Introduction to Analysis of the Infinite
This chapter explains the origin of elementary functions and the impact of Descartes’s “Géométrie” on their calculation. The interpolation polynomial leads to Newton’s binomial theorem and to the infinite series for exponential, logarithmic, and trigonometric functions. The chapter ends with a discussion of complex numbers, infinite products, and continued fractions. The presentation follows the historical development of this subject, with the mathematical rigor of the period. The justification of dubious conclusions will be an additional motivation for the rigorous treatment of convergence in Chapter III.