Squaring segments and forming rectangles from products
13 and 169, 12 and 6 giving 36, a segment split into 9 and 4
A column of figures, read from right to left, pairs line segments with numbers: one segment is marked 13 above and 169 below, giving a value and its square, while others are marked 13, 12 and 12. A parallelogram and a square divided into four each carry the label a. Lower down a segment split into the parts 9 and 4 bears a parallelogram of height 4 whose area is given as 36, another shows 12 with 6 and 6 set against the product 36, and the last segment is divided into the unequal parts 2 and 8. The sheet works out squares, products and the division of lines as geometric areas.
On this page
A segment and its square (13 and 169)
A line segment is marked 13 above and 169 below, presenting a number together with its square. Nearby single segments are labeled 13, 12 and 12.
Product shown as a rectangle: 9 and 4 give area 36
A segment is divided into the parts 9 and 4, and a parallelogram of height 4 built over it is given the area 36, the product 9 by 4. A further figure sets a segment marked 12 above and 6 below (twice) against the product 36, separated by a pen stroke.
A line divided into the parts 2 and 8
The segment at the foot of the first column is divided into the unequal partitions 2 and 8. Above it a square is quartered, with one part and the central crossing point both labeled a.