⁸ The character of Nebridius, and the intimacy of friendship between him and Augustine, may be seen in the Confessions, b. ix. c. 3.

⁹ Had Augustine been acquainted with the decimal notation, he would not have made this remark to Alypius; for in the decimal scale, when the point is inserted, tractional parts go on diminishing according to the number of cyphers between them and the point (e.g .001), precisely as the integers increase according to the number of cyphers between them and the decimal point (e.g. 100.),-there being no limit to the descending series on the right hand of the decimal point, any more than to the ascending series on the left hand of the same point.

¹⁰ Nescio quid.

¹¹ Augustine's acquaintance with the first principles of optics, and with the properties of reflection possessed by convex, plane, and concave mirrors, was very limited.

¹² Wisely resolved.

¹³ Ineptiam.

¹⁴ Present infinitive passive of cupere, to desire.

¹⁵ Infinitive passive of verbs signifying respectively to "throw" and to "catch."

¹⁶ Phantasia.

¹⁷ Quamvis non omnis phantasia cum memoria sit, omnis tamen memoria, sine phantasia esse non possit.

¹⁸ Dramatis personae in Terence.

¹⁹ Referring to Manichaean notions.

²⁰ Numeri actitantur occulti.

²¹ Pro ipsius divini juris fide.

²² Daemonibus.

²³ See Letter VII.

²⁴ Text, "deificari" for "aedificari" (?).

²⁵ A liquid praeter invicem faciunt.

²⁶ Species.

²⁷ An sit, quid sit, quale sit.