abstract: The history of astronomy, as of all other aspects of human thought, is extraordinarily complex. Much of that complexity is reflected in the subject I am about to address. For both Indian and Muslim conceptions of the forms of the heavens and earth and of the mathematics by which their several motions may be described originated in Hellenistic astronomy, but each descended through various different cultural milieus to become transformed into models, parameters, and mechanisms barely recognizable to each other. In this paper, expanding on what I have previously written on this subject1 but striving not to repeat excessively what has already been said, I intend to examine how some Indians attempted to make the Muslim interpretation of Ptolemy palatable to their fellows, who frequently dismissed it as foreign rubbish,2 while others tried to use elements of it simply to buttress the, for them, naturally declining system revealed at the beginning of the yuga by the divine knowledge of the Sun.For in the tradition of the astronomies of India it had become, by the sixteenth century in Northern India, important to many scientists to emphasize the origin of one's paksa or school in a revelation granted by either a divinity or an rsi.3 The main rivals in the resulting wars of revelations were Brahma, the creator and recreator of this universe, from whose Paitamahasiddhanta* both the Âryapakca of Aryabhata5 and the Brahmapaksa of Brahmagupta6 truthfully claimed descent, and Surya, the Sun god, whose Suryasiddhanta,1 which had been updated in the sixteenth or seventeenth century,8 was in fact principally based on the Ardharatrikapaksa of Aryabhata,9 itself a modification of his Aryapaksa. There are several other divinities and rsis who are quoted as authorities; but, in fact, all of the siddhantic tradition of cosmology, geography, and mathematical astronomy goes back to Indian adaptations in the fifth century of Greek models and parameters altered to fit existing Indian theories expressed in the Puranas.10The cosmology (khagola) of the siddhantas conceived of the universe (insofar as we can perceive or deduce it) to consist of nine intemested spheres, one for each of the seven planets in the Hellenistic order, the eighth bearing the naksatras, and the ninth being the sphere of heaven. The distances of the planetary spheres from each other is based on the theory, adumbrated by Plato, that the distance of each from the center of the earth is inversely proportional to its planet's mean velocity. While the inner eight spheres are rotated daily by the pravaha wind which is wrapped around their common axis, each planet moves independently on its own concentric orbit in a motion that is irregular because of the pulls exerted on the planet by demons stationed at the uceas on its manda and Sighra epicycles. The forces that move the celestial bodies, then, are material beings, whose execution of their self-appointed tasks is certainly not eternal, since this cosmos within the Brahmanda is destroyed and recreated to the rhythm of a Kalpa of 4,320,000,000 years; nor is it necessarily constant, since the world declines drastically over the course of a Mahayuga of 4,320,000 years. These ideas allowed Indian astronomers, if they so chose, to justify the introduction of foreign models and parameters, which could be regarded as representing the degeneration of what had existed and been described by a god or an rsi at the beginning of the yuga. But this cosmology precluded most from embracing Aristotelian concepts of natural motion. Though the Indians like Aristotle had five elements (mahabhutas), they-earth, water, air, fire, and space-all permeate the entire cosmos; in this the Indians were closer to Plato than to his pupil. Muslim astronomers, of course, being devotees of the Stagirite, believed in a radical difference between the sublunar world of naturally linear motion and celestial spheres of naturally circular motion, which ought as well, at least in principle, to be uniform and concentric. …

Journal Article
TL;DR: In the second book of the Enchronicities, the authors of the second chapter as mentioned in this paper define the sixteen topics of astronomy, which they call spherica positio, sphericus motus, and spheric motus.
