Dividing a line and its square into three parts
A square of side 12 split into strips of areas 48, 36 and 60
Horizontal lines and the rectangles built on them are cut into three parts marked a, d, c, b, and the areas are worked out in numbers. A square of side 12, whose area is 144, is divided into three strips of areas 48, 36 and 60 taken from widths 4, 3 and 5. Another example apportions a total of 120 across parts read as 10, 20, 70, 30 with a companion ratio 2, 7, 3.
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Square of side 12 divided into three strips
A square of side 12, area 144, is split into three vertical strips whose areas are given as 48, 36 and 60. These follow from widths 4, 3 and 5, which together make the side of 12.
Apportioning 120 across parts
A rectangle divided into three parts carries the total 120 distributed as the figures 10, 20, 70, 30, alongside a smaller ratio 2, 7, 3. The numbers show the same division carried through arithmetically as well as in the figure.
Line divided into three parts a d c b
A horizontal line is marked off into three segments at the points a, d, c, b. The lettered division fixes the widths that are then raised into the strips of the rectangle above and below.