A Historical Survey of Algebraic Methods of Approximating the Roots of Numerical Higher Equations Up to the Year 1819
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This method was also used for irra- tional roots later on, and European scholars standardized an adapta- tion of it for approximating irrational roots by decimal fractions.
3. The five principal approximation formulas invented and used in the Middle Ages were: (o) Va^ + b = a+ -; (b) Va^ + b = a + 2a 2a -+- I (c) VA = ~ \/Aa^; (d) ^a^ + b == a + a 3c(a -f i) -f I (e) ^a^ + b = a + 30(0 + i) IV APPROXIMATIONS FOR SPECIFIC PURPOSES I. THE RISE OF NUMERICAL HIGHER EQUATIONS AMONG THE ARABS Althoug...h the Arabs did not contribute much original matter to algebra they vitalized it and enriched its contents by applying algebraic operations to the problems of Greek geometry and to their own problems in astronomy and trigonometry. This led them directly to numerical higher equations. Archimedes's problem of the section of the sphere, which led to a cubic, was first attempted by al-Mclh&nl (c. 860), and was later solved successfully by al-Kh&zin (c. 950) with the aid of conic sections. The trisection of angles and the computation of sides of regular polygons led to other cubics,' which were also solved by conic sections; for they soon came empirically to the conclusion that cubics could not be solved alge- braically.
What to read after A Historical Survey of Algebraic Methods of Approximating the Roots of Numerical Higher Equations Up to the Year 1819?
You can find similar books in the "Read Also" column, or choose other free books by Nordgaard, Martin Andrew, 1882- to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
This method was also used for irra- tional roots later on, and European scholars standardized an adapta- tion of it for approximating irrational roots by decimal fractions.
3. The five principal approximation formulas invented and used in the Middle Ages were: (o) Va^ + b = a+ -; (b) Va^ + b = a + 2a 2a -+- I (c) VA = ~ \/Aa^; (d) ^a^ + b == a + a 3c(a -f i) -f I (e) ^a^ + b = a + 30(0 + i) IV APPROXIMATIONS FOR SPECIFIC PURPOSES I. THE RISE OF NUMERICAL HIGHER EQUATIONS AMONG THE ARABS Althoug...h the Arabs did not contribute much original matter to algebra they vitalized it and enriched its contents by applying algebraic operations to the problems of Greek geometry and to their own problems in astronomy and trigonometry. This led them directly to numerical higher equations. Archimedes's problem of the section of the sphere, which led to a cubic, was first attempted by al-Mclh&nl (c. 860), and was later solved successfully by al-Kh&zin (c. 950) with the aid of conic sections. The trisection of angles and the computation of sides of regular polygons led to other cubics,' which were also solved by conic sections; for they soon came empirically to the conclusion that cubics could not be solved alge- braically.
What to read after A Historical Survey of Algebraic Methods of Approximating the Roots of Numerical Higher Equations Up to the Year 1819?
You can find similar books in the "Read Also" column, or choose other free books by Nordgaard, Martin Andrew, 1882- to read onlineMoreLess
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