246

This section is added in C by the hand  of the corrector.

247

Cf. Issawi, pp. 141 f.

248

Cf. 1:214 f., above.

249

Cf. 3:281 f., 296, and 316 f., below.

250

Dalil "indication" might be translated "symbol" here.

251

Cf. p. 20, above.

252

That is, elementary arithmatic. Cf. 3:121 ff., below. The fact that Ibn Khaldun mentions it here among the crafts would suggest that he has in mind its accounting and bookkeeping aspects.

253

As explained below in the section on calculation, "combining" refers to addition and multiplication, "separating" to subtraction and division.

254

Cf. Qur'an 16.78 (80) and Qur'an 7.10 (9); 23.78 (80); 32.9 (8);67.23 (23). According to D, the concluding words were replaced later by "Perhaps, you might be grateful," a phrase from Qur'an 16.78 (80). C also  gives this, but the last lines of the section are aded by a later hand. Cf. also p. 419, below, however, where we find the same combination of different Qur'anic passages at a late stage in the text of Muqaddimah.