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Added to this is the fact that Your Highness did not disdain me with your singular favor, of which I could take no obscure indication: the fact that Your Highness has hitherto approved my progress in Mathematics, such as it is, in a greater manner. This matter not only gently confirmed me in those studies, but added spurs to a running horse, so that I have watched, exploring the deeper secrets of Mathematics with a much more ardent affection, when I observed that I was not neglected by so great a prince. But neither, content with these things, did Your Highness disdain to assign an ecclesiastical function to me, although unworthy.
Although these things are common to me with others, they are not the least for me. Rather, I congratulate myself that I live under the patronage of such a Prince, and am fostered by his liberality, to whom sound and uncorrupted religion is dear, and for whom the liberal arts are a care.
While I revolve these and many other things very abundantly bestowed upon me in my mind, I easily understand that I must attend with every thought of my mind, lest the most shameful mark of ingratitude be branded upon me. But when I was thinking about a convenient opportunity to declare a grateful heart (for the duties of my vocation, the salvation of the Church demands that I perform them faithfully with all my might), in the meantime, God showed a new and horrible prodigy, a Comet, of unusual magnitude. I decided that its appearance and motion should be observed by me, since the knowledge of it pertains to the Astronomer. But while I investigated its errors, I found that it does not agree much with other Comets observed heretofore. Therefore, with diligent and many meditations, yet with certain observations leading the way, and through the aid of Geometric and Arithmetical demonstrations, I collected the admirable varieties of this divine work, and I have written them down for the glory of the name of God in this His work. Having performed these things, therefore, I think that a little opportunity has come to me, by which I may in some way show myself mindful of benefits, if in the edition of this writing, in the vestibule, I mention them.