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Mathematical Treasure: Forestani's Arithmetic and Geometry

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

Lorenzo Forestani (d. 1623) was an Italian Catholic priest of a Franciscan order. Little else is known of him, but obviously he knew mathematics and was probably a teacher of the subject. His comprehensive book, Pratica d’arithmetica e geometria, published in 1603 and containing 550 pages, is an example of good pedagogical practice: the writing is concise, illustrations strategically employed, explanations thorough, and problem situations colorful. His solution of the “points problem” to produce a fair distribution of gambling winnings is noteworthy. The following images are from a 1682 edition.

Title page of Pratica d’arithmetica e geometria by Lorenzo Forestani, 1682

An introduction to the five operations of arithmetic:

Page 6 of Pratica d’arithmetica e geometria by Lorenzo Forestani, 1682

Groupings by tens in numeration are demonstrated through “millions of millions”:

Page 7 of Pratica d’arithmetica e geometria by Lorenzo Forestani, 1682

A diagram helps explain multiplication by the “chain rule”:

Page 24 of Pratica d’arithmetica e geometria by Lorenzo Forestani, 1682

The concept of a fractional fourth is graphically explained:

Page 44 of Pratica d’arithmetica e geometria by Lorenzo Forestani, 1682

The division of common fractions is discussed with the use of illustrative problems:

Page 45 of Pratica d’arithmetica e geometria by Lorenzo Forestani, 1682

The sixth book or section is on geometry. It begins with a concise set of definitions.

Page 432 of Pratica d’arithmetica e geometria by Lorenzo Forestani, 1682

Page 433 of Pratica d’arithmetica e geometria by Lorenzo Forestani, 1682

Polygonal dissections lend themselves to land measure.

Page 455 of Pratica d’arithmetica e geometria by Lorenzo Forestani, 1682

The quadrature of the circle is given a detailed discussion:

Page 484 of Pratica d’arithmetica e geometria by Lorenzo Forestani, 1682

A brief consideration of solid geometry ends with real world applications.

Page 501 of Pratica d’arithmetica e geometria by Lorenzo Forestani, 1682

The seventh and last book of the work focuses on the mathematics of surveying. Various practical situations are illustrated and discussed.

Page 519 of Pratica d’arithmetica e geometria by Lorenzo Forestani, 1682

Page 542 of Pratica d’arithmetica e geometria by Lorenzo Forestani, 1682

Page 548 of Pratica d’arithmetica e geometria by Lorenzo Forestani, 1682

Page 532 of Pratica d’arithmetica e geometria by Lorenzo Forestani, 1682

The images above were obtained through the courtesy of the University of Michigan via the HathiTrust.

Index to Mathematical Treasures

Frank J. Swetz (The Pennsylvania State University), "Mathematical Treasure: Forestani's Arithmetic and Geometry," Convergence (February 2020)

Dummy View - NOT TO BE DELETED