Roger Bacon mentioned both methods of distinction between the true and false mathematics; but statements in his different works are not in agreement as to which case it is in which the “e” is long or short. In the Opus Maius (Bridges, I, 239 and note) and Opus Tertium (caps. 9 and 65) he states that the vowel is short in the true mathematics and long in the superstitious variety; but in other writings he took the opposite view and declared that “all the Latins” were wrong in thinking otherwise (see Bridges, I, 239 note; Steele (1920) viii).
In a twelfth century MS at Munich (CLM 19488, pp. 17-23) a treatise or perhaps an excerpt from some longer work, entitled De differentiis vocabulorum, opens with the words, “Scire facit mathesis et divinare mathesis.” Roger Bacon says (Steele, 1920, p. 3), “Set glomerelli nescientes Grecum ... ex magna sua ignorancia vulgaverunt hos versus falsos:
Scire facit matesis, set divinare mathesis;
Philosophi matesim, magici dixere mathesim.”
[17] Didascalicon, I, 7.
[18] Didasc. VI, 15 (Migne PL 176, 810-12).
[19] BN nouv. acq. 1429, 12th century, fols. iv-23, and CLM 2572, written between 1182 and 1199; both end with the thirteenth chapter of Book VI, or at col. 809 in Migne. St. John’s 98, 14th century, fol. 145v, also ends at this point. Jesus College 35, 12th century, is mutilated at the close.
Other early MSS, however, include the passage on magic in the Didascalicon, and end the sixth book with the closing words of the account of magic, “Hydromancy first came from the Persians”: see Vitry-le-François 19, 12th century, fols. 1-46; Mazarine 717, 13th century, #9, closing at fol. 97v.
The passage on magic is also cited as Hugh’s by Robert Kilwardby, archbishop of Canterbury 1272-1279, in his work on the division of the sciences, cap. 67: MSS are Balliol 3; Merton 261.
In Cortona 35, 15th century, fol. 203, the Didascalicon in six books is first followed by a brief passage, Divisio philosophie continentium, which is perhaps simply the fourteenth chapter of the sixth book as printed in Migne, and then at fol. 224 by the passage concerning magic and its subdivisions.