"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 and certainly to Descartes."

“The Arabs contributed nothing new to the theory, but al-Khowârizmî states the usual rules, and the same is true of his successors.”

“Wallis was in sympathy with Greek mathematics and astronomy, editing parts of the works of Archimedes, Eutocius, Ptolemy, and Aristarchus; but at the same time he recognized the fact that the analytic method was to replace the synthetic, as when he defined a conic as a curve of the second degree instead of as a section of a cone, and treated it by the aid of coordinates.”

“Aside from Cauchy, the greatest contributory to the theory was Carl Gustav Jacob Jacobi. With him the word "determinant" received its final acceptance. He early used the functional determinant which Sylvester has called the Jacobian, and in his famous memoirs in Crelle's Journal for 1841 he considered these forms as well as that class of alternating functions which Sylvester has called alternants.”

“There are only four Hindu writers on algebra whose names are particularly noteworthy. These are Āryabhata, whose Āryabhatiyam included problems in series, permutations, and linear and quadratic equations;, whose Brahmasiddhānta contains a satisfactory rule for solving the quadratic... Mahāvīra, whose Ganita-Sāra Sangraha contains a large number of problems involving series, radicals, and equations; and Bhāskara, whose Bija Ganita ... extends the work through quadratic equations.”

“Vieta 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.”

“He... gave thirteen forms of the cubic which have positive roots, these having already been given by Omar Kayyam.”