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rarely and not without very long studies through ordinary ways, is received. What I have achieved with this work of mine, 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 one who has seen the Instruments found by others for similar purposes, although the greater part of the inventions, and the greatest ones contained in my Instrument, have not been attempted or imagined by others until now; among which, this is very principal: that of being able to solve in an instant for any person the most difficult operations of Arithmetic; of which, however, I describe only those that occur most frequently in Civil and Military matters. I regret only, Benign Reader, that although I have endeavored to explain the following things with all possible clarity and ease, nevertheless, for those who must extract them from writing, they will remain involved in some obscurity, losing thereafter much of that grace which, in seeing it actually operate and in learning it from the living voice, renders them marvelous; but this is one of those subjects that do not suffer from being described with clarity and ease, nor understood, if they are not first heard from the living voice and seen exercised in the act itself. And this would have been a powerful reason that would have made me abstain from printing this work, if it had not come to my ears that another, into whose hands I know not how one of my Instruments with its declaration has come, was preparing to appropriate it for himself; which has put me in the necessity of securing with the testimony of my prints not less my labors than the reputation of whoever might have wished to at-