Abstract: (ProQuest: ... denotes non-USASCII text omitted.)Toward the middle of the sixth century the former secretary of the Ostrogothic king, Theoderic, the Senator Cassiodorus composed for the monks of his monastic foundation, Vivarium, a guide to sacred and profane literature1. The last substantive chapter, before the conclusio, of the second book of the /nstitutiones is on the last of the seven liberal arts, De astronomia2. Cassiodorus begins this chapter with a brief compilation of appropriate passages from Scripture, and then proceeds to define the sixteen topics that he believes astronomy to consist of : «spherica positio, sphericus motus», and so on3. Certain technical terms that occur among these sixteen topics he not only defines, but for each provides the Greek equivalent. So for the forward motion of the planets, which he calls in Latin «praecedentia vel antegradatio», he gives the Greek «propodismos» ; for the planets' retrograde motion, «remotio vel retrogradado» in Latin, he gives the Greek «ypopodismos aut anapodismos» ; and for their stations, «status» in Latin, he provides the Greek «stirigmos». The Latin terms were copied by Isidore of Seville in his Etymologiae4, and thence were borrowed by numerous medieval authors ; but in the Latin literature before Cassiodorus they do not occur - except for retrogradado or retrogradus5 - in Pliny, Firmicus Maternus, Macrobius, Calcidius, or Martianus Capella. The Latin terms, then, seem to be Cassiodorus' own translations of the Greek terms that he cites.These Greek terms - TTpoTroSiapos-, unoTToOiapoc, avanooiapos-, and crrqpiypoc - are common in Greek astronomical and astrological texts. The question, then, is apparent : did Cassiodorus know enough Greek and enough astronomy to be able to peruse, say, Ptolemy's ZuvTaEic or Proclus' 'TnoTUmoais-, to pick out these terms, and to understand their meaning ? Or did he find them in a Latin text other than those we have mentioned ? Though Cassiodorus was certainly capable of translating Greek6, he does not give any evidence of having an advanced knowledge of astronomy sufficient to allow him to read Ptolemy or Proclus. But there is evidence that he consulted the Latin version of Ptolemy's Kavovec npoyeipoi or Handy Tables, that is, the Preceptum canonis Ptolomei, in whose instructions Greek technical terms are presented in transliteration7. Though the parts of the Preceptum that dealt with the forward and retrograde motion and the stations of the planets are no longer present in the manuscripts that have survived of that curious work, we shall soon see that their absence can be explained.But now we must return to the chapter De astronomia in book II of the Institutiones. Cassiodorus proceeds after his enumeration and defi- nition of the sixteen topics of astronomy to describe the literature pertinent to that science8 : «De astronomia vero disciplina in utraque lingua diversorum quidem sunt scripta Volumina ; inter quos tarnen Ptolomeus apud Graecos praecipuus habetur, qui de hac re duos codices edidit, quorum unum minorem, alterum maiorem vocavit astronomum». Ptolemy's «minor astronomus» may be the piKpoc aaTpovopoupcvoc to which the scholiast to the Vatican manuscript of Pappus, Vat. gr. 218, refers at the beginning of book VI of the Xuvaymyn9, and the piKpoc aorpovopoc that Theon is said in an anonymous text on isoperimetric figures to have commented on10. This latter text is part of the Elaayioyn to Ptolemy's ZuvTa^ic that Mogenet has shown to have probably been composed by Eutocius11, who wrote in about the year 500. The Little Astronomy was probably the collection of mainly Hellenistic texts on astronomy and geometry that are preserved as a corpus in Byzantine, Arabic, and medieval Latin manuscripts12. None of these texts, however, is by Ptolemy, so that it remains problematical why Cassiodorus should have claimed that his «minor astronomus» was by the great Alexandrian13. The «maior astronomus» of Ptolemy, however, must be his 2uvTa£ic. …

Journal Article
TL;DR: In the case of the Enuma Anu Enlil series, it is known as the IStar series as discussed by the authors, which is the largest group of cuneiform tablets known to contain planetary omens.
Abstract: Out of the vast number of cuneiform tablets identified during the last century as containing planetary omens, and therefore as connected with the series Enuma Anu Enlil, and specifically with its fourth and last section, commonly called IStar, the largest group is that devoted to Venus. This fact immediately differentiates the importance of this planet in the omen tradition from the place that it holds in the mathematical astronomy of the Seleucid period, where Venus is rather poorly represented. However, two tablets - an atypical text from the second half of the fifth century B.C.1 and an ACT procedure text2 - both from Babylon, indicate that rather complex theories of Venus involving subdivisions of the arcs and times between its characteristic phenomena were already current in the early Achaemenid period and continued in use in the Seleucid period. These are quite sufficient to show that Venus was not neglected by those who were constructing the mathematical theories of the planets, even though its orbit as seen from the earth did not fit the models that were developed for the superior planets.But, while Venus' phenomena were not amenable to description by stepfunctions or zig-zag functions, these same phenomena provided the earliest mathematical theory of any planet that we have; this is found in the 8 section of Tablet 63 of Enuma Anu Enlil, the so-called Venus Tablet of Ammicaduqa, a crude theory by which approximate dates for the successive occurrences of four phenomena - first visibilities and invisibilities in the East and in the West - could be anticipated.3 In general, however, the scribes of Enuma Anu Enlil were not interested in these Greek-letter phenomena except as parts of more complex omens - and even then, at least in my understanding of what they wrote, never directly mentioned the other two phenomena that are included in the later mathematical theory, first and second station, nor even the arc of retrogression that separates them. But in the planetary omens it is really only Mars' rather extreme and Jupiter's retrograde arcs that drew attention, as each entered a constellation and then backed out of it before plunging into it again. The exceptions in Enuma Anu Enlil outside of Tablet 63 