Rectifying the Hemisphere and Half-Oval
Finding the true lengths of the rings that clothe a hemisphere
Leonardo rectifies the curved surface of a hemisphere and of a half-oval solid. A domed hemisphere with parallel rings appears at the upper right, with a fan-shaped spread and a small triangle beside it. The whole revolution of the sphere's greatest circle makes the straight line a b, its quarter revolution the line a d; dividing the periphery a d into four equal parts gives four parallels between the lines a b, b c, c a with their true lengths, corresponding to the four rings that clothe the hemisphere a d f.
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Quarter revolution of the great circle straightened to a c
The whole revolution of the sphere's greatest circle makes the straight line a b, and its quarter revolution the straight line a d, so the curve d a straightened makes the straight line a c. Dividing the periphery a d into four equal parts, and a c likewise, yields four parallels between a b, b c and c a giving the true lengths of the four rings clothing the hemisphere a d f.
Triangle a b c equal to the skin of the half-oval
The rectilinear a b equals the curvilinear a c, and the whole triangle a b c equals the whole skin of the half oval figure divided into five annular parallels. The curved surface is thus reduced to a plane triangle.