Algebra In Sixteenth And Seventeenth Century

The sixteenth and seventeenth century is a very important period in the development of mathematics. Not only the theory of equation and the system of signs, but also logarithm and the invention of analytic geometry are all epoch-making. These provided the condition for the foundation of calculus in the seventeenth century and accelerated the birth of calculus straight. At the beginning of the foundation of calculus, many algorithms were developed based on algebra. But some of them were not narrow logically and their bases were not consummate. Even then, calculus was very helpful as a mathematical tool in the scientific fields of that time. Its algorithm was similar to the deduction of algebra formally. After seventeenth century, mathematics entered the phase of variable mathematics. Almost every science had relationship with calculus. The way of calculus was not described by the form of geometry. It quickened up the process of using algebra as a current tool. A series of algebraic signs came forth and the algebraic way was more useful. But after a while, the problems of the theoretical basis of calculus were revealed. This should be related with the insufficiencies of algorithmic prepare in algebra before. This article listed the main clue of the development of mathematics in the sixteenth and seventeenth century. Based on that, we analyzed the algebraic basis of calculus. The basis had an algorithmic character which could use program to calculate. We can see that algorithmic character based on algebra acted as the important role in mathematics during the sixteenth and seventeenth century. It existed with the deductive logic which was in the system of Hellenic axioms. It took on the leading actor in different periods and instructed the development of mathematics in different regions.Otherwise, the article tried to find some ways in the early algorithms of calculus and explained its origin by comparing with the algebraic algorithm. Actually, the European mathematics that halted in the low level for centuries soared suddenly in the sixteenth and seventeenth century and the foundation of analytic geometry and calculus were not incidental. Arabian work influenced it much without doubt. They took the practical calculation as the primacy of mathematics and established algebra based on arithmetic not on geometry. These important mathematical thought were crucial to the big change of the European mathematical thinking.