Quadrature of Triangles with Two Curved Sides
Squaring a curvilinear triangle by adding and subtracting squarable parts; with small drawn fittings
The upper sheet is filled with figures of triangles bounded by two curved sides, their curvatures born of 'sub-double' circles. Leonardo argues that such a curvilinear triangle b a c can be squared: knowing that the triangle b a d is squarable, he removes from it the equal and likewise squarable triangle c a d, and concludes by the maxim that 'drawing the known part from a known whole, the remainder is known.' Between the geometrical figures are drawn a row of small metal fittings or instrument tips and a long tapering instrument.
On this page
Figures of triangles with two curved sides
The sheet is headed with a double figure of triangles bounded by two curved sides, lettered a-d c-e b, laying out the curvilinear forms whose squaring is then argued in the notes.
Squaring the curvilinear triangle b a c
The triangle b a c, its sides curved from sub-double circles, is squared through the squarable triangle b a d; from that Leonardo removes the equal, squarable triangle c a d, so that by 'taking the known part from a known whole, the remainder is known,' triangle b a c and its parts become measurable.
Small fittings and a tapering instrument
Between the geometrical figures a row of small metal fittings or instrument tips is drawn, together with a long tapering instrument reaching across the lower left, distinct from the mathematical figures.