Water-wheel machine for polishing a concave form
With geometric studies of squares, a right triangle and a converging conic curve
A crank driven by a water wheel pulls two opposed cords, in the manner of water-saws, to grind and polish a concave surface against a matching convex one, while a winch (argano) on the convex 'bridge' lifts the rubbed piece on hooks S t so its progress can be inspected from within. The lower part of the leaf carries geometric figures: a square divided into rectangles, a square enlarged by an added right triangle, and a conic curve whose long sides are said to meet at a point ten thousand braccia away. A closing note treats the beginning of the template's curvature and a lance of uniform thickness leaned against the angle n.
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Water-wheel crank and winch for grinding concave over convex
The crank of the water wheel sets its front into a ring to which two cords are tied oppositely, as in water-saws, so that the concave piece is polished upon the convex one. The winch of the frame at the front of the convex bridge raises the rubbed concavity, fastened by the hooks S t, only so its polishing can be seen from within.
Square with an added right triangle and a converging conic
Let the square be a f c d, 10 braccia on each side, to which is added the right-angled triangle b a c whose legs are 1/100 and 1000/100 of a braccio. The two sides a b and f then meet at a point ten thousand braccia away, plus the 10 braccia of the added triangle. A perpendicular c m is dropped on line b d and a lance of uniform thickness leaned against angle n.
Squares divided into rectangles
A square is decomposed into rectangles with an added triangle, labelled a f and b c e. A second, enlarged square carries the labels a b, c d f and m. These proportional divisions accompany the study of the template's curvature.