Cf p. 311, above.


 This is not correct.


This is a translation of stoicheia, elementa. In addition to the bibliographical references in GAL, there is a recent study by E. B. Plooij, Euclid's Conception of Ratio and his Definition of Proportional Magnitudes as Criticized by Arabian Commentators, (Leiden dissertation) (Rotterdam, [1950]). Cf. also, 2:365, above.


Or "most extensive." However, since it is considered as an introduction to geometry, the above translation may be preferable.


He died ca. 260 [873]. Cf. GAL, I, 205 f.; Suppl., I, 366 ff.


He died in 288 [901]. Cf. GAL, I, 217 f.; Suppl., I, 384 ff.


That is, al-Hajjaj b. Yusuf b. Matar. Cf. GAL, 1, 203; Suppl., I, 363.


As explained in the definitions of the tenth book of Euclid, a square is called rhton, munfaq "rational," whereas its sides belong among the elements that "have power over" (ai dunamenai, al-qawiyah ala) the production of rational quantities and are called "irrational."


This cannot be the early translator Ibrahim b. ay-Salt; cf. GAL, Suppl., I, 371. Ibn Khaldun presumably had in mind Abu s-Salt Umayyah b. 'Abd-al-'Aziz b. Abi s-Salt, who lived ca. 460 [1067/68]. Cf. GAL, I, 486 f.; Suppl., I, 889. He is credited with a work on geometry by Ibn Abi Ulaybi'ah, 'Uyun al-anba', ed. Muller (Konigsberg & Cairo, 1882-84), II, 62, 1. 22. Cf. also below, p. 135.


The famous agewmetrhtoz mhdeiz eisitw, which appears in Elias' commentary on the Categories and was well known to the Arabs. It entered Arabic literature in connection with the introductions to Aristotelian phi­losophy. Cf al-Farabi, Fi-ma yanbaghi an yuqaddam qabl 'ilm al falsafah, ed. and tr. F. Dieterici: Alfarabi's Philosophische Abhandlungen (Leiden, 1890, 1892), pp. 52, 87.


Cf. also 2:365, above.


For haykal, pl. hayakil, cf. 1:151 (n. 172), above.


They lived in the ninth century. Cf. GAL, I, 216 f.; Suppl., I, 382 f. 666


Hawa 'it "gardens." Or does Ibn Khaldun mean the fixing of the boundaries of buildings?


De Slane notes that Ibn Khaldun should have said "longitudes."


Al-Hasan (Husayn) b. al-hasan (Husayn) b. al-Haytham (Alhazen), from ca. 364 [9651 to 430 [10391. Cf. GAL, I, 469 f.; Suppl., I, 861 fi.