The text on the page is enclosed within a highly decorative rectangular woodcut border featuring intricate floral and foliate scrollwork patterns.

TO THE MOST CHRISTIAN KING.

admiration of the world shine in your royal person. I will therefore restrict myself to saying only that (it is a long time ago) having been called and urgently solicited in Italy in the name of Your Majesty to move myself with honorable condition to the service of this your most invincible Crown, and I, knowing I had encountered the most magnanimous and glorious King who today reigns over Europe among Christians, just as I owe infinitely to your divine qualities and very rare gifts that Heaven has scattered in you, so I have wanted to dedicate to your most prudent and sacred valor these my Mathematical or, if we wish to call them, Mechanical Demonstrations. Which most humbly and with all the reverence possible to me, I present as a small vow consecrated to the golden Temple of your immortal virtues. I hope, besides the fact that they will bring you no little pleasure and contentment when you, being distracted somewhat from your royal affairs, will take pleasure in reading them and at times having them put into operation, that they will also serve for the greatest convenience to all your valiant captains and soldiers for facilitating and putting into effect your marvelous enterprises, every time that you, drawn by your courageous and invincible valor, present yourself (as you are accustomed to do) armed in war. They will also serve me as a unique pledge and testimony of the observance and most affectionate devotion that I bear to your most gracious and divine Name. And although my eyes are not so blind that they do not see well enough by themselves that the smallness of my understanding does not sustain the height of your sublime values, nevertheless those signaled favors which your royal benignity has always used toward me, the singular affection that you demonstrated to me at La Rochelle, when for your service I remained a prisoner and wounded to death in the hands of your enemies, the particular care and protection that you took first in Paris for my son, and finally the most amiable letters that you deigned to write back to me from Poland, when that ample kingdom had heard the sound of your terrifying