Abü Sahl Al-KüHĪ on the Distance to the Shooting Stars

The story of the modern discovery of the heights of shooting stars is told in several sources, among them Pannekoek A. , A history of astronomy (New York, 1961), 419; Watson Fletcher G. , Between the planets , rev. edn (Cambridge, Mass., 1956), 75–76; and Hughes David W. , “The history of meteors and meteor showers”, Vistas in astronomy , xxvi (1982), 327.

This approximate dating is established by al-Kūhī's dedication of the work to Ṣamṣām al-Dawla, member of the combative Būyid ruling family who seized power from each other in parts of Iraq and Iran on a regular basis. See Busse Heribert , “Iran under the Būyids”, in Frye N. (ed.), Cambridge history of Iran , iv: From the Arab invasion to the Saljuks (Cambridge, 1975), esp. pp. 289–93; and Encyclopedia of Islam, 2nd edn, i, s.v. “Buwayhids”.

This work is listed by Fuat Sezgin in his Geschichte des Arabischen Schrifttums , v: Mathematik (Leiden, 1974), as the thirteenth entry under al-Kūhī, 319. See also Berggren J. L. Van Brummelen Glen , “Abū Sahl al-Kūhī on rising times”, to appear in SCIAMVS.

This treatise, which we are preparing for publication, is listed by Fuat Sezgin in his Geschichte des Arabischen Schrifttums , vi: Astronomie (Leiden, 1978), as the fourth entry under al-Kūhī, 219.

This work, Maqāla fī Taṣaffuḥ kalām Abū Sahl al-Kūhī fī l-kawākib al-munqaḍḍa, which consisted of 15 folia, is referenced by Sezgin Fuat , Geschichte des Arabischen Schrifttums , vi: Astronomie , 219, and vii: Astrologie — Meteorologie und Verwandtes (Leiden, 1979), 291.

Al-Kūhī does refer to four ancient astronomers on the distance to astronomical bodies: Archimedes, Aristarchus, Timocharis, and Ptolemy. Presumably, al-Kūhī was thinking of Aristarchus's On the sizes and distances of the Sun and Moon and Ptolemy's Almagest and Planetary hypotheses. As for Archimedes, his work on this topic is contained in The sand reckoner and a list of Archimedean proposed planetary distances in St Hippolytus's third-century a.d. “Refutation of all heresies” (see Neugebauer Otto , A history of ancient mathematical astronomy , 3 parts (New York, 1975), Part 2, 647–51); we are unaware of any reference to these works in the Arabic literature. However this may be, al-Kūhī's comments suggest that more of Archimedes's work was known than we have yet found evidence for. Al-Kūhī's mention of Timocharis may be a reference only to his observations.

This is not to say that they were not observed; see, for instance, Cook David , “Muslim material on comets and meteors”, Journal for the history of astronomy , xxx (1999), 131–60, for a collection of Muslim reports of shooting stars and the reactions they provoked.

Aristotle , Meteorologica , transl. by Lee H. D. P. , 2nd edn (London and Cambridge, Mass., 1962), 28–35.

Lettinck Paul See , Ar̄īṡtotle's Meteorology and its reception in the Arab world (Leiden, 1999), 67, 75–89.

Seneca , Naturales quaestiones , transl. by Corcoran Thomas H. (London and Cambridge, Mass., 1971), i, 14–23.

Pliny Elder , Natural history , transl. by Rackham H. , rev. edn (London and Cambridge, Mass., 1949), i, 238–41.

See, for instance, Galen's De libris propriis, De ordine librorum, and De optima secta, quoted in Kieffer Spangler John , Galen's Institutio logica (Baltimore, 1964), 1–2.

The use of lunar eclipses dates at least as early as Hipparchus ( Neugebauer , A history of ancient mathematical astronomy , Part 1, 337). Heron's use of a lunar eclipse to find the longitudinal difference and distance between Alexandria and Rome is described in ibid., Part 2, 847–8. On the use of lunar eclipses by Ibn Yūnus and al-Bīrūnī, see Schoy Carl , “The geography of the Moslems of the Middle Ages”, Geographical review , xiv (1924), 257–69.

Abū 1-Rayḥān al-Bīrūnī, a younger contemporary of al-Kūhī, described several methods of finding the distance between two cities in his Kitāb Taḥdīd Nihāyāt al-Amākin, including some of Indian origin, but none of them uses the azimuth between the cities. See Kennedy E. S. , A commentary upon Bīrūnī's Kitāb Taḥdīd [Nihāyāt] al-Amākin (Beirut, 1973), 144–51.

Lettinck , Aristotle's Meteorology (ref. 9), 77, 88.

For bibliographic details on both manuscripts, see Sezgin , Geschichte des Arabischen Schrifttums , vi: Astronomie , 219.

Kennedy Edward S. Hermelink Hermann , “Transcription of Arabic letters in geometrical figures”, Journal of the American Oriental Society , lxxxii (1962), 204; updated in Kennedy Edward S. , “Transcription of Arabic letters in geometric figures”, Zeitschrift fīr Geschichte der Arabisch-Islamischen Wissenschaften , vii (1992), 21–22.

For a description and comparison of analysis and synthesis in ancient Greece and medieval Islam, see Berggren J. L. Van Brummelen Glen , “The role and development of geometric analysis and synthesis in ancient Greece and medieval Islam”, to appear in Moravcsik Julius Suppes Patrick Mendel Henry (eds), Ancient and medieval traditions in the exact sciences: Essays in memory of Wilbur Knorr (Stanford, CA, 2000), 1–31.

See Ito Shuntaro , The medieval Latin translation of the Data of Euclid (Tokyo/Boston, 1980), or George McDowell and Merle Sokolik, The Data of Euclid (Baltimore, 1993).

For an exposition of Aristarchus's method, see Van Helden Albert , Measuring the universe: Cosmic dimensions from Aristarchus to Halley (Chicago, 1985), 5–9.