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If I had as much health as zeal, I should go myself to present to Your Majesty a work of several years which I dare offer you from so far; and I should not suffer any other hands than mine to have the honor of bearing it to the feet of the greatest princess in the world. This work, Madame, is a machine for making arithmetical calculations without pen or counters. Your Majesty is not ignorant of the cost of time and pains of new productions, above all when the inventors wish to bring them themselves to their highest perfection; this is why it would be useless to say how much I have laboured upon this one, and I cannot better express myself than by saying that I have devoted myself to it with as much ardor as though I had foreseen that it would one day appear before so august a person. But, Madame, if this honor has not been the veritable motive of my work, it will be at least its recompense; and I shall esteem myself too happy if, after so many vigils, it can give Your Majesty a few moments' satisfaction. I shall not importune Your Majesty with the details of the parts which compose this machine; if you have any curiosity in respect to it, you can satisfy yourself in a discourse which I have addressed to M de Bourdelot; in which I have sketched in a few words the whole history of this work, the object of its invention, the occasion that led to its investigation, the utility of its applications, the difficulty of its execution, the degree of its progress, the success of its accomplishment, and the rules for its use. I shall therefore only speak here of the motive that led me to offer it to Your Majesty, which I consider as the consummation and happiest fortune of its destiny. I know, Madame, that I may be suspected of having sought honor in presenting it to Your Majesty, since it can pass only for something extraordinary when it is seen that it is addressed to you: and that whilst it should only be offered to you through the consideration of its excellence, it will be 