It is proved that the Futian calendar, a non-official one compiled in the Jianzhong reign period (780-783) in China, was brought to Japan in 957 by a Buddhist monk and was employed as the basis of horoscopes by the Buddhist school of astrology (Memo 1964). It was also used in competition with the official Chinese xuanming calendar for the usual functions demanded of a Chinese type lunisolar ephemerides, such as eclipse predictions. According to the view of the Song Dynasty Chinese scholar Wang Yinglin that the Futian calendar was “originally an Indian method of astronomical calculation” but Kiyosi Yabuuti has commented that Wang Yinglin’s appraisal of the Futian calendar is solely based on a resemblance in form as it copied the trivial point of taking its epoch as the Jiuzhi calendar according to Indian astronomical methods and does not display a fundamental understanding of the Indian calendar (Yabuuti 1944).

By the time al-Bīrūnī wrote the KH (see al-Bīrūnī’s books; see also Boilot 1960; Kennedy 1970; Khan, A.S. 1982; Khan M.S. 1975) in the first half of the eleventh century, Greek astronomy specially the Almagest of Ptolemy was fully diffused among the Arabs. They also had some knowledge of Persian astronomy (Pingree 1963)- But he was not the first Muslim scientist to write on Indian astronomy. Before he visited India (around 408/1017) he had some knowledge of this subject derived from Arabic translations of Sanskrit astronomical works. He records that the Brāhmasphuṭa-siddhānta of Brahmagupta (ca. A.D. 598) was translated by the order of Caliph Manṣūr of Baghdad (754-775 A.D.) in 154/771 or in 156/77_3(KH, p.351) and its Arabic translation was called Sindhind al-Kabīr or the Great Sindhind. He adds that he translated it into Arabic and wrote a treatise on it. He also studied its method of calculation in his treatise Tarjumah mā fī Brāhma Siddhānd min Ṭuruq al-Ḥisab (Khan, A.S.1982, p.20). Al-Bīrūnī states that he also retranslated the Khaṇḍakhādyaka by Brahmagupta, called in Arabic al-Arkand and published a new correct translation (KH, pp.346-383; Nalino 1911, p.83; Nadwi 1930, p. 139). He had written a treatise entitled Tahddhīb zīj al-Arkand in which he corrected its errors but this is not available at present (Khan, A.S. 1982, No.6, p.12). The Āryabhatīya of Āryabhata (b. A.D. 476) called Arjabhadh in Arabic was translated by Abu’l-Hasan al-Ahwāzī and it was perhaps available to al-Bīrūnī(KH, p.357; Pingree 1970, p.308; Nalino 1911, p.172-73).

Earliest visibility of the lunar crescent is an important calendrical element. It was needed in all early calendars and remains in use in some lunar calendars today. An astronomical criterion of earliest lunar visibility was therefore evolved quite early, using observations, right from the Babylonian era. In subsequent periods the Babylonian single factor ‘moonset lag’ criterion was used extensively, although gradually it was realized that it was rather simple. Recently, an improved and comprehensive global criterion of earliest visibility, developed by the author, has been used to generate an extensive inverted moonset lag data set. These data, as a function of latitude and season, all for the tirst time provide a useful comparison with the simple ancient criterion. It is found that the simple criterion is remarkably good for the latitude region where the Ancients collected their observational data, illustrating the care with which their data was gathered. At other latitudes, there are significant differences, as may be expected. Although the simple criterion may now be replaced by an accurate season and latitude dependent criterion, the former will continue to provide a useful basis. The paper discusses various related historical developments.

Arabic star names are well known in two areas: in the Orient itself, i.e. in the Arabic-Islamic civilization, and in the West where many of them were adopted since mediaeval times and continued to be used until today.

The complex known in modern Western astronomy as “Arabic star names” is the result of a historical development of almost exactly one thousand years. In mediaeval times, those names were introduced into Western use by Latin translations of Arabic astronomical and astrological works. Afterwards, since Humanist and Renaissance times, and until this present century, Western astronomers used to pick up more “Arabic” names from philological studies of orientalists who tried to describe and explain the stellar nomenclature of the Arabs and other Oriental peoples. As outstanding examples, I mention the studies of Joseph Scaliger and his follower Hugo Grotius (both printed in 1600) whose nomenclature was borrowed by Johannes Bayer into his star atlas Uranometria of 1603; Thomas Hyde’s commentary to his edition of Ulugh Bēg’s star catalogue (Oxford, 1665) from which Giuseppe Piazzi borrowed a great number of names into the second edition of his Palermo Catalogue, 1814; German studies by F.W.V. Lach (1796) and Ludwig Ideler (1809) which were used by continental astronomers such as J.E.Bode and many others; and still the book on star names by R.H. Allen (1899) from which several new names appear in astronomical books and atlases of our times.

