Pietro Mengoli's 1650 Proof that the Harmonic Series Diverges

摘要

Pietro Mengoli proved that harmonic series diverges in his 1650 Novae quadraturae arithmeticae - the first published proof of this result. His proof is discussed in a number of places in the secondary literature, but is often misrepresented in a crucial manner. We give a full English translation of the proof with explanatory notes and argue for a less anachronistic interpretation of it.