The gnomon and Thabit's theorem ('De Tebit')
A smaller square, a larger square and a gnomon that 'does not alter,' with a right triangle and its squares
The folio is headed 'De Tebit' (Thabit ibn Qurra) and explores the gnomon: a smaller square and a larger square are related by a gnomon which, Leonardo notes, 'does not alter' the figure. Two constructions build the gnomon around the smaller square, and a right triangle with squares on its sides is added, cited 'by the penultimate, by the 20th and by the third of the first' (Euclid I.47, I.20, I.3). The diagrams show the smaller square with its base extended and the resulting gnomon figures.
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Smaller and larger squares related by a gnomon
A smaller square (labelled a - b) and a larger square (labelled c - d) are set against a gnomon figure. The gnomon is the L-shaped region between the two squares.
'The gnomon does not alter' the figure
An analogous figure repeats the gnomon and is annotated that the gnomon does not alter [the figure]. The remark isolates the gnomon as the area added without changing the underlying square relation.
Right triangle and squares on the sides added to the square
The smaller square with its base extended has a right triangle added, justified 'by the penultimate, by the 20th and by the third of the first' (Euclid I.47, I.20, I.3). A right triangle with squares on its sides accompanies the construction.
Constructing the gnomon around the smaller square
Two figures are given for the construction of the gnomon around the smaller square. Together with the extended-base square they show how the gnomon is fitted around it.