The oldest European mythological figures of the star constellations originate from the Farnesian Globe of the 3rd century B.C. The “Centaurus” with the Therion “Lupus” is the most important constellation from which I derive all the series specified. Centaurus holds the wolf with one hand on the hind leg; in the other hand he holds a lance with which he cuts the wolf’s throat. This constellation is incorrectly drawn in the first publication of the Farnesian Globe by Bianchini. These antique figures were the pattern for Cod. Vind. 5415, probably by John Dorn, a Dominican, who made also the globe of Bylica at the Budinian court of the king Mathias. This globe is at present the property of the University-Museum of Krakau. The antique constellation-forms were the pattern for the celestial maps of Sebastian Sperantius of Nurnberg in 1503. Due to Albrecht Durer these mythological figures of the constellations re-appeared in the renaissance. We can find them by John Honterus, John Middoch, on many globes for example that of Coronelli, or of the manuscript globe of the Bibiliotheca Cassanatense in Rome of Moroncelli from the year 1716. They survived till modern times in the “Uranometria” of John Bayer, in the star-atlases of John Flamsteed, John Erlet Bode as well as in the latest star atlas with allegoric figures of Rudiger-Meisner from the year 1805.

The Muslim Calendar spread into China in 1385 where it was immediately translated into Chinese by the astronomer Yuan Tong and came into use. In 1477, it was further translated by the astronomer Bei Lin and compiled into the “Qi Zheng Tui Bu”, a work more or less the same in substance with the Muslim Calendar recorded in the “Ming Shi Li Zhi”, both being works of the same source. They left for us the valuable data of the results of research of ancient Arabian astronomers.

On different occasions in the Muslim Calendar, values different with one another are used for the same kind of data. In that case, which of them are used for them are accurate values surveyed and calculated by people who originally worked out the Muslim Calendar? And how are these values calculated from data now available?

Alphonse X, King of Castille (1252-1284), sponsored astronomical work previous to the compilation of the Alphonsine Tables, carried out by his two Jewish collaborators Yehudah ben Mosheh and Isaac ben Sid. On the one hand, these tables can be considered the first European attempt to develop original research in astronomy, but on the other hand, an analysis of this work should be concerned, first of all, with its Islamic precedents. This is why I tend to consider the Alphonsine Tables as another zīj which should be studied in the light of what we know concerning the development of Islamic zījes in Medieval Spain. Of these, two seem to be well documented as having been known and used by the Alphonsine collaborators. One of them is al-Battānī’s zīj, the canons of which were translated into Spanish (Bossong, 1978), and which may have been used to compute the solar positions for the end of each month appearing in four Alphonsine works (Astrolabio redondo, Cuadrante para rectificer, Relogio dell agua, and Lámina Universal). These positions have been computed, however, with the Alphonsine Tables themselves. The second zīj known in the Alphonsine circle was al-Zarqalluh’s Toledan Tables, used — as O. Gingerich has established — to compute the solar and planetary positions in the horoscope which was cast to establish the propitious moment to start the Latin translation of Ibn Abī-l-Rijāl’s Kitāb al-bāric fī ahkām al-nujūm (Hilty, 1954, lxii-lxiii).

A commentary, on the spherical astronomy in the Zīj-i Īlkhanī[1], written by the famous Naṣīr ad-Dīn aṭ-Ṭusī (c. 1270) would be an important contribution to the history of medieval astronomy. But we postpone this and attempt here to describe the contents of the third and fourth sections of Treatise III of this zīj. We hope that it will serve to elucidate a small part of this work, which has remained unexploited. I have made a preliminary English translation of the entire Zīj-i Īlkhanī, which awaits final revision and preparation for publication.

The rules explained verbally and without proof by Naṣīr ad-Dīn in the sections under consideration are similar to the ones described by Kāshi in his Zīj-i khāqānī and analysed by E. S. Kennedy in [2]. Therefore, we do not present our proofs of the rules, but refer the reader to [2].

The earliest astronomical instruments in India are the śaṙku (gnomon) and the ghaṭikā (clepsydra). The former is mentioned in the Śulbasūtras, and the latter in the Vedāṅqajyotiṣa. Aryabhaṭa described a rotating model of the celestial sphere. After Aryabhaṭa, several instruments were described by Varāhamihira, Brahmagupta,Lalla, Śrīpati , and Bhāskara II. After Bhāskara II , some Sanskrit texts specialized on astronomical instruments were composed. The earliest text of this kind is the Yantra-rāja (AD 1370) written by Mahendra Sūri. It is also the first text on the astrolabe in Sanskrit. After Mahendra Sūri, Padmanābha, Cakradhara, Ganeśa-Daivajña etc. composed Sanskrit texts on instruments, but most of them remain unpublished.

