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(a.), a term in Islamic astronomy denoting the sighting of the lunar crescent. In this article, astronomical aspects are covered. Muslim astronomers from the 2nd/8th century onwards performed calculations to predict the visibility of the lunar crescent, of particular importance for the fixing the beginning and end of Ramaḍān and the festivals [see hilāl , i. In religious law; ʿīd; ramaḍān ; ṣawm ; taʾrīk̲h̲ ]. Over the centuries, the techniques and visibility conditions that they used became more sophisticated. Even the simplest procedures involved a knowledg…

(a.), or taʿdil̄ al-ayyām bi-layāl̄ihā , the equation of time, a fundamental notion in mathematical astronomy. Times derived from observations of the sun [see mīḳāt ] need to be corrected by a function which takes into consideration the fact that the true sun does not move on the celestial equator but on the ecliptic [see minṭaḳat al-burūd̲j̲ ] and the fact that its motion on the ecliptic is not uniform. This correction, which varies throughout the year, is the equation of time, and it was tabulated in Islamic astronomical handbooks [see zid̲j̲ ]. Since tables of …

(a.), in planetary astronomy the correction or equation (corresponding to medieval Latin aequatio ) applied to mean positions of the sun, moon and planets to derive the true positions [see ḳamar ; s̲h̲ams. i. ; taḳwīm ; zīd̲j̲ ]. Muslim astronomers generally tabulated these functions in the same way as Ptolemy had done in the Almagest [see baṭlamiyūs ] but occasionally introduced more extensive sets of tables to facilitate the tedious application of more than one equation (as in the case of the moon and planets). (D.A. King) Bibliography E.S. Kennedy, Solar and lunar tables in early…

(a.), azimuth or direction, a term in frequent use in Islamic astronomy. It is usually applied to the direction of a celestial object measured on the horizon, determined by the arc of the horizon between the east- or west-points and the foot of the vertical arc through the celestial object. The Arabic plural al-sumūt gave rise to the term azimuth and its equivalents in numerous European languages. But whilst in mediaeval astronomy the azimuth was usually measured from the east- or west-points, in modern astronomy it is measured clockwise from the north point. The complementary arc measu…

, Abū ʿAlī al-Ḥasan b. ʿAlī , astronomer of Mag̲h̲ribī origin who worked in Cairo. In ca. 680/1281-2, he compiled a compendium of spherical astronomy and astronomical instruments entitled Kitāb D̲j̲āmiʿ al-mabādiʾ wa ’l-ghāyāt fī ʿilm al-mīḳāt , which is perhaps the most valuable single source for the history of Islamic astronomical instrumentation. In this work, which exists in several manuscript copies, al-Marrākus̲h̲ī presented a detailed discussion of the standard problems of spherical astronomy [see mīḳāt. 2. Astronomical aspects], and then dealt with different ki…

(a.), literally, “quarter”, in Islamic astronomical terminology, quadrant. The kind of large mural quadrant ( libna ) with a graduated altitude scale described by Ptolemy (see baṭlamiyūs ] was used by a series of Muslim astronomers over the centuries. Descriptions exist of i.a. those used in the Damascus observations in the early 3rd/9th century ( ca. 5 m in radius), by the astronomer Ḥāmid b. K̲h̲iḍr al-K̲h̲ud̲j̲andī at Rayy in the late 4th/10th century (called al-suds al-Fak̲h̲rī , radius ca. 20 m), and in the early 9th/15th century observatory of Ulugh Beg [ q.v.] at Samarḳand (radius ca…

(a.), lit. “leg” or “thigh”, used in various senses in Islamic mathematics and astronomy. Thus, for example, sāḳ means the foot of a compass, the perpendicular of a right-angled triangle with horizontal base, or the equal sides of an isosceles triangle. Another term for the foot of a compass is rid̲j̲l , and ḍilʿ is also used for any side of any triangle. (See further ʿilm al-handasa , in Suppl.). In astronomy [see nud̲j̲ūm ] sāḳ may refer to a star that is in a leg of a constellation figure representing a person or an animal, as in sāḳ al-asad or sāḳā ’l-asad ¶ (dual) for either or both of α Boo…

