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34 years of age, and begged him to publish a description of it. In his work Scholarum Mathematicarum Libri XXXI., published at Basle in 1569 (only a few months before his conversation with Tycho), Ramus had advocated the building up of a new astronomy solely by logic and mathematics, and entirely without any hypothesis, and had referred to the ancient Chaldeans and Egyptians as having had a science of this kind, which had gradually by Eudoxus and that terrible Aristotle been made absurd through the introduction of solid spheres and endless systems of epicycles. Ramus explained his views to Tycho (who has left us an account of this conversation ); but he answered that astronomy without an hypothesis was an impossibility, for though the science must depend on numerical data and measures, the apparent motions of the stars could only be represented by circles and other figures. But though Ramus could not bring over the young astronomer to his views, they could cordially agree in the desire of seeing the science of astronomy renovated by new and accurate observations, before a true explanation of the celestial motions was attempted; and it can hardly be doubted that the conversation of this rational, clear thinker (so different from a Leovitius, with his brain crammed full of astrology and other hazy and fanciful ideas) took root in the thoughtful mind of the young astronomer, and bore fruit in after years in that reformation of his science for which Ramus had hoped.

Tycho Brahe left Augsburg in 1570, but the exact month is not known, nor the route by which he travelled. We only know that he passed through Ingolstadt, and called on Philip Apianus, a son of Peter Apianus (or Bienewitz), whose name is well known both by his having pointed