[598] The first is from the Hannover algorismus, thirteenth century. The second is taken from the Rollandus manuscript, 1424. The others in the first two lines are from Cappelli, twelfth (3), fourteenth (6), fifteenth (13) centuries, respectively. The third line is from Chassant, loc. cit., p. 113, no mention of dates.
[599] The first of these forms is from the Hannover algorismus, thirteenth century. The following are from Cappelli, fourteenth (3), fifteenth, sixteenth (2), and eighteenth centuries, respectively.
[600] The first of these is taken from the Hannover algorismus, thirteenth century. The following forms are from Cappelli, twelfth, thirteenth, fourteenth (5), fifteenth (2), seventeenth, and eighteenth centuries, respectively.
[601] All of these are given by Cappelli, thirteenth, fourteenth, fifteenth (2), and sixteenth centuries, respectively.
[602] Smith, Rara Arithmetica, p. 489. This is also seen in several of the Plimpton manuscripts, as in one written at Ancona in 1684. See also Cappelli, loc. cit.
[603] French algorismus, c. 1275, for the first of these forms. Cappelli, thirteenth, fourteenth, fifteenth (3), and seventeenth centuries, respectively. The last three are taken from Byzantinische Analekten, J. L. Heiberg, being forms of the fifteenth century, but not at all common.
[604] For the first of these the reader is referred to the forms ascribed to Boethius, in the illustration on p. [88]; for the second, to Radulph of Laon, see p. [60]. The third is used occasionally in the Rollandus (1424) manuscript, in Mr. Plimpton's library. The remaining three are from Cappelli, fourteenth (2) and seventeenth centuries.
[605] Smith, An Early English Algorism.
[606] Kuckuck, p. 5.