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Mathematical Treasure: De Morgan’s Trigonometry (1837)

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

The British mathematician Augustus De Morgan (1806-1871) was particularly noted as an excellent teacher. All of his texts were written with the learner in mind: De Morgan supplied details and insights tailored especially for the student. De Morgan’s Elements of Trigonometry and Trigonometrical Analysis (1837) provides a good example of this policy.

Title page for Elements of Trigonometry and Trigonometrical Analysis by Augustus De Morgan

De Morgan provided a detailed explanation of the basic trigonometric functions as functions.

Page 16 of Elements of Trigonometry and Trigonometrical Analysis by Augustus De Morgan

Using a geometric demonstration, De Morgan “connected” the functions, showing their relationships to each other.

Page 22 of Elements of Trigonometry and Trigonometrical Analysis by Augustus De Morgan

Page 23 of Elements of Trigonometry and Trigonometrical Analysis by Augustus De Morgan

This text was written for future university calculus students. The differentiation of the trigonometric functions is discussed. Note the “operator” form of the derivative.

Page 108 of Elements of Trigonometry and Trigonometrical Analysis by Augustus De Morgan

Page 109 of Elements of Trigonometry and Trigonometrical Analysis by Augustus De Morgan

The images above were obtained through the courtesy of the University of California Libraries. The book may be viewed in its entirety in the Internet Archive.

Index to Mathematical Treasures 

Frank J. Swetz (The Pennsylvania State University) , "Mathematical Treasure: De Morgan’s Trigonometry (1837)," Convergence (January 2018)

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