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TO THE MOST CHRISTIAN KING.

most invincible Crown of yours, and knowing I that I have had in lot a more magnanimous and glorious King than reigns today in Europe among Christians, just as I owe without end to the divine qualities and rarest 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 every possible reverence I now offer you, as a small vow consecrated to the golden Temple of your immortal virtues. I hope, besides that they will bring you not little pleasure and contentment when You, abstracted somewhat from your royal affairs, will take delight in reading them and at times having them put into operation, that they will serve also easily for the greatest convenience to all your valiant Captains and soldiers in facilitating and effecting your stupendous enterprises, every time that You, drawn by your strenuous invincible valor, present yourself (as you are accustomed to do) armed in war. To me together they will suffice as a unique pledge and testimony of the observance and most affectionate devotion that I bear to your most gracious and divine Name. And even if my eyes are not so blind that they do not see well enough by themselves that the lowness of my talent does not sustain the height of your sublime merits, nonetheless those signaled favors that your Royal kindness has always produced toward me, the singular affection that you showed me at La Rochelle original: "la Roccella", while I remained a prisoner for your service and wounded to death in the hands of your enemies, the particular care and protection that you primarily had taken in Paris of my son, and finally the most loving letters that you deigned to write to me even from Poland, after that ample Kingdom, having heard the cry of the most intrepid valor and most prudent judgment that with other infinite virtues reigns in your Royal and Heroic breast, had (as only one worthy in the world) above so many other Kings and Princes who competed for that crown, with inenarrable applause and triumphant joy of those Palatines original: "Palatini" - high-ranking nobles of Poland, and of all those peoples, elected and almost by force led to crown themselves their King. All which favors of your ingenuous mind, which in every century will impress me, and more than ever now are impressed, in my memory; just as inviolably