59. Not all of these names and signs were used to the same extent. Since ½ + ⅓ = ⅚, there was used in ordinary life and ½ and ⅓ (semis et triens) in place of 5/6 or 10/12 (decunx). Nor did the Romans confine themselves to the duodecimal fractions or their simplified equivalents ½, ⅓, ¼, ⅙, etc., but used, for instance, ⅒ in measuring silver, a libella being ⅒ denarius. The uncia was divided in 4 sicilici, and in 24 scripuli etc.[1] In the Geometry of Boethius the Roman symbols are omitted and letters of the alphabet are used to represent fractions. Very probably this part of the book is not due to Boethius, but is an interpolation by a writer of later date.
60. There are indeed indications that the Romans on rare occasions used letters for the expression of integral numbers.[2] Theodor Mommsen and others discovered in manuscripts found in Bern, Einsiedeln, and Vienna instances of numbers denoted by letters. Tartaglia gives in his General trattato di nvmeri, Part I (1556), folios 4, 5, the following:
|
A
|
500
|
|
I
|
1
|
|
R
|
80
|
61. Gerbert (Pope Sylvestre II) and his pupils explained the Roman fractions. As reproduced by Olleris[3], Gerbert’s symbol for ½ does not resemble the capital letter S, but rather the small letter (
symbol characters).
- ↑ For additional details and some other symbols used by the Romans, consult Friedlein, p. 33-46 and Plate 3; also H. Hankel, op. cit., p. 57-61, where computations with fractions are explained. Consult also Fr. Hultsch, Metrologic. scriptores Romani (Leipzig, 1866).
- ↑ Friedlein, op. cit., p. 20, 21, who gives references. In the Standard Dictionary of the English Language (New York, 1896), under S, it is stated that S stood for 7 or 70.
- ↑ Œuvres de Gerbert (Paris, 1867), p. 343-48, 393-96, 583, 584.
