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many friends, to whom I could not honorably refuse, first so that I might translate Apollonius himself as clearly as I could, and in this part, which seemed to need help the most, I might succor the nearly sick and struggling mathematical discipline; and then, in truth, so that I might make the lemmata of Pappus and the commentaries of Eutocius on Apollonius into Latin. In these, because they were affected by many faults, I spent even more labor and work than I did on Apollonius himself, since I found it necessary in many places to restore entire demonstrations, of which hardly any traces appeared. Afterwards, because I was already inflamed with a more vehement love for the work begun and a zeal for common utility, as I have always been otherwise, I also wished to declare them with my own commentaries so that everything might be easier to know. It came about that I brought no small amount of light and splendor—as the thing itself will indicate to those who wish to learn—to a doctrine once wrapped in the infinite shadows of antiquity and ignorance. Therefore, whatever these may be, I publish and disseminate them all at this time, bound in one volume in your name for the common utility of all, GUIDOBALDO, most excellent Duke. When I do this, I do not only serve my duty, so that I may follow with all cultivation and observance him in whose dominion and command I was born, but I also follow the example of the most learned men in this: that they should especially adorn with all literary monuments the one from whom letters have received the most ornament and support. You, however, are the one to whom the studies of learning themselves owe a great part of the ornaments that your family retains. For FEDERICO, your great-grandfather, who first brought the Ducal honor into your family, not only flourished with many praises in military affairs, but also gained the greatest glory for himself because he always uniquely loved letters and learned men. This is testified to by the many books published in his name by learned men, as well as by his library, wonderfully stocked with a wealth of Hebrew, Greek, and Latin books. His son GUIDOBALDO followed his footsteps, and he himself, besides the hereditary praise of warfare, was learned in all letters and always took wonderful delight in the talent of learned men. These same men were embraced and cultivated with the greatest zeal by his grandson FRANCISCUS MARIA, your own father, although he was intent on the study of military affairs, in whose glory he flourished beyond others. You have succeeded to the praises of all these in such a way that you do not have to draw much for your own honor from paternal and domestic glory. For you hold military affairs in such a way that you excel in them, and you are as learned in Latin and Greek letters as if you had spent your whole life in this study. There-