Aside from Cauchy, the greatest contributory to the theory [of determinants] was Carl Gustav Jacob Jacobi. With him the word "determinant" received i… - David Eugene Smith

Of the contemporaries of Newton one of the most prominent was John Wallis. ...Wallis was a voluminous writer, and not only are his writings erudite, but they show a genius in mathematics... He was one of the first to recognize the significance of the generalization of exponents to include negative and fractional as well as positive and integral numbers. He recognized also the importance of Cavalieri's method of indivisibles, and employed it in the quadrature of such curves as y=xⁿ, y=x^1/n, and y=x⁰ + x¹ + x² +... He failed in his attempts at the approximate quadrature of the circle by means of series because he was not in possession of the general form of the binomial theorem. He reached the result, however, by another method. He also obtained the equivalent of <math>ds = \!dx \sqrt{1+(\frac{dy}{dx})^2}</math> for the length of an element of a curve, thus connecting the problem of rectification with that of quadrature.

Algebra in the Renaissance period received its first serious consideration in Pacioli's Sūma (1494)... which characterized in a careless way the knowledge... thus far accumulated. By the aid of the crude symbolism then in use it gave a considerable amount of work in equations.
The noteworthy work... and the first to be devoted entirely to the subject, was Rudolff's Coss (1525). This work made no decided advance in the theory, but it improved the symbolism for radicals and made the science better known in Germany. Stiffel's edition of this work (1553-1554) gave the subject still more prominence.
The first epoch-making algebra to appear in print was the Ars Magna of Cardan (1545). The next great work... to appear in print was the General Trattato of Tartaglia...

He used capital vowels for the unknown quantities and capital consonants for the known, thus being able to express several unknowns and several knowns.