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Vir Bonus Quadrato Lapidi Comparatur

Published online by Cambridge University Press:  31 August 2011

Arnold Ehrhardt
Arnold Ehrhardt
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Birch-in-Rusholme, (Manchester)
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Extract

In an article published recently on the English pupils of St. Anselm, the saying which forms the title of this essay is quoted from the Dicta Anselmi. The same sentence appears in Ps. Anselm's Similitudines, and in Eadmer's Sermon on Gregory the Great. This coincidence is used as evidence for the dependence of the two latter works upon the former. But the saying is of much greater antiquity.

Type
Research Article
Information
Harvard Theological Review , Volume 38 , Issue 3 , July 1945 , pp. 177 - 193
Copyright
Copyright © President and Fellows of Harvard College 1945

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References

1 Medieval and Renaissance Studies 1, 1941, 9.

2 Plato, Protag. 339B; 344A; Aristot., Eth. Nic. 1.10.11; Rhet. 3.11.2; Bekker. Method. Resurrect. 2.3.5; Bonwetsch, p. 334, 21; Julian, Conviv. Caes. 333B; Damascius in Suidas, s.v. tetragonos. “Without hands and feet” is the Agathodaimon, Philo Bybl. in Euseb., Praep. Ev. 10.1.46.

3 Aspas, in Eth. Nic, ed. Heylbut, p. 29, 29, stresses the significance of this omission.

4 R. Eisler, Philologus 68, 1909, 118 sq.; 461 sq. L. Ampel. 8.11. Mundus, Festus, p. 346 Th.

5 E.g. Apollod. frg. 30 Müller; Heraclit. Quaest. Homer. 72; Plut. Quaest. Conviv. 9.3.2.

6 Cornut. ed. Land, p. 23, 11 sq. Jambl., Theol. Arithm. de Falco, p. 28, 1 sq. Magic, Pap. Lond. 1, 7 v. 401 sq.; 105 v. 668 sq.; Arch. Pap. Forsch. 2, 1903, 209, 4, cf. Hoefer in Roscher's Lexikon s.v. tetragonos. Apollo Agyieus, schol. Aristoph. Thesmoph. 489, and Rutherford's note. Zeus Teleios, Pausan. 8.48.6. Janus, cf. Gavius Bassus in Macrob. Sat. 1.9.12. Saturnus, Tertullian adv. Marc. 1.18. Ares, cf. Suidas s.v. Theusares, cf. Max. Tyn. 28 (Hobein) Jerusalem, cf. Antoninus Itin. Hieros. 23. The Alexandrine god Aion seems to have been four-square too, R. Reitzenstein Iran. Erlosungsmyst., 1921, 214 n. 1. Men and women, Plut. Quaest. Rom. 102.

7 Babylon, R. Koldewey, Wiedererst. Babylon 4th ed., 1924, 2; B. Meissner, Assyrien u. Babylonien 1, 312. Roman colonies, W. Nissen, Templum, 1869, 167; Orientation 1, 1906, 86 sq. Fabricius in Pauly-Wiss. 2nd ser. 3.2, 1929, 2000 sq. Greek testimonies, e.g. the square ground-plan of Nephelecoccygia, Aristoph., Av. 1004 sq.; Nicea in Bithynia, Strabo, 12.4.7.

8 Jewish, R. Eisler, Weltenmantel u. Himmelszelt, 1912, 2, 623 sq. Anatolian, W. M. Ramsay, Asianic Elements, 1927, 212 sq.

9 Olympiod. in Plat. Phaed. Norvin, p. 238, 13 sq. Three regular solids, sch. in Euclid. Elem. 13; Heiberg 5, 654, 1 sq., cf. E. Sachs, Fünf Platon. Körper, 1917, 79 sq. Central fire, Ueberweg-Praechter Philos. d. Alt. 12th ed., 1926, 68.

10 Cleomedes Motu circ. 1.8.44.

11 Boisacq, Dict. Etym. Gr., is silent with regard to the assumed etymology, but remarks that the pyramid is of an origine étrangère. Plato, Tim. 49 sq., esp. 55C sq. Predecessor, “Pythagoras” in Stob. Flor. 1.21.6c Wachsm. 1, 186, cf. E. Frank, Plato u. d. Pythagoraeer, 1923, 233 sq.

12 Ps. Tim. Locr. 98C; Albin. Isag. 13, cf. Apulei. de Platone 1.7. Hermias Irrisio 8 M. Gr. 6, 1178.

13 Cf. on archaic formulae concerning the tetrad, which “always aims at the universal deity,” R. Reitzenstein, Mysterien-Relig., 3rd ed., 1927, 152.

