Franco of Liège: De Quadratura Circuli

Franco, master of the cathedral school of Liège in the eleventh century, wrote a treatise in six books on squaring the circle, the problem of constructing a square equal in area to a given circle. The text printed here is brief and consists mainly of the prologues. In the first, Franco addresses a high-ranking churchman, his patron, explaining that he has no gold, horses, embroidered garments or gems to offer in return for his generosity and so offers the fruit of his study instead. In another, he notes that the problem has defeated the learned men of Italy, Gaul and Germany, including Adelbold, the great teacher Wazo, and Gerbert, the restorer of learning.

Franco’s work is one of the most notable mathematical treatises of the eleventh century in the Latin West, an attempt to solve a classical problem with the limited geometrical knowledge then available. The prologues are valuable for showing the scholarly community of the Lotharingian schools and the reputation of figures such as Gerbert, later Pope Sylvester II, as authorities in the mathematical arts. Readers should note that the treatise itself is only partly represented here.