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is received, not without very long studies via the ordinary paths. What I have achieved with this my work, I will not say, but I will leave it to be judged by those who have learned it from me thus far, or will learn it in the future, and in particular by those who have seen the Instruments invented by others for similar purposes, although the greater part of the inventions, and the most significant ones contained in my Instrument, have not been attempted or imagined by others until now. Among these, the most principal is that of being able to resolve for any person in an instant the most difficult operations of Arithmetic, of which I describe only those that occur most frequently in Civil and Military matters. I only regret, Kind Reader, that although I have endeavored to explain the following things with all possible clarity and ease, nevertheless, to those who must extract them from the writing, they will remain involved in some obscurity, losing thereafter much of that grace which, in seeing them actually operated and in learning them from the living voice, renders them marvelous. But this is one of those subjects that do not suffer being described or understood with clarity and ease if they are not first heard from the living voice and seen exercised in the very act. And this would have been a powerful reason that would have made me abstain from printing this work, if it had not reached my ears that others, into whose hands one of my Instruments—I know not how—has arrived, were preparing to appropriate it for themselves; which has put me under the necessity of securing with the testimony of my prints not only my labors but also the reputation of him who might have wished to attribute them to himself.