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Mathematical Treasure: Alexander's Synopsis Algebraica

Frank J. Swetz (The Pennsylvania State University)

Figure 1. Title page of Synopsis Algebraica

Synopsis Algebraica (1693) was written for the teaching of mathematics at Christ’s Hospital, London. The interesting feature of this book is that it is a mathematical workbook; opposite each page of text is a blank page allowing for annotations and computations. Little is known about the original author, Johann Alexander, other than that he identified himself as being from Bern, Switzerland, and he was dead by 1693, as the book was published posthumously. An edited and corrected version of this work was made by the British mathematician Humphrey Ditton (1675-1715) and published in 1709. Ditton served as the Mathematics Master at Christ’s Hospital.

Figure 2. Page 28 of Synopsis, containing an explanation of cube root extraction, and the originally blank page opposite it

Page 28 (see Figure 2, above) contains a discussion of cube root extraction. Note the use and development of symbolism. The cube root is first expressed as cub. and then shortened to c. Further down the page, several examples of extraction of cubes are given. On the page opposite page 28, it appears that a student developed a cubic equation by using a diagram to obtain a quadratic equation and then multiplying the equation by its factor, \((a + b).\)

Figure 3. Page 60 of Synopsis, and its opposite page, where a student has written several equations in attempting to solve Problem 35. Are the equations correct?

These images are presented courtesy of Archives and Special Collections, Dickinson College, Carlisle, Pennsylvania. You may use them in your classroom and/or for private study; for all other purposes, please obtain permission from Archives and Special Collections, Waidner-Spahr Library, Dickinson College, Carlisle, PA.

Index to Mathematical Treasures

Frank J. Swetz (The Pennsylvania State University), "Mathematical Treasure: Alexander's Synopsis Algebraica," Convergence (February 2014)