TO THE MOST SERENE DON COSIMO DE' MEDICI PRINCE OF TUSCANY, ETC. If Most Serene Prince, I wished to set forth in this place all the praises due to your Highness' own merits and those of your distinguished family, I should be committed to such a lengthy discourse that this preface would far outrun the rest of the text, whence I shall refrain from even attempting that task, uncertain that I could finish half of it, let alone all. Besides, it was not to magnify your splendor (which already shines like a rising sun on all the West) that I took occasion to dedicate the present work to you, but rather that this should always carry the embellishment and ornamentation of your name written in front of it, as in my mind, bringing grace and splendor to its dark shadows. Nor do I step forth as an orator to exalt your Highness' glory, but as your most devoted servitor and humble subject I offer you due tribute as I should have done before, had not your tender age persuaded me to await these years more suited to such studies. I doubt not that this little gift will be gladly received by you, not only because your infinite native gentility so persuades me, but because I am sure this reading is proportioned to your many other regal exercises, besides which experience itself confirms me in this, you having deigned during most of last summer to listen benignly to my oral explanation of many uses of this Instrument. May your Highness therefore enjoy this, my mathematical game so to speak, nobly suited to your first youthful studies. And advancing with age in these truly royal disciplines, expect from my simple mind from time to time those more mature fruits that Divine Grace has conceded it to me to gather. And so, with all humility, I bow to kiss reverently your robe and pray God for your great happiness. From Padua, the 10th of July 1606. From your Highness' Most Humble and Obliged Servant Galileo Galilei.