Prove formula (e) of Theorem 3 using the following method published by Abu Bekr Mohammed
Chapter 0, Problem 40(choose chapter or problem)
Prove formula (e) of Theorem 3 using the following method published by Abu Bekr Mohammed ibn Alhusain Alkarchi in about ad 1010. The figure shows a square ABCD in which sides AB and AD have been divided into segments of lengths 1, 2, 3, . . . , n. Thus the side of the square has length nsn 1 1dy2 so the area is fnsn 1 1dy2g 2 . But the area is also the sum of the areas of the n gnomons G1, G2, . . . , Gn shown in the figure. Show that the area of Gi is i 3 and conclude that formula (e) is true
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