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 best. Returning to Pisa, he published, in 1202, his great work, the Liber Abaci. A revised edition of this appeared in 1228. This work contains about all the knowledge the Arabs possessed in arithmetic and algebra, and treats the subject in a free and independent way. This, together with the other books of Leonardo, shows that he was not merely a compiler, or, like other writers of the Middle Ages, a slavish imitator of the form in which the subject had been previously presented, but that he was an original worker of exceptional power.

He was the first great mathematician to advocate the adoption of the "Arabic notation." The calculation with the zero was the portion of Arabic mathematics earliest adopted by the Christians. The minds of men had been prepared for the reception of this by the use of the abacus and the apices. The reckoning with columns was gradually abandoned, and the very word abacus changed its meaning and became a synonym for algorism. For the zero, the Latins adopted the name zephirum, from the Arabic sifr (sifra = empty); hence our English word cipher. The new notation was accepted readily by the enlightened masses, but, at first, rejected by the learned circles. The merchants of Italy used it as early as the thirteenth century, while the monks in the monasteries adhered to the old forms. In 1299, nearly 100 years after the publication of Leonardo's Liber Abaci, the Florentine merchants were forbidden the use of the Arabic numerals in book-keeping, and ordered either to employ the Roman numerals or to write the numeral adjectives out in full. In the fifteenth century the abacus with its counters ceased to be used in Spain and Italy. In France it was used later, and it did not disappear in England and Germany before the middle of the seventeenth century.[22] Thus, in the Winter's Tale (iv. 3), Shakespeare lets the clown be embarrassed by