Squaring the circle; a water-raising machine and pulleys
Vitruvius and Archimedes on the quadrature of the circle, beside machine studies
The leaf opens with a note on the squaring of the circle: Vitruvius measured miles by counting whole revolutions of cart wheels but never grasped the means of squaring, which Archimedes of Syracuse first found, namely that the semidiameter times half the circumference yields a rectilinear figure equal to the circle. Below, a red-chalk scheme lays out a water-raising machine measured five ounces from pump to pump, with spokes one ounce thick and a scanduppo one ounce. A pulley study lettered m and n reasons that three against one weighs only as one, so n feels two and m feels four.
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Who first squared the circle
Leonardo recounts that Vitruvius, measuring miles by the many whole revolutions of cart wheels, laid out along his stadia many circumferential lines but learned them only from the draught animals and never recognised the means of squaring. That means, he notes, Archimedes of Syracuse first found: multiplying the semidiameter of a circle by half its circumference yields a rectilinear quadrilateral equal to the circle.
Hydraulic-wheel machine, pump to pump
A scheme of the machine with its hydraulic wheel is measured five ounces from one pump to the other, the spokes one ounce thick per side and the scanduppo one ounce.
Parts of the same machine
Further parts of the same machine are drawn out in red chalk and pen, the wheel with its frame and vertical members, without accompanying measures.
Pulleys m and n
A pulley study lettered m and n reasons that three set against one in the balance weighs only as one; therefore n feels two and m feels four.