In 1343 appointed, by the bull Unigenitus Dei filius, that the jubilee should recur every fifty years instead of every hundred years as had been originally contemplated in the constitution of Boniface; Urban VI., who was badly in need of money, by the bull Salvator foster ij1 1389 reduced the interval still further to thirty-three years (the supposed duration of the earthly life of Christ); and Paul II.
At Winsford, where the same formation seems to recur, it is 159 yds.
Similar situations recur in the reigns of Ahaz and Jehoram.
In the Avesta all these recur ad nauseam, so much so that the primitive spirit of the religion is stifled beneath them, as the doctrine of the ancient prophets was stifled in Judaism and the Talmud.
If b 2 /a 2, 3 /a 3 ..., the component fractions, as they are called, recur, either from the commencement or from some fixed term, the continued fraction is said to be recurring or periodic. It is obvious that every terminating continued fraction reduces to a commensurable number.