A Discourse Concerning Algebra: English Algebra to 1685 by Jacqueline A. Stedall

By Jacqueline A. Stedall

A Discourse referring to Algebra, offers a brand new and readable account of the increase of algebra in England from the Medieval interval to the later years of the seventeenth Century.Stedall's e-book follows the reception and dissemination of vital algebraic rules and techniques from continental Europe and the resultant revolution within the country of English arithmetic within the seventeenth century.

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41 One of the earliest, well known to Wallis, was in verse, the Carmen de algorismo (Song of algorithm) which, like the ψηϕOϕOpiα described the numeral figures as Indian. The first few lines set out the numerals and explained the principle of place-value:42 Haec Algorismus ars praesens dicitur, in qua Talibus Indorum fruimur bis quinque figuris. 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.

1145) and by Gerard of Cremona (c. 93 Leonardo, like al-Khwārizmī, considered only positive solutions, but where two such solutions existed he could produce both. He also treated equations of higher degree that were essentially quadratic in form, for example A DISCOURSE CONCERNING ALGEBRA 37 x 8 + 100x4 = 10 000. In describing such equations (his exposition, like all earlier ones, was entirely verbal) he introduced Latin names that were to remain in use for centuries: numerus for a given or known quantity; radix, res, causa or cosa for the unknown root, or thing; quadratus or census (literally ‘wealth’ or ‘excess’) for its square;94cubus for its cube; census de censu for the fourth power and cubus cubi for the sixth power (not, as one might imagine, the ninth).

The first generally used consistent symbolic representation of powers. (Nicholas Chuquet in. )103 The first printed text to include some algebra was the Summa de arithmetica of Luca Pacioli, published in Venice in 1494 (Fig. 7). cu, denoted a sixth power, not a fifth. In this system a new name or symbol is required for every prime power, and Pacioli called the fifth power primo relato, the seventh secondo relato and so on. , a system that became standard during the sixteenth century. The precise symbols used varied from author to author: one of the earliest printed texts, the Summa arithmetica of 1521 of Francesco di Ghaligai, used charming but not very practical squares and rectangles to denote powers, but most authors used some variation on the letters R, Z and C for an unknown, its square and its cube.

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