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Mathematical Treasure: 18th Century German Geometria

Frank J. Swetz (The Pennsylvania State University)

An anonymous German manuscript, Geometria, estimated to be from the early eighteenth century, covers a broad scope of topics: plane geometry, trigonometry, logarithms, stereometry, perspective, and horology. The manuscript begins with a “Table of Geometric Abbreviations and Symbols.” Note the term “mixta” referring to an irregular curve.



Chapter II considers various geometric construction “Problems.”                                        

Chapter III introduces the reader to “Theorems.”

Constructions in the plane and their applications to land measure and surveying are considered.

Chapter X, Trigonometry, begins with a geometric definition of the basic circular functions as ratios.

An example is provided in how to employ trigonometry in determining inaccessible distances, i.e. the width of a river.

The images above were obtained through the courtesy of the University of Pennsylvania Libraries. The complete item can be viewed via its reference number, LJS 320.

Index to Mathematical Treasures

Frank J. Swetz (The Pennsylvania State University), "Mathematical Treasure: 18th Century German Geometria," Convergence (June 2017)