Euclid manages to obtain a rigorous proof without ever dealing with infinity, by reducing the problem [of the infinitude of primes] to the study of finite numbers. This is exactly what contemporary mathematical analysis does.

Many scholars have felt that the Heronian passage [on a pipe-organ moved by an anemourion-like wheel] can be disregarded because it is not confirmed by other writings. Heron presumably mentioned the anemourion in a moment of distraction, forgetting that it had not been invented yet. We know that he was given to such lapses.

Unfortunately, the optimistic view that "classical civilization" handed down certain fundamental works that managed to include the knowledge contained in the lost writings has proved groundless. In fact, in the face of a general regression in the level of civilization, it's never the best works that will be saved through an automatic process of natural selection.

The age-long history of thinking on gravitation, too, was erased from the collective consciousness, and that force somehow became the serendipitous child of Newton's genius. The new attitude is well illustrated by the anecdote of the apple, a legend spread by Voltaire, one of the most active and vehement erasers of the past. ... The need to build the myth of an ex nihilo creation of modern science gave rise to much impassioned rhetoric.

The oft-heard comment that Leonardo [da Vinci]'s genius managed to transcend the culture of his time is amply justified. But his was not a science-fiction voyage into the future as much as a plunge into the past.

Since UFO stands for "unidentified flying object", the word ufology means approximately "knowledge about unknown flying objects", and is therefore a "science" whose content is void by definition. Similar considerations hold for parapsychology.

Today Eratosthenes' method [of calculating the circumference of the earth] seems almost banal... yet it is inaccessible to prescientific civilizations, and in all of Antiquity not a single Latin author succeeded in stating it coherently.