Pythagorean proof on sides 6, 8 and 10
Squares on 6, 8 and 10 with the numerical check 100 = 64 + 36
This leaf continues the Pythagorean study with a second figure: squares built on sides 6, 8 and 10, their sides labelled with those numbers. Leonardo proves that the line a d is the side of the square that contains within itself the squares n and m. He carries out the arithmetic explicitly: 10 times 10 is 100, 8 times 8 is 64, and 6 times 6 is 36, so that 64 and 36 together make 100.
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Squares on sides 6, 8 and 10; line a d as the containing side
The diagram shows squares whose sides are marked 6, 8 and 10, with a tilted square of side 10 adjoining an upright square of side 8. Leonardo argues that the line a d is the side of the square that holds within itself the square n and the square m. The largest square is thus shown to contain the two smaller ones.
The check 10x10 = 8x8 + 6x6 (100 = 64 + 36)
The proof is completed numerically: the side of the containing square is 10, and 10 times 10 makes 100. The middle square's side is 8, giving 8 times 8 as 64, and the smallest side is 6, giving 6 times 6 as 36. The 64 and the 36 together make 100, confirming the relation.