|
|
|
653 |
Cf
p. 311, above. |
|
654 |
This
is not correct. |
|
655 |
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. |
|
656 |
Or
"most extensive." However, since it is considered as an
introduction to geometry, the above translation may be
preferable. |
|
657 |
He
died ca. 260
[873]. Cf. GAL, I,
205 f.; Suppl.,
I, 366 ff. |
|
658 |
He
died in 288 [901]. Cf. GAL, I, 217 f.;
Suppl., I, 384 ff. |
|
659 |
That
is, al-Hajjaj b. Yusuf b. Matar. Cf. GAL, 1,
203; Suppl., I, 363. |
|
660 |
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." |
|
661 |
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. |
|
662 |
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. |
|
663 |
Cf.
also 2:365, above. |
|
664 |
For
haykal, pl. hayakil, cf. 1:151 (n. 172),
above. |
|
665 |
They lived in the ninth century. Cf. GAL,
I, 216 f.; Suppl., I, 382 f.
666 |
|
666 |
Hawa 'it "gardens."
Or does Ibn Khaldun mean the fixing of the boundaries of
buildings? |
|
667 |
De
Slane notes that Ibn Khaldun should have said "longitudes." |
|
668 |
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. |
|
|