# Dividing Fields Among Partners

Part of the Sources and Studies in the History of Mathematics and Physical Sciences book series (SHMP)

The title of the chapter may suggest more than it offers. Except in two problems, there is no discussion of the partners; they are in the background, taken for granted. The emphasis is on the kinds of fields and how to divide them, given a variety of conditions. Fibonacci offered a simple introduction dividing the chapter in four parts, each named after the shape of the field to be partitioned: triangular, quadrilateral, multilateral, and circular. The Table of Contents displays the complexity as the chapter develops, the figures ranging from triangles through quadrilaterals to pentagons, circles, and parts of circles. The conditions for dividing the figures are these: in two equal parts, several equal parts, two parts in a given ratio, and several parts in a given ratio. The divisions contain additional conditions. They require drawing a line that passes through a point situated at a vertex of the figure, at a vertex or a point on a side, on a side not produced, on one of two parallel sides, on the middle of the arc of a circle, on the circumference or outside of the circle, inside the figure, outside the figure, either inside or outside the figure, either inside or outside or on a side of the figure, and in a certain part of the plane of the figure. Furthermore, the line may be drawn parallel to the base of the proposed figure or parallel to the diameter of the circle. It may also be required to draw more than one transversal, such as through one point, through two points, or lines parallel to one another in which case the problem is indeterminate. Finally, circles and their parts are also divided.

## Keywords

Equal Part Draw Line Quadrilateral Abcd
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