JOHANNES KEPLER’S

PREFACE TO DIOPTRICS, ON THE USE AND EX-

cellence of the recently invented telescope: and concerning the new celestial

wonders detected through it.

I am presenting a mathematical booklet, friend reader, that is not so easy to grasp: it is one that requires not only intelligence in the reader, but also a particular focus of mind, and an incredible desire to understand the causes of things.

While I consider this, it seemed appropriate to comment on the excellence of Dioptrics or Telescopes original: "Perspicillorum", and their wonderful effect in extending the boundaries of philosophy: so that talented youths and other cultivators of Mathematics, spurred on by this incentive of usefulness, might be encouraged to grasp the principles of the instrument from this booklet.

Many and great are the things which Jean Pena of France original: "Ioannes Pena Gallus," a 16th-century mathematician who challenged the idea that the heavens were made of solid spheres., formerly Royal Mathematician, wrote in his preface concerning the use of the whole of Optics in his edition of Euclid’s Optics and Catoptrics, which he himself translated: yet, however great those things may be, compared to those which have been revealed in this past two-year period by the benefit of telescopes original: "dioptrarum", they can be considered plainly childish.

And because I recommend that preface to the reader by this mention, come, let us examine its principal points briefly; lest I should seem to have knowingly and deliberately concealed the doubtful and false things which I cannot deny are interspersed there among the true and famous things. When I have completed this, then finally I will add those new things which the discipline of the Telescope original: "Perspicillaria disciplina" has detected in this time.

First, I establish with Pena a dogma concerning the Heavens, solidly demonstrated from Optics: namely, that the physicists—and even some theologians—are vehemently deceived when they think there are nine or ten transparent spheres embracing this Elementary world, just as the white of an egg usually embraces the yolk, or as the layers of an onion enclose one another. For since the eccentric paths of the planets are established by necessary reasoning, it is correctly gath- The text ends mid-word on the Latin "colligit," meaning "gathered" or "inferred."