to this general neglect of the Greek-letter phenomena are the rather banal protases: "Venus in the winter rises in the East, in the summer in the West" and its opposite;4 then, "Venus in the winter rises in the East and does not set" and its permutations;5 and "Venus stands in the West and sets - on the 7th day it rises in the East", and the impossible transposition of this correct period of invisibility at inferior conjunction to the period of Venus' invisibility at superior conjunction.6Given, then, that the Venus phenomena considered ominous in Enuma Anu Enlil - and in the Reports and Letters sent by the diviners to Esarhaddon and Assurbanipal7 - were not in general the Greek-letter phenomena, what were they? This is a question Erica Reiner and I have been wrestling with for some time as we have sifted through, ordered, and attempted to impose some meaning on the numerous fragmentary texts that will be included in the next fascicle of Babylonian Planetary Omens.* This paper is an attempt to summarize our tentative conclusions.As far as can be determined, either five or six Tablets of some canonical Enuma Anu Enlil were devoted to the enumeration of omens in which the main element of the protasis was the planet Venus; these were numbered either 58 or 59 to 63. The last, the Venus tablet of Ammicaduqa, states in its colophon that it is the 63rd Tablet, and then gives the catchline of a Tablet devoted to Jupiter. On the other side of the Venus block Tablet 56 concerns various planets, and Tablet 57 seems to have obscure contents. We know nothing of the omens contained in Tablet 58. But Tablets 59 and 60 record Venus omens arranged by months, the first six on Tablet 59 and the last six on Tablet 60. The beginning of the sequence of omens was missing already in antiquity since various derivative texts knew nothing of the omens from the beginning of month 1 ; needless to say the extant copies of Tablet 59 are also broken at the beginning, but this is an accidental coincidence. …

Journal Article
TL;DR: In this paper, it was shown that the celestial body in the upper left quadrant of the print must be a star or a planet rather than the comet that it is usually interpreted to be.
Abstract: Upon recently reading William Heckscher's fascinating study of Camerarius's description of Durer's Melencolia I,1 I was led to consider some interpretations of this enigmatic print (PI. 35c) which I believe have not been noticed hitherto. I present them in this note for others more expert than I both in iconography and in Durer's art to appreciate or to deprecate. Certainly 1 do not pretend to have any evidence that these meanings were intended by the artist.The basis of the new interpretations is a consideration of the composition as a whole, whereas previously scholars have tended to concentrate on individual elements.* Three linked states of being are represented in the print (PI. 35c) : the celestial occupies the upper third, including both the celestial body to the viewer's left and the upper parts of the ladder and tower to his right; the terrestrial is depicted in the centre left; and an intermediate state appears in the centre right and lower third. The two main figures in the rint-the block of stone and Melancholy crself-arc located in the intermediate state.I begin to justify this analysis by the observation that the celestial body in the upper left quadrant of the print must be a star or a planet rather than the comet that it is usually interpreted to be. This is indicated by the rays extending from it in all directions to the limits §C the visual field. These are not, however, rays of light; for the presence of the rainbow, eccentric to the celestial body, shows that the Sun has not yet set but is in the west-in the direction from which the viewer beholds the scene- while the celestial body itself is rising in the East.* The rays are rather those by which, according to astral magic, the planets effect their influence in the sub-celestial world.* In a depiction of Melancholy, the celestial body emitting magical rays can only be Saturn.In the same plane with Saturn are two other celestial symbols.8 To the right is the magic square of Jupiter, whose influence must be combined with Saturn's to produce the melancholic philosopher;* and in the centre hang the scales of Libra, the exaltation of Saturn. The upper third of the picture, then, represents the celestial configuration under which Saturn is most effective in producing philosophers: Saturn is rising in its exaltation in association with Jupiter.Above the frame of the print extends the supercclestial world, which is, quite literally, imperceptible to us. Into this lead the ladder and the tower. The latter is, as Heckscher shows, a House of Wisdom ; more specifically, it symbolizes the intellectual mode of ascent to the supcrcelestial, as the ladder refers to ascent by faith.7 The intellectual character of the tower is indicated by the four objects hung on its exterior wall, which represent the external or practical aspects of the quadrivium. The scales represent the Arithmetic of weighing and measuring; the hourglass the Astronomy of time-keeping; the bell the Music of rhythmic sound; and the magic square the Geometry of the lines, squares and triangles that constitute that particularobject.8The seascape with its fringe of inhabited land clearly represents our sublunar world; the four elements are also indicated, fire and air above earth and water. The scene in the foreground, then, bounded by the block of stone on the left and by Melancholy herself on the right, lies between this world and the heavens. It represents those hypostases placed by some Neoplatonists and astral magicians between the spiritual and the material worlds, wherein, under celestial influence, the elements9 and the human Spiritus10 are formed. In fact, Durer shows under Saturn what appears to be an inchoate octahedron, the second of Plato's five perfect solids,11 though others have interpreted it, less persuasively, as a truncated cube.11 In one passage in the Timaeus (53c) the second of the elements is earth, which possesses the two qualities of Saturn, dryness and cold; in another passage (55c! …

Journal Article
TL;DR: The Indian influence on Sasanian astronomy was syncretistic-a blend of concepts and methods derived not only from Iran's indigenous traditions, but also from those of her neighbours, and especially of India and the Hellenistic world.
