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John of Salisbury and Boethius on Arithmetic

  • Gillian R. Evans (a1)


The Cornificians, says John of Salisbury in the Metalogicon, find new laws for every subject of study in the schools; grammar is revised, dialectic altered, rhetoric despised, and ‘abandoning the rules of former masters’, they put forward ‘new ways’ for all the subjects of the quadrivium. In fact, they despise the real quadrivium, and prefer a quasi quadrivium in which the four ‘ways’ are ways of making money or influencing events: by entering the clerical or the medical profession, or seeking a position at Court, or becoming a merchant.



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1 Metalogicon i.3, p 12 lines 2-6.

2 Metalogicon i.4, p 15 line 26.

3 Metalogicon i.24, p 54 line 30-p 55 line 2.

4 Policraticus i.6.

5 Policraticus ii. 18-19; cf Isidore, Etymologiae VIII. ix. 24-5 (ed W. M. Lindsay: Oxford 1911) on mathematica.

6 Metalogicon ii. 10, p 80 lines 4-10.

7 Cf Hugh of St Victor, Didascalion vi.15 (ed C. Buttimer: Washington 1939).

8 Boethius, , Arithmetica i. 1 (ed Friedlein, G.: Leipzig 1867); Petrus Abaelardus: Diabetica (ed L. M. de Rijk: Assen 1956), p 59.

9 Arithmetica p 8 lines 1-13.

10 Durham Cathedral Library MS C.IV.7: on these commentaries see Fredborg, K. M., ‘The Commentaries on Cicero’s De Inuentione and the Rhetorica ad Herennium by William of Champeaux’, Cahiers de l’institut du moyen age grec et latin, 17 (Copenhagen 1976).

11 MS C.IV.7 fol 51 col 2.

12 Metalogicon ii. 17, p 93 line 27.

13 The discrepancy arises because Boethius borrows Nichomachus’ list in making his translation from the Introduction to Arithmetic, but does not comment on its differences from Aristotle’s list.

14 Policraticus ii.18, p 106 line 12; Arithmetica p 9 lines 13-18.

15 Arithmetica p 7 line 22.

17 E.g. Commentaries on Boethius by Thierry of Chartres and his School (ed N. M. Häring: Toronto 1971), p 267 line 87.

18 Two attempts to use the demonstrative method in theology are printed in PL 210: Alan of Lille’s Regulae Theologicae and Nicholas of Amiens’ De Articulis Catholicae Fidei. On the authorship of these two works see M.-T. d’Alverny, Textes inédits d’Alain de Lille (Paris 1965). On the question of the circulation of Euclid see Claggett, M., ‘The Medieval Translations from the Arabic of Euclid’s Elements with special emphasis upon the versions of Adelard of Bath’, Isis, 44 (1953) pp 146.

19 Metalogicon iv.6, p 171 lines 3-5.

20 Posterior Analytics i. 12, 77a-b.

21 Boethius, Theological Tractates (ed H. F. Steward and E. K. Rand: London 1953), pp 40-l.

22 Policraticus vii.7, 2, pp 115-16.

23 Gilbert of Poitiers, Commentaries on Boethius (ed N. M. Häring: Toronto 1966), pp 189-90; PL 210, 621-2.

24 Policraticus vii.7, 2, p 116 line 21.

25 Arithmetica ii.2, pp 80-1.

26 Policraticus ii.18, 1, pp 102-3.

27 Metalogicon ii.17, p 94 lines 3-5; cf Arithmetica p 8 lines 3-4.

28 Metalogicon iv.35, pp 204-5.

John of Salisbury and Boethius on Arithmetic

  • Gillian R. Evans (a1)


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