Equal Rectangles with Reciprocally Proportional Sides
Rectangles of area 12 joined and completed
A pencil page headed with a note on 'reciprocal sides' and sketches of rectangles that are joined and then completed. The measures given, 6 and 2, then 3 and 4, each multiply to 12, so the rectangles are equal in area while their sides stand in reciprocal proportion, a result from Euclid's Book VI. A last analogous figure is drawn without numbers. The pencil work is faint.
On this page
Rectangles equal in area
The first rectangle is marked a 6 d, 12, 2, b c, and is joined to a second marked e 3 - 4, 12, 12. Since 6 by 2 and 3 by 4 both give 12, the two rectangles enclose equal areas.
Reciprocally proportional sides
The heading notes 'reciprocal sides': in rectangles of equal area the sides are reciprocally proportional, so that as one side grows the other shrinks to keep the product constant. The joined-and-completed figure carries the numbers 12, 2, 6 and 6, 3, 4 illustrating this.