"There is an important curve not known to the ancients which now began to be studied with great zeal. Roberval gave it the name of" ," Pascal the name of "roulette," Galileo the name of "." The invention of this curve seems to be due to Charles Bouvelles who...in 1501 refers to this curve in connection with the problem of the . Galileo valued it for the graceful form it would give to arches in architecture. He ascertained its area by weighing paper figures of the cycloid against that of the generating circle and found thereby the first area to be nearly... thrice the latter. A mathematical determination was made by his pupil ... By the Method of Indivisibles he demonstrated its area to be triple that of the revolving circle and published his solution. This same quadrature had been effected a few years earlier (about 1636) by Roberval in France, but his solution was not known to the Italians. ... another prominent pupil of Galileo, determined the tangent to the cycloid. This was accomplished in France by Descartes and Fermat."