14 Foundation of the universe, H. Usener, Rhein. Mus., 1903, 341. Tetraktys, e.g. Hierocl., in Carm. Aur. 20 and A. Boeckh, Kl. Schr. 3, 141 sq. The first systematic description of the Pythagorean theory of the four is Meursius Denarius, Pythagoric, ch. 6, cf. A. Lobeck, Aglaophamus, 430 sq.

15 Plut., Defect. Orac., 34; Cebes Tab., 7.1; 18.3.

16 Dike and δἰχα, Aristot., Eth. Nic. 5.7, 1132a, cf. Xenocrates, frg. 15 Heinze, where [μητρς θεν] gives an interesting illustration of her connection with Magna Mater. Jambl., Theol. Arithm. de Falco, p. 18, 11 sq., cf. Etym. Gudian s.v. Dike; Favon. Eulog. in Somn. Scip. Holder, p. 3, 32 sq. Mother Earth, cf. Other Pastors of Thy Flock, 1942, 20 sq., and Precatio Terrae Baehrens Poet. Lat. Min. 1, 138 sq. “caeli ac maris diva arbitra rerumque omniumque.” Isis, Porph. Agahn. frg. 10 Bidez, p. 19, 13 sq. The earliest testimony for the identification of Isis with justice is, according to R. Reitzenstein, Zwei Religionsgesch. Fragen, 1901, 105 n. 6, CIG. 2, 2295. Isis and equality, Jambl., Theol. Arithm. de Falco, p. 18, 11 sq.; Arithm. Nic. Pistelli, p. 13, 9 sq.; 81, 15 sq.

17 Dikaiosyne and four, Ps. Aristot. Magn. Mor. A. 1, 1182a, 11. Quadrata iustitia, Philo Opif. Mundi 16.51; Clem. Alex. Strom. 6.102.4 sq.; Plotin. Enn. 6.6, 675B; Jambl., Theol. Arithm. de Falco, p. 29, 5 sq.; Mart. Cap. 7.732, cf. F. Doelger Sonne d. Gerechtigkeit u. d. Schwarze, 1919, 90 sq. Quadratum corpus, e.g. Celsus 2.1 Daremberg, p. 28, 23 sq. Forehead, Damasc. in Phot. Bibl. Bekker, p. 336a, 4 sq. Philostrat Vita Apoll. 7.42; Heroic 2;9 even praises the beauty of a “square” nose.

18 Geometrical row, Nicom. Geras. in Phot. Bibl. Bekker, p. 144b, 35, cf. Macrob. in Somn. Scip. 1.5.17, identifying justice with eight. Eighth sphere, Poimandr. 26a W. Scott 1, 128, 14 sq. Seven gates of hellt R. Reitzenstein, Festschr. F. Andreas, 1916, 36 sq. Worship of Ogdoas, earliest testimony, Euandres, head of the Academy from 215 B.C., in Leutsch-Schneidewin Paroemiogr. 1, 151. It is not accidental that Herod. 1.181, says that the Babylonian tower had eight stories, R. Reitzenstein, Iran. Erlösungsmyst. 207 n. 2 is mistaken.

19 Political mathematics, Platonic view in Plut., Quaest. Conviv. 8.2.2. Pythagorean view, Ps. Archyt. in Stob. Flor. 3.43.137 Hense 4, 84. Neo-Platonic view, Jambl., Comm. Math. 15 Festa, p. 56, 4; Herm. Alex, in Plat. Phaedr. Couvreur, p. 95, 29 sq.; Procl. in Euclid. I Friedlein, p. 23, 12 sq.; 62, 26 sq. Epicurean ridiculing of the scheme, Philodem., Rhet. frg. 8, col. 13. Dike three, Plut., de Iside 75, 381E, cf. Euseb. Tric. 6. 13. Dikaiosyne five, Jambl., Comm. Math. 18 Festa, p. 60 sq.

20 Ez., 41.4; 48.8, cf. Exod., 27.1, etc.; Landersdorfer, Baal Tetramorphos, 1918. Job, 38.38 in the LXX version. Philo, Opif. Mundi 30 sq.; Spec. Leg. 2.212. Jos. Bell. 6.311, cf. R. Eisler, Jesus Basileus, 1930, 2, 593 n. 1.

21 Rev., 21.15 sq., cf. Ps. Cypr. Monte Sina 10 Hartel, p. 116. Herod., 1.178 sq.; Diod. 2.9. Cf. the symbolic square wall drawn around Rome by Vespasian of 120 to 110 actus, H. Nissen, Rhein. Mus., 1894, 282.

22 Hermas, Sim. 9.2.1. This passage may be open to a connection with the religion of Cybele if M. Dibelius, Handb. z. N.T. Erg. Bd., 1923, 605, is right in assuming that the rock is hollow, for the cave in the cube is the characteristic of her cult.

