Two Triangles in Discontinuous Proportion (Euclid, Book VI)
Under the heading 'Sixth book', triangles measured to show discontinuous proportion
Under the heading 'Sixth book' — the sixth book of Euclid, on ratio and proportion — Leonardo draws two triangles whose sides carry the values 3, 6, 9 and 2, 4, 6 and calls their relation a 'discontinuous proportion' (proporzione incontinua). A second pair of triangles below repeats the exercise with the values 16, 8, 12 against 4, 2, 3. The two examples compare sets of proportional magnitudes through simple line figures.
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Two triangles in discontinuous proportion
Opening a section headed 'Sixth book' (the sixth book of Euclid, on proportion), Leonardo draws two triangles whose sides are marked 3-6, 9 and 2-4, 6, labelled a, b, c and d, e, f. He names the case 'discontinuous proportion' (proporzione incontinua), where the four terms compared are all distinct.
A second pair of triangles
A further pair of triangles is set below with the values 16-8, 12 and 4-2, 3, again labelled a, b, c and d, e, f. The two rows of numbers form matching ratios, continuing the study of proportional magnitudes.