A Discourse Concerning Algebra - English Algebra Since 1685 by J. Stedall

By J. Stedall

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Between 1643 and 1646 he met the English mathematician John Pell, then teaching in the Gymnasium at Amsterdam, and it may have been Pell who later suggested De scientiis as a useful source to Wallis. Wallis's copy of De scientiis is preserved in the Bodleian Library and his frequent and detailed annotations show how thoroughly he read it. Vossius classified the mathematical sciences as arithmetic, geometry, logistics, music, 20 HOW ALGEBRA WAS ENTERTAINED AND CULTIVATED IN EUROPE optics, and so on, and for each branch he wrote a description and history, followed by a chronological list of writers on the subject.

The influence of al-Khwārizmī's Al-jabr was not to be felt in England for many years. A much more immediate and revolutionary consequence of the discovery of Arabic mathematical and scientific texts was the introduction of the Hindu–Arabic numerals. Wallis claimed that algebra could hardly have developed without the invention of an efficient numeral system, and devoted three of his opening chapters to exploring the origins and spread of the Hindu–Arabic system. He had already written a brief history of the 24 HOW ALGEBRA WAS ENTERTAINED AND CULTIVATED IN EUROPE numeral system in his Mathesis universalis of 1657,34 but by the 1670s he could add much that was new, and we shall pause to look at his researches on this subject before returning to algebra itself.

88 Fig. 6 The geometrical method of solving x2 + 10x = 39. A square of area 25 units is required for the completing, or setting together (al-jabr) of the larger square. Balancing (al-muqābala) is achieved by adding the same 25 units to the quantity on the right. 36 HOW ALGEBRA WAS ENTERTAINED AND CULTIVATED IN EUROPE The subject of al-Khwārizmī's treatise is the handling of linear and quadratic equations of the following six types:89 There is no symbolic notation in al-Khwārizmī's Al-jabr: each type of equation is described verbally, and the method of solution is given as a recipe or set of instructions for each case.

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