Introductio in analysin infinitorum

According to Henk Bos, Euler accomplished this feat by introducing exponentiation ax for arbitrary constant a in the positive real numbers.

The reference here is to Gregoire de Saint-Vincent who performed a quadrature of the hyperbola y = 1/x through description of the hyperbolic logarithm.

Here he also gives the exponential series: Then in chapter 8 Euler is prepared to address the classical trigonometric functions as "transcendental quantities that arise from the circle."

Carl Benjamin Boyer's lectures at the 1950 International Congress of Mathematicians compared the influence of Euler's Introductio to that of Euclid's Elements, calling the Elements the foremost textbook of ancient times, and the Introductio "the foremost textbook of modern times".

[5] Boyer also wrote: The first translation into English was that by John D. Blanton, published in 1988.