(a.), declination, an important notion in spherical astronomy. Declination is a measure of the distance of a celestial body from the celestial equator. Muslim astronomers tabulated either the declination and right ascensions of stars or their ecliptic coordinates [see maṭāliʿ ]. Also of concern to them was the solar declination, mayl al-s̲h̲ams . They distinguished two kinds of solar declination, al-mayl al-awwal, the distance δ1 of the sun from the ecliptic measured perpendicular to the celestial equator, and al-mayl al-t̲h̲ānī , the distance δ2 of the sun from the ecliptic m…

(a.), the term used in mediaeval Islamic scientific texts for the magnetic compass. The earliest references to the magnetic compass in the Islamic written sources have been surveyed by E. Wiedemann in mag̲h̲nāṭīs . 2. to which see also the addenda in volume IX. To these sources may now be added: 1. A treatise on the magnetic compass (called ṭāsa ) used for finding the ḳibla , compiled by the Rasūlid Yemeni Sultan al-As̲h̲raf ca. 690/1290 (first studied by P. Schmidl in 1994); see PL V. There is no mention of any deviation of the compass needle from the meridian, but w…

b. Muḥammad b. Maʿrūf, sometimes given the nisbas al-Dimas̲h̲ḳī, al-Ṣahyūnī or al-Miṣrī, the most important astronomer of Ottoman Turkey, b. Cairo or Damascus in 927/1520-1 or 932/1525 (the sources are not consistent), d. Istanbul, 993/1585. He studied theology in Cairo, served as ḳāḍī in Nābulus, and in 979/1571 was appointed müned̲j̲d̲j̲im bās̲h̲i̊ in Istanbul. He was largely responsible for persuading the Ottoman Sultan Murād III to build an observatory in Istanbul. This was achieved in 987/1579. However, the building wa…

(a.), literally, correcting between the two lines, an expression used in Islamic mathematics and mathematical astronomy for interpolation. Muslim scientists used linear and non-linear procedures for calculating intermediate values in mathematical and astronomical tables. (D.A. King) Bibliography J. Hamadanizadeh, A survey of medieval Islamic interpolation schemes, in D.A. King and G. Saliba (eds.), From deferent to equant. Studies... in honor of E.S. Kennedy, New York 1987, 143-52. See also King, Ibn Yūnus’ Very Useful Tables for reckoning time by the sun, in Archive for Hist…

(a.), the rising point of a celestial body, usually a star, on the local horizon. This concept was important in Islamic folk astronomy [see anwāʾ and manāzil on some aspects of this tradition], as distinct from mathematical astronomy [see ʿilm al-Hayʾa ], because it was by the risings and settings of the sun and stars that the ḳibla ¶ [ q.v.] or direction of Mecca was usually determined in popular practice. The terms used for the rising and setting points of the sun were usually mas̲h̲riḳ and mag̲h̲rib , maṭlaʿ being generally reserved for stars. The directions…

(a.), sundial. This term and sāʿa s̲h̲amsiyya are used in modern Arabic, but in mediaeval Islamic times horizontal sundials were referred to either as ruk̲h̲āma , lit. “marble” or basīṭa , lit. “flat”, and vertical sundials as munḥarifa , lit. “inclined”. The gnomon was usually called s̲h̲ak̲h̲ṣ , s̲h̲āk̲h̲iṣ or miḳyās . One expression of the Muslim concern with timekeeping and regulating the times of prayer [see mīḳāt ] was an avid interest in gnomonics, the theory and practice of sundial construction. Muslim astronomers made substantial c…

(a, pl. of maṭlaʿ ), ascensions, an important concept in mediaeval spherical astronomy and astronomical timekeeping [see mīḳāt ]. Ascensions represent a measure of the amount of apparent rotation of the celestial sphere, and are usually measured from the eastern horizon, hence the name ascensions. Two kinds were used: (1) right ascensions, or ascensions in sphaera recta; and (2) oblique ascensions, or ascensions in sphaera obliqua [see also falak and maṭlaʿ ]. (1) Right ascensions refer to the risings of arcs of the ecliptic over the horizon of a locality with latit…