In Fig.1, let U be the rising point of the ecliptic (udayalagna), T be the nonagesimal (tribhona-lagna) and M be the meridianecliptic point (madhya-lagna). Since T is at a distance of one quadrant from U along the ecliptic, the complement of the zenith distance of, that is the arc TK, will be the required angle between the ecliptic UTM and the horizon NUEKS. The equivalent problem in Indian astronomy is therefore to find what is called ‘dṛkkṣepa-jyā’ or the sine of the zenith distance of the nonagesimal.

The people of Yemen as a whole, and the Jews of that country in particular, possess a very rich cultural heritage, including achievements in the field of astronomy. The medieval astronomical sources were the subject of an exhaustive study by David A. King (Mathematical Astronomy in Medieval Yemen, Malibu 1983). Some material concerning Jewish interest in the subject was collected by Bernard R. Goldstein (The Survival of Arabic Astronomy in Hebrew, J. for the Hist, of Arabic Science 3, 1979, 31-39, note 2c.) The author of this paper has recently completed a monograph on the exact sciences among the Jews of Yemen. In this paper we present some discrete items of mainly bibliographic interest which emerged from that study. Note that our sources are all Arabic manuscripts, written in Hebrew characters.

Ptolemy’s Almagest has been criticized by Islamic astronomers in two different ways: criticisms of Ptolemaic parameters and criticisms, like those of the Maragha school, of the geometrical models used as they contradicted certain basic principles like the principle of uniform motion.

Jabir ibn Aflah’s Islah al-Majisti seems to be outside the two aforementioned ways of criticizing the Almagest for he gives an excellent and faithful qualitative account of his kinematical models. He pretends, on one side, to give a complement to the mathematical basis of the Almagest and, on the other, he seems to consider this work as having, in his time, only a theoretical value; due to the modifications of parameters introduced by Islamic astronomers, the Almagest itself has lost, in Jabir’s opinion, all practical value for computation. He also gives a list of mistakes he thinks Ptolemy made, but I will limit myself here to analyse what Jabir seems to consider a methodological lack of which I will give only one example: Jabir criticizes Ptolemy’s determination of the relative positions of the centre of the equant, the centre of the deferent and the centre of the universe in the case of the models for the superior planets, for he considers that Ptolemy did not give any proof of the fact that the centre of the deferent is the midpoint between the two others.

In Greece, Autolycos (4th cent. B.C.), Aristarchos of Samos (3rd cent.B.C.), Hipparchos (2nd cent.B.C.), Menelaos (1st cent. A.D.), and Ptolemaos (2nd cent. A.D.) are the forerunners of trigonometry. The Greeks used chords and prepared a table of chords.

Later, the Hindus produced Siddhāntas (4th cent.A.D.). The most important feature of these works is the use of jyā instead of chords, and utkramajyā (versed sine).

In Islam, al-Battānī al-Ṣābī (858-929) used the sine, cosine, tangent, and cotangent with clear consciousness of their individual characteristics.

As is known, trigonometry developed as a branch of astronomy. Although in the thirteenth century Naṣīr al-Dīn al-Ṭūsī (in the Islamic world) and in the fifteenth century Regiomontanus (in the West) established trigonometry as a science independent of astronomy, the essential situation did not change, and the subject went on developing as before.

A characteristic feature of Arab-islamic astronomy during the Middle Ages is the promotion and tremendous growth of practical astronomy which was in turn manifested primarily by the establishment of scores of observatories in West-Central Asia, from Abbasid Caliph al-Māmūn (813-833) to the Turkish king Murād III (1574-1595), and by the production of copious literature on astronomical Tables (the zījes) as well as on astronomical instruments (ālāt al-rasad). The enormity of the literature on the latter could be gauged by the list of extant works as given by Matvievskaya and Rosenfeld (1983) in their recent Biobibliography: 349 treatises on astrolabes, 138 on sine-instruments, 81 on quadrants, 4 on sextants and octants, 41 on armillary spheres and celestial globes, 77 on sundials and again 77 on “other instruments”—in all 767 treatises. As a matter of fact the instruments developed by Arab-islamic astronomers could be broadly classified into four groups: a) Time measuring instruments (e.g. sundials, shadow quadrants), b) Angle measuring instruments for astronomical parameters (e.g. armilla of various kinds, dioptre and parallactic rulers), c) instruments for transformation of system of coordinates and/or solving nomographical problems (e.g. astrolabes, quadrants, dāstūr instrument), d) Mathematical instruments for evaluating trigonometric functions, (e.g. sinequadrants). Apart from the fourth and the most important of all, the astrolabe, which in turn embodies all the four groups of instruments to a certain extent, works on “other instruments” were compiled in almost every century (down from 9th to 18th A.D.), also by well-known Arab-Islamic astronomer-mathematicians.

