Roger Cotes - Harmonia mensurarum, sive analysis & synthesis per rationum - 1722

Rare and important first edition of one of the foundational works of eighteenth-century mathematics, published in Cambridge in 1722, six years after the author’s death.

Roger Cotes (1682–1716), an English mathematician and astronomer, was one of Isaac Newton’s most brilliant collaborators. He took a direct part in preparing the second edition of Newton’s famous Philosophiae Naturalis Principia Mathematica, published in 1713.

Published posthumously by Robert Smith, Harmonia Mensurarum is the principal record of Cotes’s mathematical research; during his lifetime, he published only one scientific paper.

A work of exceptional scientific importance

This major treatise brings together fundamental research on logarithms, trigonometry, the properties of the circle, infinitesimal calculus, and methods of integration.

The historian of mathematics Augustus De Morgan emphasized the importance of this work in the development of the applications of logarithms and the properties of the circle to the calculus of fluxions.

The work is also renowned for the research that led to the Newton–Cotes formulas, which are still studied in the field of numerical integration.

It includes, in particular, discussions of the properties of trigonometric functions and calculation methods that contributed to the development of modern mathematics.

Bibliographical description

* Author: Roger Cotes (1682–1716)
* Title: Harmonia Mensurarum, sive Analysis & Synthesis per Rationum & Angulorum Mensuras promotae
* Place: Cambridge
* Date: 1722
* Scientific editor: Robert Smith
* Edition: Original, first edition
* Language: Latin
* Format: Quarto
* Pagination: 398 pages, including preliminary leaves
* Illustrations: Numerous mathematical figures in the text and one folding engraved plate
* Binding: Contemporary full calf

Condition

Copy preserved in its contemporary full-calf binding.

The interior is remarkably fresh for a work over 300 years old. The paper is particularly white, with very few spots of foxing. The type and mathematical figures are sharp and clear.

The binding shows wear and deterioration to the leather, mainly on the boards. Old repairs are noted, particularly to the boards and spine. The spine remains in generally satisfactory condition.

Despite these external defects, the volume is sound and holds together well.

A folding plate accompanies the scientific figures in the text.

Historical and bibliophilic interest

This first edition is an important record of the European mathematical revolution of the early eighteenth century.

Roger Cotes’s association with Isaac Newton, the significance of the discoveries presented, and its posthumous publication in Cambridge make this a particularly interesting work for collectors of scientific books, the history of mathematics, and Newtonian thought.

An appealing copy of this important 1722 first edition, notable for its fresh interior and its scientific and historical interest.