Squaring Curved Figures; a Note on Etching Plates for Print
Removing equal areas to square lunes, with a recipe for etching relief letters onto a plate
The recto opens with a technical recipe headed 'On casting this work in print': the plate is grounded with white lead in egg, the design scratched in mirror-writing, varnished with lead-tin yellow or red lead, then soaked so the ground lifts and leaves the letters standing in relief on the copper, which is finally tinted with sulphur fume. The rest of the sheet returns to geometry, squaring curvilinear figures by removing equal areas from two equal surfaces and comparing circle-portions in ratios of 1/16 to 1/8 and 1/3 to 2/3. Two tall cone-like figures and smaller triangles illustrate the demonstrations.
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Etching letters in relief on a plate for printing
The plate is grounded with white lead in egg and the letters scratched in reverse; after varnishing with lead-tin yellow or minium and soaking, the ground and red lead break away, leaving the letters in relief on the copper. Mixing the minium with Greek pitch makes it more brittle, and sulphur fume tints the plate so the letters read clearly.
Squaring a curved figure by removing equal areas
From two equal surfaces n o m f and o f g the common area o f is removed, so the remainders n m and g are equal; taking the rectilinear m from g leaves a straight-sided area equal to the curvilinear n, squaring it.
Subtracting triangles to recover a set-aside portion
Having squared n and set aside o, Leonardo subtracts the rectilinear triangle m f from the larger triangle f g so that the remainder is squared and equal to the portion set aside, since g alone equals n m.
Circle-portions in ratios 1/16 to 1/8 and 1/3 to 2/3
Because the portions are born of circles double one to another, 1/16 of the greater equals 1/8 of the lesser, and if o is 1/3 of n then n is 2/3 of o; subtracting o from each portion leaves c equal to n.
