PREFACE

I freely leave these matters to others. However, some points regarding the age of the collection and the ancient commentaries term: scholia (singular: scholium); these are explanatory notes or comments written in the margins of ancient manuscripts by students or teachers. seem worth mentioning.

It is debatable whether arithmetic problems were admitted into earlier Anthologies before Constantinus Cephalas, who compiled the so-called Palatine corpus of epigrams at the end of the tenth century. At least from the notes I have provided on pages 43 to 72, it can be demonstrated that two collections were available to Cephalas. One bore the name of a sufficiently ancient poet, namely Socrates, who was mentioned by Diogenes Laertius. The other was attributed to the more recent Metrodorus. No ancient commentaries were found in the first collection, except perhaps for certain solution numbers written in the margin. The only exceptions are those seven notes written for epigram XIV, 7 after the time of Emperor Julian. I believe these were written by various people at widely different times, certainly by men with little skill in anything but practical arithmetic. We find remains of this kind far too rarely. I have attempted to demonstrate elsewhere, with a single example, what they can contribute to the history of common calculation original: "vulgaris calculi" ¹).

However, for every epigram in the collection of Metrodorus, Constantinus Cephalas found existing commentaries, which he incorporated into his own text ²). But since he had already transcribed certain problems found in the Socratic collection (namely epigrams XIV, 2, 3, 6, and 7), he did not repeat them. Instead, he added the numbers from Metrodorus to the Socratic ones and placed the commentaries in the margin. The true order

Review of Greek Studies, Volume 7, pages 204 and following: The calculation of proportional parts among the Byzantines.
Please note the errors in the expanded abbreviations on page 44, line 18; page 53, line 16; page 70, lines 7 and 14; likewise a gap on page 55, line 20.