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 practical and commercial worth than on its value as a factor in the expansion of the mental powers. Cardinal Sadoleto, writing in 1549, points out the necessity of adding arithmetic to the school curriculum, but only because without its aid we cannot tell how many fingers we have or with how many eyes we see.

On this position a great advance is made by Robert Recorde, who published his Arithmetic in 1561 under the title The Grounde of Artes. According to Recorde the great claim of arithmetic is that it exercises the mind purely, apart from lines as in geometry and from spheres and axes as in astrology. The capacity for mathematics is the special prerogative of man. “Whoso setteth small price by the witty device and knowledge of numbring, he little considereth it to be the chief point (in manner) whereby men differ from all brute beasts; for as in all other things (almost) beasts are partakers with us, so in numbring we differ cleane from them and in manner peculiarly, sith that in many things they excell us againe.” It must not be imagined from this quotation that the Grounde of Artes is of a philosophical nature. It is a very practical arithmetic, and is of special interest as being written in English. In his work on algebra also, The Whetstone of Witte, published in 1557, Recorde discards Latin in favour of the vernacular.

In France a staunch upholder of mathematics was that many-sided man of learning, Peter Ramus. Himself the author of an Arithmetic, he was at some pains to ascertain the modes of instruction most approved of in other countries. In a letter to John Dee, dated 1565, he begs him to say what old mathematical books he has in his library, who are the teachers of mathematics in English