A Treatise of Algebra in Three Parts

by Colin MacLaurin

Treatise of Algebra in Three Parts
Title not held by The Wolf Law Library at the College of William & Mary.
Author	Colin MacLaurin
Editor
Translator
Published	:
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Edition	Precise edition unknown
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Volumes	volume set
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Desc.	8vo

Scottish mathematician Colin MacLaurin (1698–1746) was born in Kilmoden, Argyll, Scotland, in February of 1698. His father was a minister, and demonstrated academic prowess through his correspondence with American metaphysician Jonathan Edwards. He also portrayed intellectual strength by translating the psalms into Gaelic. MacLaurin’s father died weeks after his birth, and his mother died when he was only nine years old. He moved in with his uncle before beginning at the University of Glasgow at age 11. Throughout his career, MacLaurin held teaching positions at the University of Aberdeen and the University of Edinburgh. He was a fellow of the Royal Society and a winner of the Grand Prize from the Académie des Sciences.

MacLaurin was a follower and a defender of the ideas of Isaac Newton. It is likely that Newton and MacLaurin met during MacLaurin’s first visit to London. Additionally, it was a recommendation from Newton that helped MacLaurin secure his position at the University of Edinburgh. His defense of Newton’s calculus, made in response to the attacks made by George Berkeley, brought Maclaurin particular prominence.

Maclaurin’s thesis at the University of Glasgow touched on many Newtonian ideas. It was centered on the theory of gravity. He did not diverge greatly from Newton’s "observed law of terrestrial gravity" as explanation for "lunar and planetary motion." But, his thesis also touched upon the interrelated nature of gravitational forces and divinity, arguing "that [gravity] can only be accounted for as the direct result of divine will." After successfully defending his thesis, he remained at the University of Glasgow for one additional year and studied divinity, but he left the school before completing any additional official degree.

Before taking up his teaching post at the University of Edinburgh, MacLaurin taught at the University of Aberdeen, beginning his professorial career at age 19. While he was the chair of Aberdeen's Mathematics department, he toured Europe for two years with George Hume, the son of Lord Polwarth. The university was not pleased, because while Maclaurin had ensured that someone would fill in for him to teach his classes, he had otherwise wholly abandoned his post for his travels. Hume died while abroad, prompting MacLaurin’s return to Scotland. He then pursued a teaching post at the University of Edinburgh.

While teaching in Edinburgh, Maclaurin was a popular professor. He wrote "A Treatise of Algebra" to use in his own courses, but the book was only published officially posthumously. It was a popular textbook, and was reprinted in many editions.

In the field of Mathemetics, MacLaurin is most famously known for the "Maclaurin Series," which is a variation on the "Taylor Series." He also created the Euler-Maclaurin Summation Formula, as well as the Maclaurin-Cauchy Integral Test for Convergence.

MacLaurin also is involved in the history of the city of Edinburgh, and the history of Scotland. First, he aided in expanding the Medical Society of Edinburgh, which later became the Royal Society of Edinburgh. Second, he had an important marriage to Anne Stewart, the daughter of Scotland’s solicitor general. Most significantly, he had deep involvement in Edinburgh’s resistance to the Jacobite rebellion. He performed challenging physical labor in an attempt to reinforce the city's defenses in anticipation of the Jacobite's 1745 invasion. In fact, it is believed that his work in resisting the Jacobite rebellion, and his flight into England after the city's occupation, led to the illness that brought about his eventual death.

This treatise of algebra includes a breakdown of basic algebraic formulas. An instruction manual for schooling, this text also focuses on the application of algebra and geometry to each other and an Appendix containing the basic principles of geometrical lines. Clarity and simplicity were the main goals of this volume in distilling the more abstruse theorems into a simple presentation.

Evidence for Inclusion in Wythe's Library

Listed in the Jefferson Inventory of Wythe's Library as "Mc.laurin's Algebra. 8^vo." and given by Thomas Jefferson to his grandson Thomas Jefferson Randolph. The Brown Bibliography lists the first edition published in London in 1748. George Wythe's Library on LibraryThing states "Precise edition unknown. Octavo editions were published in 1748, 1756, 1771, 1779, 1788, and 1796." The Wolf Law Library has yet to purchase a copy of McLaurin's Treatise of Algebra.

See also

• Jefferson Inventory
• Wythe's Library

External Links

Read the 1748 edition of this book in Google Books.