Part IV

. (pp. 57-255) contains an elaborate treatise on mathematics, "the

alphabet of philosophy," maintaining that all the sciences rest ultimately on mathematics, and progress only when their facts can be subsumed under mathematical principles. This fruitful thought he illustrates by showing how geometry is applied to the action of natural bodies, and demonstrating by geometrical figures certain laws of physical forces. He also shows how his method may be used to determine some curious and long-discussed problems, such as the light of the stars, the ebb and flow of the tide, the motion of the balance. He then proceeds to adduce elaborate and sometimes slightly grotesque reasons tending to prove that mathematical knowledge is essential in theology, and closes this section of his work with two comprehensive sketches of geography and astronomy. That on geography is

## particularly good, and is interesting as having been read by Columbus, who

lighted on it in Petrus de Alliaco's _Imago Mundi_, and was strongly influenced by its reasoning.

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