*Demonstrationes mathematicae oder Untersuchung derer mathematischen warheit* *und unwarheiten* (1698) [*Mathematical Demonstrations or Investigations as to Mathematical Truths and Falsehoods*] presents an interesting tour of mathematical ideas and applications. Little is known about the author, Christian Schessler, except that he was German and wrote several books on mathematics, especially arithmetic and geometry. Judging by his writing, he may have been an engineer or architect by profession.

On page 8, under the heading “Other Questions in Geometry,” three tasks or constructions are required: I. Construct a spiral; II. Find the center of gravity for a given triangle; III. Given the irregular polygon \(a, b, c, d, e,\) construct a triangle, a parallelogram, and a square of the same area. The accompanying Table illustrates these situations.

The construction required on page 11 refers to figures 9, 10, and 11 of the previous Table.

On page 32, Schessler discussed the Platonic solids and their properties, as illustrated in the accompanying Table.

On page 60, the author began a discussion of the parabola and its properties. Schessler’s approach to the parabola is rather technical. He appreciates its reflective properties and relates the story of Archimedes setting ships afire with reflected sunrays. He is also mindful of the parabola’s application to trajectories.

*The images above are presented courtesy of the University of Pennsylvania Libraries.*

Index to Mathematical Treasures