164 PROCEEDINGS OP THE AMERICAN ACADEMY 



According to Servius, in his comment on this verse, this superstition 

 was " that odd numbers were immortal, because they cannot be divided 

 into two equal parts ; the even being mortal." But this is an imperfect 

 explanation of the matter. The superior virtue ascribed to odd num- 

 bers lay not merely in their indivisibility, — a quality which was an 

 attribute of the divine nature, but also in the fact that they seemed 

 stronger than the even ; for in joining odd and even together, the 

 sura was always odd. Hence, a masculine nature was ascribed to 

 them.* 



Three had dignity as the first of the odd numbers, — the first number 

 complete with beginning, middle, and end. By it the triangle, the simplest 

 of planes, was formed ; in it were included all bodies under their three 

 dimensions. Five was honored as the first compound of odd and even, 

 and was regarded as thus including the virtues of both in itself. But 

 seven was specially sacred : its properties were so numerous and so 

 remarkable that even Cicero, in the person of Scipio, could say 

 "rerum omnium fere nodus est."t 



It might, at first sight, seem that all this subject of the mystical pro- 

 perties of numbers might well be relegated to the domain of merely 

 curious learning. But the ancient doctrine of numbers, as taught by 



* See Plutarch, " Of EI at Apollo's Temple," § 8, Goodwin's edition of "Plu- 

 tarch's Morals," IV. 485. Also, " Roman Questions," § 25 ; Id. II. 218. " Cur 

 impares numeros ad omnia vehementiores credimus ? " asks Pliny, N. H. xxviii. 

 5. " Imparnumcrus mas, par femina vocatur." Macrobius, "Somn. Scip." I. vi. 

 " Numerus impar niaribus attributus est." Mart. Capella, " I)e Nuptiis," &c., II. 

 § 106. " Imparem numerum antiqui prosperiorem liominibus esse crediderunt," 

 Festus, cited by Hardouin in his note on the passage of Pliny quoted above. 



t " De Republica," VII. 11. The comment of Macrobius on this passage, 

 " Somn. Scip." I. 6, is full of illustration of the ancient ideas concerning this and 

 other numbers. Of five, he says, " Hie ergo numerus simul omnia et supera et 

 subjecta designat ; aut enim deus summus est, aut mens ex eo nata in qua 

 species rerum contincntur, aut mundi anima-quaa animarum omnium fons est." 

 See, also. Aulas Gellius, " Noct Attic. " III. 10. Morhof, in his once-noted 

 "Polyhistor," says, " Quantae, quam arcanae numerorum potestates sint, ne in 

 hunc quidem diem satis cognitum est;" and, going on to speak of the special 

 numbers, he says, " Quinarius rpocphs, item yd/xos dicitur, quod ex binario et 

 ternario, quasi ex femina et mare, conflatus est. Divinus allis dicitur . . . Sep- 

 tenarium omnium nvixriKwraTov esse nemo nescit." I. i. xii. 19. In regard to 

 five and seven, see Plutarch, " Of EI," §§ 6-17. " Every number will afford 

 you," says Plutarch, " sufficient matter and argument of praise, if you will but 

 take the pains to look into it ; for, to say nothing of others, a whole day would 

 not be enough to express in words all the virtues and properties of the sacred 

 number Seven dedicated to Apollo," § 17. 



