Leon Battista Alberti, De lunularum quadratura

Abstract

The way of measuring a two-cusped² figure composed of two curved lines as shown in the figure³ Contrary to the opinion of the many who say that figures composed of lines that are curved and circular cannot be squared perfectly, most of all of those that are portions of circles, they say this in my opinion by the authority of Aristotle, who says that quadratura circuli est scibilis, sed non scita quia est impotentia naturœ,⁴ squaring the circle is knowable though not found but it is in nature’ s power; and not being able to give the squaring of the circle perfectly, they argue that it is impossible to give the perfect squaring of figures made of curved lines first and foremost circular ones; since I have found the perfect squaring of the figure shown here, that is, a figure with two cusps in the shape of the moon marked AB, I say that if we had had careful investigators, then if squaring the circle is in nature’ s power, it is likewise in men’ s power. Thus to demonstrate the squaring of said figure AB, after first noting two propositions of Euclid pertaining to the declaration, I will tell the way it is done.