De Analysi per Aequationes Numero Terminorum Infinitas

Isaac Newton's work, De Analysi per Aequationes Numero Terminorum Infinitas (1669), meaning "On Analysis by Equations with an Infinite Number of Terms," was a foundational text in the development of calculus. This treatise introduced the concept of infinite series, which Newton used to find series for many algebraic functions.12

Newton's work on infinite series allowed him to derive series for integrals of algebraic functions, such as the logarithm and inverse sine series. He also developed methods for inverting series, enabling him to find the exponential and sine series. This demonstrated his mastery of calculus, which he saw as an algebraic analogue to arithmetic with infinite decimals. Newton's insights into infinite series and calculus were crucial for the advancement of mathematics and physics.134