TREATISES WHICH ARE

contained in this volume.

Arithmetical Theorems.
On the principles of the operations of perspective.
On Mechanics.
Disputations on certain opinions of Aristotle.
On the fifth book of Euclid.
Physical and Mathematical responses by way of Letters.

TO THE MOST SERENE

CHARLES EMMANUEL

Duke of Savoy, etc.

Decorative woodcut initial 'A' featuring floral motifs and architectural scrollwork.

IT IS NOW the nineteenth year since, summoned by the letters of the most Serene father of your Highness, I betook myself from the city of Parma to this city. He received me so kindly upon my arrival, and thereafter embraced me with such great liberality, that I, in turn, was kindled with so vehement a desire to serve him, that I resolved to spend what remained of my life under his rule. His kindness toward me, and my respect toward him, increased in a wondrous manner through mutual familiarity and custom, so that the same Duke wished me to be with him while he stayed in the country, and often even to stay overnight; at which time indeed he would discuss the Mathematical sciences with me, in the learning of which he employed my assistance, proposing questions concerning Arithmetic, Geometry, Optics, Music, or Astrology. So that I might satisfy him to the best of my ability, I applied myself more sharply than before to those studies (toward which, however, I was always most inclined). And by his imitation (as others generally imitate the pursuits of Princes), not a few, either in person or by letters, consulted me concerning various Mathematical questions. And since I have never shunned labor for the sake of friends, it happened that after the course of so many years, having searched through my desks, I found so many completed questions that it seemed a modest volume could be formed from them. Since I had decided to publish these for the reasons set forth in the following letter, I wished them to appear under no other name and auspices than those of your Highness; both because it was fitting to return to the son a book owed to the father, and because...