Fibonacci's De Practica Geometrie

Leonardo da Pisa, perhaps better known as Fibonacci (ca. 1170 – ca. 1240), selected the most useful parts of Greco-Arabic geometry for the book known as De practica geometrie. Beginning with the definitions and constructions found early on in Euclid’s Elements, Fibonacci instructed his reader how to compute with Pisan units of measure, find square and cube roots, determine dimensions of both rectilinear and curved surfaces and solids, work with tables for indirect measurement, and perhaps finally fire the imagination of builders with analyses of pentagons and decagons. His work exceeded what readers would expect for the topic. Practical Geometry is the name of the craft for medieval landmeasurers, otherwise known as surveyors in modern times. Fibonacci wrote De practica geometrie for these artisans, a fitting complement to Liber abbaci. He had been at work on the geometry project for some time when a friend encouraged him to complete the task, which he did, going beyond the merely practical, as he remarked, “Some parts are presented according to geometric demonstrations, other parts in dimensions after a lay fashion, with which they wish to engage according to the more common practice.”

This translation offers a reconstruction of De practica geometrie as the author judges Fibonacci wrote it. In order to appreciate what Fibonacci created, the author considers his command of Arabic, his schooling, and the resources available to him. To these are added the authors own views on translation and remarks about prior Italian translations. A bibliography of primary and secondary resources follows the translation, completed by an index of names and special words.

• Area
• DEX
• Division
• Euclid
• Fitting
• Geometrie
• Prolog
• boundary element method
• construction
• geometry
• measure
• time

From the reviews:

"This is a translation of a book written in 1223. It was designed for those who had to solve practical problems such as finding areas and roots, measuring fields of all kinds, dividing fields among partners, measuring dimensions of bodies and heights, depths, longitude of planets, etc. It’s a joy to read. The translation is charming. … De practica geometrie belongs in every library that supports graduate mathematics programs and also those that support programs in education." (Donald Cook, Mathematical Reviews, Issue 2008 k)

"In this book Fibonacci not only collected the plane geometry of Euclid but went far beyond. He included the use of trigonometry and algebra to solve geometrical problems … . Each chapter is accompanied by comments which serve as guidelines through the book. The book can be read with much pleasure. … Hughes has certainly presented a major scholarly work and … his translation will be read by many interested mathematicians and historians of science." (Thomas Sonar, Zentralblatt MATH, Vol. 1145, 2008)

• Encino, USA

  Barnabas Hughes

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