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Our earliest examples of these often splendid products of Persian craftsmanship date from the late tenth century. Ptolemy’s planetary models consist of couplings of circles.Each epicycle, or small circle of given radius, bears on its circumference one of the planets (with the exception of the sun) and rotates in a clockwise direction for the moon, in a counter-clockwise direction for the five star-planets.A solution to the problem of the equant was proposed by the astronomers of Marāḡa in the thirteenth century.The device that they utilized—a small circle whose radius is half that of a larger circle within which it rolls—is called a Ṭūsī-couple after its “inventor” (it was, in fact, known to Proclus, but not employed by him in an astronomical context), Ḵᵛāǰa Naṣīr-al-dīn Ṭūsī (1201-74).A number of his minor works on observational instruments and on astronomical problems connected with the Muslim calendar and Islamic religious practices also survive. He was also the author of a partially preserved commentary on the became the accepted text throughout the Middle East.
This work contains a unique exposition of a Syrian planetary theory that combines Aristotelian and Ptolemaic theories with what appear to be Indian ones transmitted through Sasanian Iran. Nowbaḵt Ḥakīm was an astrologer from Iran contemporaneous with Māšāʾallāh; his son, Abū Sahl Fażl, also an astrologer, was one of the leading intellectuals in the Baghdad of Hārūn al-Rašīd. The few astronomical theories with which his name is associated are Indian; he presumably derived them from Pahlavi books. By this translations, and that of the commentary of Ebn al-Moṯannā by Hugh of Sanctalla, and by the is also the basis of the astronomy of the Samaritans. Abī Manṣūr, who came from Ṭabarestān to the court of al-Maʾmūm in Baghdad, was the principle author of the . In his , written between 226/840 and 246/860, he combined the Indian, Sasanian, and Greek astronomical traditions to which Islam was heir, and attributed the resulting amalgamation of disparate elements to an antediluvian Persian text that he claimed to have been written in the reign of Ṭahmūraṯ. Ḥabaš Ḥāseb from Marv wrote at least two s in the middle of the ninth century, which represent the beginnings of the development of trigonometry and the construction of new astronomical tables that characterized the next, otherwise Ptolemaic, period of Islamic astronomy. Moḥammad Farḡānī, also in the middle of the ninth century, wrote an abridgement of Ptolemaic astronomy that was translated into Latin by John of Seville in 1135 and by Gerhard of Cremona in the 1170s; this work maintained its popularity in the west as an astronomical textbook into the sixteenth century.The center of the epicycle rotates in a counter-clockwise direction on the circumference of a deferent circle; but this circular motion is uniform, not with respect to the center of the deferent, but with respect to another point called the equant.Moreover, the center of the earth lies not at the center of the deferent circles, but in the case of each in the opposite direction from the equant and at the same distance from the deferent-center.The earliest mathematical astronomy that developed in territory under Iranian control was that which originated in Mesopotamia, was improved during the Achaemenid period, and culminated in the Babylonian solar, lunar, and planetary theories of the Seleucid and Parthian periods. We have no direct evidence, however, that would clarify the nature of Iranian astronomy during the Achaemenid period. Arabic texts also preserve numerous fragments of other lost Pahlavi astronomical and astrological texts; and it appears probable that Sasanian scientists transmitted some Indian theories to Syria.That some of this Babylonian astronomy and the astral omen literature that was associated with it was adopted by scholars in Iran itself is implied by its transmission to India in the late fifth or early fourth century B. and by the preservation of Babylonian methods of interpreting gnomon-shadows. In the Parthian period, however, we do find evidence from eastern Iran that Babylonian mathematical astronomy and astral omens continued to be studied and that Indian concepts had begun to be influential. The latter were originally 27 or 28 constellations, in one of which the moon appeared to be on each night of a sidereal month; they had become, in the second half of the first millennium B. From this evidence and from passages in the s, for instance, and repeats a primitive Indian explanation of the cinematics of the planets, according to which their motion is effected by cosmic chords.