Measuring All Kinds of Fields

Abstract

The longest of the eight chapters, Chapter 3 focuses on measuring fields of all geometric descriptions. Within its scope are triangles, quadrilaterals, other polygons with straight sides, circles and their parts, and oblique figures with straight and curved sides including fields along the sides of mountains. Fibonacci began the measurement of triangles in a very general way, identifying the three types of triangles and stating what is necessary to find the area of each, enough information to satisfy practitioners, but not so for theoreticians. For the latter and considering the various types of triangles, he discussed all possible ways an altitude may be drawn (he used the word cathete for altitude). A few remarks on the Pythagorean theorem, the use of Hero’s formula for finding the area of a triangle given the lengths of its sides, and the method used by surveyors to measure fields rounds out the section on the measurement of triangular fields.