Cours d'Analyse

Analyse algébrique ("Analysis Course" in English) is a seminal textbook in infinitesimal calculus published by Augustin-Louis Cauchy in 1821.

On page 1 of the Introduction, Cauchy writes: "In speaking of the continuity of functions, I could not dispense with a treatment of the principal properties of infinitely small quantities, properties which serve as the foundation of the infinitesimal calculus."

Cauchy continues: "As for the methods, I have sought to give them all the rigor which one demands from geometry, so that one need never rely on arguments drawn from the generality of algebra."

On page 10, Bradley and Sandifer confuse the versed cosine with the coversed sine.

In the translation, however, the cosinus versus (and cosiv) are incorrectly associated with the versed cosine (what is now also known as vercosine) rather than the coversed sine.

The translators observe in a footnote: "The notation “Lim.” for limit was first used by Simon Antoine Jean L'Huilier (1750–1840) in [L’Huilier 1787, p. 31].

On page 21, Cauchy writes: "We say that a variable quantity becomes infinitely small when its numerical value decreases indefinitely in such a way as to converge towards the limit zero."

be an infinitely small quantity, that is a variable whose numerical value decreases indefinitely.

, namely enter into the same calculation, these various powers are called, respectively, infinitely small of the first, the second, the third order, etc.

Cauchy writes: "If, beginning with a value of x contained between these limits, we add to the variable x an infinitely small increment