(a.), azimut ou direction, terme d’usage courant dans l’astronomie islamique. Il s’applique habituellement à la direction d’un objet céleste mesurée sur l’horizon, déterminée par l’arc de l’horizon entre les points Est ou Ouest et le pied de l’arc vertical passant par cet objet. C’est le pluriel al-sumūt qui est à l’origine du mot azimut et de ses différentes formes dans les langues occidentales. Mais alors qu’en astronomie médiévale l’azimut était normalement mesuré à partir des points Est ou Ouest, dans l’astronomie moderne, il est mesuré…

(A.), nom du marquage d’une projection stéréographique universelle qui caractérise une famille d’instruments astronomiques utilisables pour toutes les latitudes terrestres. L’astrolabe [voir Asṭurlāb] standard comporte une série de tympans pour différentes latitudes. A l’origine, dans les astrolabes grecs et les premiers astrolabes islamiques, ils desservaient les sept climats de l’Antiquité [voir Iḳlīm]. Toutefois, dès le IIIe/IXe siècle, des latitudes spécifiques furent sélectionnées, et des listes de localités desservies étaient parfois gravées s…

, Abū ʿAlī al-Ḥasan b. ʿAlī, astronome d’origine mag̲h̲ribine qui travailla au Caire. Vers 680/1281-2, il écrivit un compendium sur l’astronomie sphérique et les instruments astronomiques intitulé Kitāb Ḏj̲āmiʿ al-mabādiʾ wa-l-g̲h̲āyāt fī ʿilm al-mīḳāt, qui est peut-être la meilleure source pour l’histoire de l’instrumentation astronomique de l’Islam. Dans cet ouvrage, qui existe en plusieurs manuscrits, al-Marrākus̲h̲ī présente une étude détaillée des problèmes courants d’astronomie sphérique [voir Mīḳāt. 2. Aspects astronomiques], puis traite de différentes …

(a.), ou taʿdīl al-ayyām bi-layālīhā, l’équation du temps, notion fondamentale en astronomie mathématique. Les heures déduites de l’observation du soleil [voir Mīḳāt] nécessitent d’être corrigées grâce à une fonction prenant en compte le fait que le soleil réel ne se meut pas sur l’équateur céleste, mais sur l’écliptique [voir Minṭaḳat al-Burūd̲j̲], et le fait que son mouvement sur l’écliptique n’est pas uniforme. Cette correction, qui varie tout au long de l’année, est l’équation du temps, et a été mise en tables dans les manuels astronomiques islamiques [voir Zīd̲j̲]. Les tables…

(a.), cadran solaire. Ce terme et sāʿa s̲h̲amsiyya sont usités en arabe moderne mais, à l’époque médiévale, les cadrans solaires horizontaux étaient désignés sous le nom de ruk̲h̲āma «plaque de marbre» ou basīṭa «plate», les verticaux étaient dits munḥarifa «inclinée». Le gnomon était généralement appelé s̲h̲ak̲h̲ṣ, s̲h̲āk̲h̲iṣ ou miḳyās. Le souci qu’avaient les Musulmans de connaître l’heure et de régler les ¶ moments de la prière [voir Mīḳāt] s’exprimait dans leur vif intérêt pour la gnomonique, c’est-à-dire la théorie et la pratique de la construction des ca…

(a.), «jambe, cuisse», avec des sens variés dans les mathématiques et en astronomie arabes. Par exemple, sāḳ désigne la branche d’un compas, la hauteur d’un triangle rectangle à base horizontale, ou les côtés égaux d’un triangle isocèle. La branche d’un compas s’appelle aussi rid̲j̲l, et ḍilʿ s’applique également au côté de n’importe quel triangle (voir aussi ʿIlm al-handasa, au Suppl.). En astronomie [voir Nud̲j̲ūm], sāḳ peut désigner une étoile située dans la jambe d’une constellation représentant une personne ou un animal, comme dans sāḳ aî-asad ou sāḳā l-asad (au duel) pour ch…