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Mathematical Treasure: Metius on Applications of Arithmetic and Geometry

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

Adriaan Metius (1571-1635) published Manuale arithmetice et geometrie practice in 1634.  Although Metius had published an earlier arithmetic and geometry text in 1626 (see Mathematical Treasure: Arithmetic and Geometry of Metius), this new work was much more comprehensive and stressed the practical applications of mathematics.

Title page of Manuale arithmetice et geometrie practice by Adriaan Metius, 1634

In his introductory pages, he explains the rationale for the work.

First page of preface from  Manuale arithmetice et geometrie practice by Adriaan Metius, 1634

Second page of preface from  Manuale arithmetice et geometrie practice by Adriaan Metius, 1634

Third page of preface from  Manuale arithmetice et geometrie practice by Adriaan Metius, 1634

On the first pages of instruction, the author discusses the four operations of mathematics.

Page 1 of  Manuale arithmetice et geometrie practice by Adriaan Metius, 1634

Page 2 of  Manuale arithmetice et geometrie practice by Adriaan Metius, 1634

Page 7 includes an illustration of the multiplication of two multi-digit numbers. The algorithm employed is readily recognized as the modern accepted form.

Page 7 of  Manuale arithmetice et geometrie practice by Adriaan Metius, 1634

On page 15, an example of the “downward method" of division is demonstrated. It is noted that in this instance eight separate operations (subtractions) must be undertaken.

Page 15 of  Manuale arithmetice et geometrie practice by Adriaan Metius, 1634

The discussion of geometry includes a categorization of polygons: triangles, quadrilaterals and regular and irregular others.

Page 79 of  Manuale arithmetice et geometrie practice by Adriaan Metius, 1634

The mathematics of land survey and layout is discussed.

Page 93 of  Manuale arithmetice et geometrie practice by Adriaan Metius, 1634

Page 203 of  Manuale arithmetice et geometrie practice by Adriaan Metius, 1634

Page 204 of  Manuale arithmetice et geometrie practice by Adriaan Metius, 1634

Solid geometry is considered later in the text.

Page 119 of Manuale arithmetice et geometrie practice by Adriaan Metius, 1634

Page 125 of  Manuale arithmetice et geometrie practice by Adriaan Metius, 1634

The full work can be viewed courtesy of the University of Bordeaux, Library of Science and Technology, through BabordNum.

Index to Mathematical Treasures

Frank J. Swetz (The Pennsylvania State University), "Mathematical Treasure: Metius on Applications of Arithmetic and Geometry," Convergence (January 2020)

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