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Landen’s 'Residual Analysis'

Frank J. Swetz (The Pennsylvania State University)

The British surveyor turned mathematician John Landen (1719-1790) made several noteworthy contributions to mathematics. Inventive and creative, he also developed theories that were controversial; such was his “residual analysis,” a computational system based on algebra and geometry, to circumvent calculus. Landen published a book explaining his theory in 1758 titled A Discourse Concerning the Residual Analysis.

The name and address of a previous owner of this book is written on the inside cover: “M. Liouville, Rue Sorbonne, No. 7.” Could this “Monsieur Liouville” be the French mathematician Joseph Liouville (1809-1882)? It is known that this book was obtained from France.

Landen explained his theory in the first few page of the “Preface”.

In 1764, Landen published his The Residual Analysis, A New Branch of the Algebraic Art.

In the Preface” of this book he also justified his method as an alternate to the calculus.      

These images were obtained through the courtesy of ETH-Bibliothek Zürich. The book may be viewed in its entirety at e-rara:

Index to Mathematical Treasures

Frank J. Swetz (The Pennsylvania State University), "Landen’s 'Residual Analysis'," Convergence (July 2017)