# Mathematical Treasure: Maclaurin's Treatise on Fluxions

Author(s):
Frank J. Swetz (The Pennsylvania State University)

Colin Maclaurin (1698-1746) grew from a child prodigy to being one of Scotland’s greatest mathematicians. He was Professor of Mathematics at the University of Glasgow and a strong advocate for the work of Isaac Newton (1643-1727). He extended Newton’s work in calculus, geometry, and the theories of gravitation. In 1742, he published a major work consisting of two volumes comprising 763 pages, A Treatise of Fluxions, of which images are shown elsewhere in Convergence. At the time, it received much attention but exerted little influence on the teaching of mathematics. The second edition of this work, titled A Treatise on Fluxions, appeared in 1801 and, as a tribute to its author, contained a biography of him. The frontispiece and the title page of this edition are shown above and its Preface is shown below in its entirety.

In his “Preface,” Maclaurin defended Newton’s theory of fluxions against the attacks of critics, particularly those of the Rev. George Berkeley (1685-1753) as expressed in The Analyst (1734). The entire Preface appears above.

Page 50, above, contains the last comments of Maclaurin’s “Introduction.” Note the references to other prominent mathematicians: Pierre de Fermat, Christiaan Huygens, Galileo Galilei, and Isaac Barrow. Chapter I and the actual instructive text begin on page 51. Note the reference to “The Ancient Geometricians.” Maclaurin possessed a special interest in the work of the classical geometers and often reflected it in his writings.

Volume II of Maclaurin’s Fluxions is considered in the following images.

This is the title page for volume II of Maclaurin’s A Treatise on Fluxions.

On pages 172-173 of volume II, above, we encounter a discussion of what we know as the differentiation of an expression raised to a power, i.e. $A^n.$ The reader should attempt to work the example using the method of fluxions.

The two images of volume II, directly above, are presented courtesy of the Pennsylvania State University Library. All other images above were obtained from the Pennsylvania State Library, Harrisburg, Pennsylvania. Dr. Iren Snavely, Curator of Rare Books and Manuscripts, was particularly helpful in securing these six images.

Index to Mathematical Treasures

Frank J. Swetz (The Pennsylvania State University), "Mathematical Treasure: Maclaurin's Treatise on Fluxions," Convergence (May 2015)