14 quotes
He used capital vowels for the unknown quantities and capital consonants for the known, thus being able to express several unknowns and several knowns.
History of Mathematics (1925)
With the coming of the Jesuits in the 16th century, and the consequent introduction of Western science, China lost interest in her native algebra...
History of Mathematics (1925)
He... gave thirteen forms of the cubic which have positive roots, these having already been given by Omar Kayyam.
History of Mathematics (1925)
He states that the root of x^3 + 6x = 20 isx = \sqrt[3]{\sqrt{108} + 10} - \sqrt[3]{\sqrt{108} - 10}.
History of Mathematics (1925)
The excellent work of Tropfke is an example of the tendency to break away from the mere chronological recital of facts.
History of Mathematics (1923)
The Arabs contributed nothing new to the theory, but al-Khowârizmî (c. 825) states the usual rules, and the same is true of his successors.
History of Mathematics (1925)
Among his [John Wallis'] interesting discoveries was the relation
\frac{4}{\pi} = \frac32\cdot\frac34\cdot\frac54\cdot\frac56\cdot\frac76\cdot\frac78\cdots
one of the early values of π involving infinite products.
History of Mathematics (1923)
Vieta (c. 1590) rejected the name "algebra" as having no significance in the European languages, and proposed to use the word "analysis," and it is probably to his influence that the popularity of this term in connection with higher algebra is due.
History of Mathematics (1925)
The first writer on algebra whose works have come down to us is Ahmes. He has certain problems in linear equations and in series, and these form the essentially new feature in his work. His treatment of the subject is largely rhetorical.
History of Mathematics (1925)
The field of mathematics is now so extensive that no one can [any] longer pretend to cover it, least of all the specialist in any one department. Furthermore it takes a century or more to weigh men and their discoveries, thus making the judgment of contemporaries often quite worthless.
The first epoch-making algebra to appear in print was the Ars Magna of Cardan (1545). This was devoted primarily to the solution of algebraic equations. It contained the solution of the cubic and biquadratic equations, made use of complex numbers, and in general may be said to have been the first step toward modern algebra.
History of Mathematics (1925)
The law which asserts that the equation X = 0, complete or incomplete, can have no more real positive roots than it has changes of sign, and no more real negative roots than it has permanences of sign, was apparently known to Cardan; but a satisfactory statement is possibly due to Harriot (died 1621) and certainly to Descartes.
History of Mathematics (1925)
Although Cardan reduced his particular equations to forms lacking a term in x^2, it was Vieta who began with the general formx^3 + px^2 + qx + r = 0and made the substitution x = y -\frac{1}{3}p, thus reducing the equation to the formy^3 + 3by = 2c.He then made the substitutionz^3 + yz = b, or y = \frac{b - z^2}{z},which led to the formz^6 + 2cz^2 = b^2,a sextic which he solved as a quadratic.
History of Mathematics (1925)
In connection with the study of curves Fermat proceeded to apply the idea of infinitesimals to the questions of quadrature and of maxima and minima as well as to the drawing of tangents. In this he seems to have anticipated the work of Cavalieri, but the date of his discovery is unknown.
History of Mathematics (1925)