The Britannica Guide to Algebra and Trigonometry (Math by William L Hosch

By William L Hosch

Calculating and manipulating the unknown has been the company of the sector of algebra seeing that its earliest inception in Babylon and historical Egypt. Trigonometry attracts on ideas provided in algebra and makes use of perspective measurements to intricate on geometric calculations. necessary to extra mathematical and clinical examine, either algebra and trigonometry supply the most important instruments in handling variables and figuring out the relationships among them. This quantity offers the basics of those attention-grabbing components of arithmetic whereas chronicling their respective histories.

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The abacists first began to introduce abbreviations for unknowns in the 14th century—another important milestone toward the full-fledged manipulation of abstract symbols. For instance, c stood for cossa (“thing”), ce for censo (“square”), cu for cubo (“cube”), and R for Radice (“root”). Even combinations of these symbols were introduced for obtaining higher powers. This trend eventually led to works such as the first French algebra text, Nicolas Chuquet’s Triparty en la science des nombres (1484; “The Science of Numbers in Three Parts”).

His widely read Ars Magna (1545; “Great Work”) contains the Renaissance era’s most systematic and comprehensive account of solving cubic and quartic equations. Cardano’s presentation followed the Islamic tradition of solving one instance of every possible case and then giving geometric justifications for his procedures, based on propositions from Euclid’s Elements. He also followed the Islamic tradition of expressing all coefficients as positive numbers, and his presentation was fully rhetorical, with no real symbolic manipulation.

In 1202, soon after his return to Italy, Fibonacci wrote Liber Abbaci (“Book of the Abacus”). Although it contained no specific innovations, and although it strictly followed the Islamic 35 7 The Britannica Guide to Algebra and Trigonometry 7 Hindu-Arabic numerals, the evolution of which is shown above, are used throughout the world today, though they originated in India and were first introduced to the Europeans by Arab mathematicians. Modified from Karl Menninger, Number Words and Number Symbols: A Cultural History of Numbers, Cambridge, MA: The MIT Press, 1969 tradition of formulating and solving problems in purely rhetorical fashion, it was instrumental in communicating the Hindu-Arabic numerals to a wider audience in the Latin world.

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