In the course of a systematic search in the “Technical Museum” of Vienna for instruments of astronomical importance, a Moorish astrolabe with Cufic lettering was discovered by the present author. Being labelled as “sun-moon-dial” its correct function had not been recognized before or forgotten. The device came into the museum’s possession in April 1937 through exchange with a theodolite from the Jesuit College at Kalksburg where the astrolabe had been kept after it remained in Vienna during one of the two Turkish sieges of the city (probably in 1683). The brass instrument has a diameter of 15,7 cm and is well equipped with 8 ṣafīḥas ( = tympans). Its conservation state is rather good, even the original red and gold ‘ilāqa ( = cord) is in place. The specimen is of undated planispheric northern type (shamālī musattah). It shows the typical small kursī ( = throne) of occidental instruments, cast in one piece with the ḥajra (= limb) and umm ( = mater) forming the main body of the astrolabe. This fact sets it apart from instruments of European origin where the kursī sometimes was fastened with screws to the main body (W. Morley, reprinted in R. Gunther, 1976).

Sawai Jai Singh, the statesman astronomer of 18th century India, designed instruments, built observatories, prepared Zīj, and sent a fact-finding scientific mission to Europe. His high-precision instruments were designed to measure time and angles with accuracies of ± 2 second, and ±1’ of arc respectively. The Ṣaṣṭhāmsa, a meridian dial with aperture, can still measure angles with precision of ± 1’ of arc. In the age of Newton and Flamsteed, Jai Singh and his associates remained medieval, in the tradition of Ulugh Beg, and did not initiate the new age of astronomy in the country. A complex interaction of poor communications, religious taboos, theological beliefs, national rivalries and plain simple human shortcomings are to be blamed for the failing.

Research conducted over the past several years has revealed a richly diverse astronomical tradition in the Indo-Malay cultural area. I wish, in this paper, to share some of this richness by describing several of the many and diverse observational techniques used by the Indo-Malay peoples to help regulate their agricultural cycles.

Inhabiting mountain sides, river valleys, and coastal plains, the Indo-Malay peoples are faced with a rather unpredictable tropical monsoon climate. In response to this geography and climate they have adopted two distinct types of rice farming: swidden and padi, or dry and wet.

Padi farming is sedentary and relies upon heavy monsoon rains and/or irrigation for the rather large and dependable supply of water required: rice plants must be submerged from the time that they are planted in the nursery through transplanting and until seed is set. From thereon, dry weather is essential for the seed to properly ripen. Padi fanning is widely practiced on coastal plains and terraced hillsides by people such as the Javanese, the Sasak of Lombok, and the Malays of Kedah and Perak.

It has been shown by Aveny (1981) that the development of indigenous astronomical systems in tropical cultures, whether the motive was religious or practical, centered toward a reference system consisting of zenith and nadir as poles and the horizon as a fundamental reference circle. Such a reference system differs remarkably to the celestial pole-equator (or ecliptic) systems employed by civilizations in temperate zones (also see Brennand, 1896; Stencel, et.al., 1976).

In order to obtain more insight of the view expounded by Aveny (1981) the authors undertook a test case study of the astronomically related time-keeping practice in Java. “Pranotomongso” has been chosen as it is well documented since 1855. According to Daldjoeni (1984) the “pranotomongso” (literaly means the arrangements of seasons) functions well as a practical guide for agricultural activities for the rural peasants in Central Java.

Ancient astronomical data are a limited resource that can fill unique needs in modern research. Records from the Orient are of particular value because they were taken more or less continuously, as parts of dynastic and local histories – often for astrological purposes. We review three problems in modern astronomy that lean heavily on ancient records from the Middle East and Orient: the study of solar variability; studies of the variable rotation of the earth; and studies of the occurrence and physics of novae, supernovae and comets.

The works of Eddy (1976) and Clark and Stephenson (1978) on the ancient sunspot records are reviewed and a plea is made for the search for ancient records of astronomical events and phenomena in India.