23 Christian, Didache 10.5; Theophil. Ant., ad Autolyc. 1.32; Origen in Ev. Joh. 1.4.21 Preuschen; Filastr., Haer. 129. 5 sq. Marx. Pagan; cf. A. Dieterich in Fleckeisen's Jahrb. Suppl. 16, 1888, 773; Mithras-Liturgie, 1903, 63, quoting Porph. Antr. 25 Nauck, p. 71.

24 Marcosii, cf. F. Dornseiff, Das Alphabet, 1922, 128. Acta Joh. 95 Bonnet- Lipsius. Valentinus, Hippol. Philos. 6.2.32; 34; 31.7; 9; Tertullian, adv. Val. 27. Basilides, Clem. Alex. Strom. 4.162.1. Jewish theory, Bousset-Gressmann, Relig. d. Judent. 3rd ed., 1926, 245 sq. Pistis Sophia, cf. the index of K. Schmidt's translation.

25 Clem., Alex. Strom. 7.102.2 sq.; Hippol., Philos. 4.43.12. Lact., Div. Inst. 7.14 sq. Method. Symp. 3.7; 7.6 Bonw., p. 34; 77. Number seven, Cypr., ad Fortun. 11 Hartel, p. 338; Victorin., Petav. Comm. Rev. 1.1; 1.7; 8.2; 10.2 Haussl. p. 16; 27; 86; 90; Rufin., Pentec. 2 Engelbrecht, p. 142, 7 sq. St. Thecla, F. J. Doelger, Antike u. Christentum 4, 1934, 153 sq. The earliest Greek instance of such a ground-plan is the “tower of the winds” at Athens.

26 Cardinal virtues, Hierocl., in Carm. Aur. 10 Mullach 1, 436. Quadrato agmine, Seneca, Ep. ad Lucil. 6.7.7. Square man, Himer., Or. 7.12 Duebner. Square justice, Clem., Alex. Strom. 6.102.4 sq. Small temple, eod. 7.82.4; Quis Dives 32.4. City of God, Ps. Clem. Rom. de Virg. 1.9.2. Funk. Tower of the Church, Hermas, Vis. 3.2.4; Origen, Princ. 2.11.3 Koetschau, p. 186, 11; Method., adv. Porph. 1.7 Bonw., p. 304; Ps. Cypr. de Pascha comp. 17, Hartel, p. 264.

27 Ascl. 1.7b W. Scott, 1, 296, 28 sq., cf. Method., Constant, schol. in Acta Marinae Usener, p. 49, 27; 51, 8. Doctrine of the five, see F. Wilhelm, Rhein. Mus. 70, 1915, 213 n. 2, on Neo-Pythagoreanism; Zepf, Arch. Relig. Wiss. 25, 1937, 226 sq. on Aion as the fifth god and the fifth element; Ovid., Fast. 3.849; Serv., in Georg. 1.277, on five as sacred to Minerva, cf. F. Altheim in Pauly-Wiss. 15.2, 1779 s.v. Minerva; R. Reitzenstein, Myster. Relig. 3rd ed., 1927, 265 sq., on Iranian beliefs.

28 Eusthat., in Hom. Od. 5.262, p. 1534, 36 sq. Quotation, Virgil, Ecl. 8.75, cf. Serv. ad h. 1.; Lutat. Placid, in Stat. Thebaid. 5.86. Mandaic, a hymn published by Lidzbarski, Florileg. de Vogüé, 1909, 371 v. 260, describes the firmament as eightcornered, a cube or octagonal, and in Ginza sin. 52 transl. Lidzbarski, p. 578, the eight appears as propitious; but in Ginza rect. transl. Lidzbarski, p. 332, 28 sq.; 459, 25 sq., and sin., p. 594, 13, all even numbers are regarded as ominous, and the eight in particular in Johannesbuch transl. Libzbarski, p. 41, 17.

29 The Rev. W. Telfer, D.D. reminds me that we read in the creed of the second council of Sirmium (A.D. 357), G. L. Hahn, Bibl. d. Symb. 3rd ed., 1897, 201, “integer perfectus numerus trinitatis est.” This may indicate that the Arians at that time had already some such monophysite leanings. See also Athanas. adv. Arian. 1.30 (Bright p. 32).

30 Basil, Ep. 21 ed. Deferrari, p. 126.

31 Ambrose, Incarn. 7.77 sq. M. Lat. 16, 838. Jerome in Mark 11.1–10 Aneed. Mareds. 3, 356, 5 sq. August, Ep. 140.5.12 Goldbacher. Coll. Avel. 73–78 Guenther.

