FRANK BIGELOW TARBELL

1853-1920

The death of Frank Bigelow Tarbell, on December 4, 1920, has taken from us an outstanding personality among the veteran classical scholars of America, and one of the first in this country definitely to devote himself to the field of classical archaeology.

Mr. Tarbell was born in Groton, Massachusetts, in 1853, and graduated from Yale College in 1873 at the head of his class. He taught Greek at Yale 1876-87, was annual director of the American School of Classical Studies at Athens 1888-89, instructor in Greek at Harvard 1889-92, secretary of the School at Athens 1892-93, and then became permanently settled in the University of Chicago, until his retirement from the chair of Classical Archaeology in 1918. His period of freedom from academic duties proved all too short.

The writer has enjoyed the rare privilege of knowing Mr. Tarbell, not only as a colleague for more than twenty-five years, but still earlier as teacher and adviser. My admiration of his scholarship and of his character runs back to the time when every undergraduate of Yale College came under his instruction in Greek, in those last days of the old classical curriculum. Many a student came to realize for the first time in his classes in Aristophanes or in the Private Orations of Demosthenes, that Athens was a real place and the Athenians real people. The affectionate regard which is so often expressed by Yale students of that period may well be the envy of any teacher.

In Chicago, Mr. Tarbell's career changed from that of a college teacher with large undergraduate classes to that of the specialist dealing with relatively small numbers. If he sometimes missed the larger contact, as I think he did, he fully realized the better opportunity for the training of scholars and for his own research. He had the satisfaction of seeing former pupils take their place as productive scholars. He was not himself a voluminous writer, but all his published work, from his edition of the Philippics of Demosthenes, in his twenties, to his most recent technical articles, bear the stamp of his severely accurate scholarship and trenchant criticism. As a scholar and in his personal relations he was a man of the utmost sincerity, of sometimes appalling frankness, the uncompromising foe of unsound learning and of unsound character. Always reserved, he was withal a man of the deepest feeling and kindliest nature, as those know well who knew him best.

C. D. B.

The problem attacked in the following pages is the determination of the sources and relationships of the ancient arithmological writings, including principally those of Varro, Philo, Nicomachus, Theon of Smyrna, Anatolius, the compilator of the Theologumena Arithmeticae, Chalcidius, Macrobius, Martianus Capella, Favonius Eulogius, and Johannes Laurentius Lydus. The difficulty of the problem, the necessity of hypothetical reasoning, and the ease with which error may be committed are acknowledged at the outset.

The situation presented by the above-mentioned writings much resembles that seen in the Synoptic Gospels, and methods similar to those used by New Testament critics should be employed in its elucidation. Whole passages of one author are repeated in one or more others, and the topics of arithmology are so frequently paralleled that to determine the exact provenance of any one may be well-nigh impossible. The problem therefore has to be handled in a large way and the main currents of influence determined, a thing which the previous essays in this field' have not satisfactorily done. They have, moreover, without exception followed Schmekel in regarding

1 The following are most frequently referred to: A. Schmekel, Die Philosophie der mittleren Stoa in ihrer geschichtlichen Entwickelung, Berlin, 1892; G. Borghorst, De Anatolii fontibus, Berlin, 1905; G. Altmann, De Posidonio Timaei Platonis commentatore, Berlin, 1906; B. W. Switalski, "Des Chalcidius Kommentar zu Platos Timaeus," Beiträge z. Gesch. d. Phil. d. Mittelalters, III (Münster, 1902), 6; F. Skutsch, “Zu Favonius Eulogius und Chalcidius," Philologus, LXI (1902), 193 ff.; C. Fries, "De M. Varrone a Favonio expresso," Rheinisches Museum, N.F., LXVIII (1903), 115 ff. [CLASSICAL PHILOLOGY XVI, April, 1921] 97

Posidonius as the universal source of arithmology-an error, as I have shown elsewhere.1