Abstract: The study of the history of astronomy and astrology in Iran during the Sasanian period (226-652)1 is rendered difficult by the fact that none of the contemporary Persian works on these subjects written in the Pahlavi language have been preserved in their original form. But there are numerous passages in other texts of the Sasanian period, and especially in the apologetic literature of the ninth century1, which give us some inkling of what those works were like. Thus, the Bundahishn devotes its second chapter to a discussion of the stars®, and its fifth chapter is concerned with the horoscope of the creation of Gayomart, the first man, and with other astrological details4. The Denkart informs us of the traditional Iranian view of the transmission of the science8; this account is repeated and supplemented by a Persian astrologer whom Hârun al-Rashid (786-8O9) placed in charge of his Khizânat al-hikma, Abu Sahl al-FaSasanian astronomy, as is characteristic of Sasanian thought in most fields of science and philosophy, was syncretistic-a blend of concepts and methods derived not only from Iran's indigenous traditions, but also from those of her neighbours, and especially of India and the Hellenistic world (this latter influence was felt both directly through Greek and indirectly through Syriac). It is primarily the Indian influence that will be investigated here.Our sources inform us that the first two Sasanian emperors-Ardashir I (226-240) and Shâpur I (240-270)-were dedicated to the expansion of the Iranian intellectual tradition, and supported the translations of Greek and Sanskrit books into Pahlavi10. Thus we know that versions were made of Ptolemy's Syntaxis mathematike, which the Dinkart calls M.g.st.yk. (Megiste, whence the name al-Majistl11; the ninth century scholar Manushchihr mentions Ptalamayus (Ptolemaios) in connection with Indian and Iranian astronomical tables Z$k t Hinduk and the Zik C Skahriyâmn)13. Also translated into Pahlavi from Greek were the hexameters of the Pentateuch, an astrological poem written in the first century by Dorotheus of Sidon1*., as well as an unknown text attributed to one Cedrus of Athens, the Paranatellonia of Teucer of Babylon, and the Anthologien of Vettius Valens. Ibn Nawbakht tells us that there was also translated a work by an Indian named Faramâsb, which Justi conjectures to be ParamAava14.Other Indian astronomical and astrological ideas were spread to Sasanian Iran through the translations of Buddhist texts which were made in the Eastern provinces of the empire. The Sardulakarnavadona1* Was certainly known among the faithful of this area since the Parthian prince An Shi-kAo14 translated the introductory story into Chinese in 148, and a long fragment of the Sanskrit text copied in c. 500 was found south of Yarkand17; this work contains a summary of the Babylonian-influenced astronomy and astrology which was current in India between c. 500 B.C. and 100 A.D.18. Another such text is the Mohumayurimanjari1*, which deals in part with naksatraastrology ; fragments of fifth century manuscripts are preserved among the Bower and Petrovski manuscripts from Kashgar. From such sources as these are probably derived the Iranian references to the naksatras80, to Rahu (who is called Gocihr)81, and to shadow-tables**.The earliest attempt to compose a set of astronomical tables, the Zikt t (Ztj al-Shâh in. Arabic)-however, was apparently composed in 450, during the reign of Yazdijird II (438-457). A reference is preserved from this work by Ibn Yunis in his Ztj al-Hukimi **: the longitude of the apogee of the Sun at Gemini 17 ; 55°. This parameter is derived from the tradition of the Paitdmahasiddhdnta of the Visnudharmottarapurdna *4. …