32 Hermes Logos, Suidas s.v. Hermên; Hermôn; tetragonos. John Lydus, De mens. 4 Wuensch, p. 129, 18 sq. The trigonos, probably omitted by a copyist who scented blasphemy, was ingeniously supplied by G. Wissowa. For the meaning of polygonos as immoral cf. also Jamblich. Vita Pyth. 77 fin. An attempt to describe Christ in terms belonging to Hermes Logos was made by Claudian the Younger, Anth. Pal. 1.20–22, cf. R. Reitzenstein, Zwei relig.-gesch. Fragen 107 n. 2.

33 Procop., Gaz. in Deut. 25.3 M. Gr. 87, 937, copied by Hraban. Maur. in Ez. 11 M. Lat. 110, 801.

34 John Philop. Opif. Mundi 3.10 Reichardt, p. 139, 13 sq. Earlier authority, Const. Apost. 7.35.5 Punk. Cosm. Indie. 4; 7M. Gr. 88, 181 sq.; 881. Max. Conf. Loci Comm. 1; Mystag. 7; Ambig. M. Gr. 91, 725C; 684 sq.; 1396 sq.

35 Dike, Olympiod. 17 Bertholot, Ms. Alch. Gr. 2, 79, 5 sq. Adam, Zosim. Panop. de Instr. 10 Berthelot 2, 232 sq. Five, Olympiod. eod. 2, 79, 21 sq. I should also refer to the doctrine of the five in the newly discovered Kephalaia of Mani, and to the idea of a quinta essentia and its possible relation to ancient Indian philosophy. Three, Berthelot 1, 27, 14 sq.

36 Martian., Cap. 2. 106, cf. Macrob. in Somn. Scip. 1.6.40 sq.

37 Jerome, Anecd. Mareds. 3, 356, 17 sq. Filastr. Haer. 80. 7 Marx, p. 43, cf. John of Gaza, Image of the World ed. Friedlaender, p. 137, v. 35. John Cassian 8.3. 4 Petschenig, p. 35 sq. Sedul. Carm. Pasch. 5.190 Huemer, p. 128.

38 Noah's ark, Civ. 15.26; Enarr. Ps. 86.3; adv. Faustin. 12.12. Millennium, Civ. 20.7, cf. eod. 18. 23. The connection with Neo-Platonism appears from a comparison with dicta of Augustine's pupil Favon. Eulog. in Somn. Scip. Holder, p. 3.32 sq.; 5.16 sq. and Augustine's own idea of the eight generations after Adam, Civ. 15.15.

39 Faust. Rei. De Spir. 2 Engelbrecht, p. 139.

40 Paulin. Adv. Felicem 1.57 M. Lat. 99, 415 sq.

41 Felix, cf. Paulin. op. cit. col. 391 sq. Hincmar, Mon. Germ. Script. Merov. 3, 276, 22 sq. Legal documents, Du Cange s.v. quadratus orbis; quadrifidus orbis. Inventio Quintini, Mon. Germ. Poet. Carol. 4, 2, 1000.

42 Cf. Vulfin. Carm. de Marc. Mon. Germ. Poet. Carol. 4.2, 970 1.189 sq., “… quadrati climate mundi semina missurus.…” and Thiofrid Vita Willebrordi 1.18; 3.45; Hraban. Maur. Cler. Inst. 3.22. M. Lat. 107, 400.

43 Vita Niv. 5 Mon. Germ. Scrip. Merov. 5, 163, 3 sq. Flodoard, Mon. Germ. fol. Script. 13, 566, 37 sq. Cardinal vices, Hraban. Maur. in Genes. 2. 15 M. Lat. 107, 539.

44 M. Grabmann, Scholast. Methode 1, 177; 180 sq.

45 Rodulfus Glaber, Mon. Germ. fol. Scr. 7, 51. Representative are the following words, line 33 sq., “quotuor sunt ergo Evangelia quae constituunt in nostris mentibus supernum mundum. Tot enim constant elementa quae perficiunt istum infirmum. Quatuor quoque virtutes.… quatuor sensus existunt corporis, praeter tactum.…” Comm. Anon, in Prud. 2. 972; 973 ed. Burnam p. 178 sq.

46 Greg, in Ez. 2.9.5; 8 M. Lat. 76, 1044.

47 Comm. in Ps. 86; Templ. Salom. 4; Hexaem. 2 M. Lat. 91, 744; 81.

48 Hraban. Maur. in Ez. 40. 42 M. Lat. 110, 951, cf. also Peter Damiani Ep. 2.5 ed. Cajetani 1, 61, who claims that the saints form the throne from which God pronounces His edicts of Justice.