The results won in the previous paper may serve as a startingpoint for the present inquiry; namely, that Posidonius was not the author of the arithmology seen in Philo, Theon, and the rest, but quoted from an already existing arithmological work, the introduction of which Sextus Empiricus reproduces quite fully in Adv. math. iv. 2 ff., Anatolius and Theon in abridged form, and other parts of which were used by many authors. The existence of this work, at least, is proven, and if it be granted that Posidonius quoted it, it existed before his time, that is, by the last half of the second century B.C. For the reasons collected in the former article and for others that may appear later, the writer is ready to abandon the noncommittal attitude previously adopted and to believe that he actually did quote it, as Sextus Empiricus Adv. math. vii. 91 ff. shows. Since this document was so universal a source for later writers, it will for convenience be referred to as S ("source").

4

Anatolius2 and Theon3 give the best idea of the character of S, preserving as they do its introduction and a considerable part of its ten chapters on the numbers of the first decade. Since any reader can see in a moment that they ultimately come from a common ancestor, this will be assumed without argument. These two writers, in fact, may be used as a sort of standard for judging whether others have drawn upon S. It may safely be believed that material common to both of them is from S; if we find the same matter in other writers, they also derived it from S. If certain other writers,

1 "Posidonius and the Sources of Pythagorean Arithmology," Classical Philology, XV (1920), 309–22.

2 Ed. J. L. Heiberg, Annales internationales d'histoire, Congrès de Paris, 1900, 5e section, Histoire des sciences, Paris, 1901, pp. 27 ff. Anatolius is also extensively quoted in the Theologumena Arithmeticae (ed. Ast, 1817).

Expositio rerum mathematicarum ad legendum Platonem utilium, ed. E. Hiller, Leipzig, 1878.

4 Except in one place, to be discussed below, these two are never at variance in making different statements about the same topic; one of them, however, usually Anatolius, may present topics which the other omits. Anatolius' treatise is apparently a set of notes for the use of students, hence a mere outline, devoid of literary elaboration. Theon's too is greatly condensed but somewhat more elaborate rhetorically; he is apt to say more about a given topic than Anatolius, while the latter preserves many more topics than Theon. Some of Anatolius' material, not found in Theon, is perhaps not from S; but this forms no great part of the whole.

of whom it is thus known that they used S as a source, parallel material in Anatolius not attested by Theon, this too may be claimed for S, and so, when reasonable presumptions have thus been created, the circle of the influence of S may be enlarged and defined.

I do not, however, intend to point out all the S material that can be identified in ancient literature, but will turn to the real point at issue, the method of transmission of S material.

Very little inquiry shows that Theon and Anatolius both present S in an abridged form. Philo, who in the De mundi opificio certainly used S, has in cc. 30-42 of that work a treatment of the number 7 which in general agrees throughout with Anatolius, the latter here as usual being more voluminous than Theon. Philo's account, however, is far longer even than Anatolius', containing many more topics and saying more about each one; yet probably every one of these topics, whether or not paralleled by Anatolius, is from S; the exceptions are certainly very few. This is proved by the fact that practically all of them are found, in connection with S material, in still other writers, Lydus1 in particular showing a close likeness to Philo. But though Philo's chapters give us our best idea of the original text of S, still even they are abridged, for they omit several topics which must certainly be referred to the anonymous source because of their occurrence in several of the writers of our group.2 Evidently some had only abridged versions of S, while others used full or but slightly abridged texts.

Among the descendants of S, Philo, as far as the De mundi opificio is concerned, Anatolius, and Lydus give evidence of forming a closely related group. Theon, as far as he goes, generally agrees with them, but he differs from them radically in the insertion in the seventh chapter of a block of material, set in a context showing the closest agreement with Anatolius, but differing wholly from the pronouncements of the three first mentioned upon the same subject, the control exercised by the number 7 over birth and the "ages of man." It will later be seen that by agreeing here with Theon rather than with Anatolius, Philo, and Lydus, a group including Chalcidius,

1 De mensibus ii. 12.

2 E.g., the 7 numbers used in Plato's Timaeus, and the flow of euripi, both to be found in Theon, Anatolius, and Lydus.