By Jean-Etienne Montucla

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1220 (though Wallis thought he lived around 1200);57 and in astrological diagrams dated 1216 (Fig. 58 Like Kircher, Wallis recognized that one of the earliest ways Hindu–Arabic numerals reached northern Europe was through astronomical tables but, unlike Kircher, he knew that the Alphonsine tables were not the ﬁrst to spread beyond Spain. Before that, the Toledan tables, originally compiled in the eleventh century, were used throughout Europe and adapted for different cities: Marseilles (c. 59 Wallis knew the London edition, translated by Robert of Chester, from a copy in the Savile Library, and at this point in his research went to some trouble to discover Robert of Chester's identity, but never made the vital connection with Robert the 28 HOW ALGEBRA WAS ENTERTAINED AND CULTIVATED IN EUROPE Fig.

Even more inﬂuential than Ville Dieu's Carmen was the Algorismus of Johannes Sacrobosco (c. 47 Like the Carmen, the Algorismus dealt with the material ﬁrst set out by al-Khwārizmī: place-value, addition, subtraction, doubling and halving, multiplication and A DISCOURSE CONCERNING ALGEBRA 27 division, all for integers. To these Sacrobosco added cube roots and an elementary treatment of arithmetic progression. Sacrobosco's Algorismus became by far the best known of the medieval algorisms. It remained in use as a university text across western Europe for three centuries,48 and set the pattern for all subsequent texts on arithmetic for many years after that.

1. Primoque signiﬁcat unum: duo vera secunda Tertia signiﬁcat tria: sic procede sinistra Donec ad extremam venias, qua cifra vocatur; Quae nil signiﬁcat; dat signiﬁcare sequenti. 1. The ﬁrst signiﬁes one: two the second The third signiﬁes three: thus proceed left Until you come to the end, which is called ‘cifra’; Which signiﬁes nothing; it gives signiﬁcance to what is behind it. If you put any of these in the ﬁrst place, It signiﬁes simply itself: if in the second, Itself tenfold… The Carmen, written by a French Franciscan, Alexandre de Ville Dieu (d.