Another question concerns the oscillations of pendulums, and it falls into two parts. One is whether all oscillations, large, medium, and small, are truly and precisely made in equal times. The other concerns the ratio of times for bodies hung from unequal threads; the times of their vibrations, I mean. … As to the prior question, whether the same pendulum makes all its oscillations – the largest, the average, and the smallest – in truly and exactly equal times, I submit myself to that which I once heard from our Academician [Galileo]. He demonstrated that the moveable which falls along chords subtended by every arc [of a given circle] necessarily passes over them all in equal times. …

As to the ratio of times of oscillations of bodies hanging from strings of different lengths, those times are as the square roots of the string lengths; or should we say that the lengths are as the doubled ratios, or squares, of the times.