Preface

THEORY To the Illustrious French Royal Academy, recently established for promoting Mathematical, Physical, and Medical studies, and for increasing the benefits to the human race.

Among so many achievements of your GREAT KING, worthy of that fortune and spirit by which such a mass of power is most wisely governed, there is reason why I believe that no small things are to be expected in the future, through you. For he is concerned not only for his own people, but for the whole human race. It is a great thing to make his domain the most cultivated of all from a wild state; to bless it through the happiness of the sea; to join seas with ships and navigate through the roots of the Pyrenees; to connect the commerce of the world; and to substitute something else for the Herculean labors against infamous pirates. It is a great thing to rise in naval power and reach the pinnacle of military affairs, making himself formidable to Christians and a terror to Barbarians.

But it is a greater thing to subject nature to art, to propagate the boundaries of human power, and to conquer those most invisible internal enemies against whom no force is sufficiently strong by the fates. How often have the greatest Heroes, who had hundreds of thousands of men ready at their nod, succumbed to a minor disease before their time? And yet perhaps some little old woman in a neighboring neglected and abject hut held the reason for conquering it. Happy would we be, and perhaps we would be masters of our own bodies, if that which has now barely begun had been done ten centuries ago. But useful things are never started too late; at least posterity will give thanks to our age, and will place among the stars the Prince under whose auspices the barriers of nature were broken through. His glory, the innate high mind of the most Christian King, his institution, strength, resources, and the flower of abundant geniuses move toward these things. If we act with serious and greater effort, we can, while living, attain…

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…to enjoy the fruit of the labors of our time. Nor is it a wonder that one thing will hardly be achieved in a century, which in a hundred years—when even a hundred joined together will act a hundred times—is scattered so many times. They have scattered incoherence, even contradictions; many easier things are often done than needed, and of the greatest and most useful things, nothing. They mix poverty with abundance. Joined together, they not only diminish the labor of such a great task but also season the difficulty for themselves with the sweetness of mutual applause.

Your example will teach this to the world, since among your first members are men of such great stature: Auzout, Bullialdus, Cassini, Huygens, Pecquet, Petit, Roberval, Thévenot, and so many others who have gathered. What can be expected from your combined counsels except something great, honorable for you, glorious for the King, and fruitful for the human race? Nor do you need my praises; the world has long felt these things about you. Nevertheless, let me also join the public voice. Since there was recently a mention of me to Carcavi, a man of distinguished fame and learning, and from the elite flower of men with whom you abound, and since I was chosen for the care of the Royal Library and this very Academy, an occasion was offered to me by the most humane Mr. Ferrand. I preferred to add this sheet, however small and unelaborated, rather than come with entirely empty hands.

The argument is certainly worthy of your attention: for it evolves a labyrinth of primary continuities and compositions of motion that fold the geniuses of many. It refers to establishing the foundations of the sciences; checking the triumphs of the Sceptics; placing the Geometry of Indivisibles and the Arithmetic of Infinites—parents of so many distinguished theorems—on solid ground; elaborating a Physical Hypothesis congruent in all things; and what is greatest, providing geometric demonstrations concerning the nature of intimate Thought, the perennial nature of the Mind, and the First Cause, which have hitherto been untouched. Whence the sources of the Good, the Just, the Equitable, and of Laws—at once so clear and pure, so small in simultaneous scope and yet flowing from profound roots—might suffice as a compendium for great volumes and for solving all cases. Nothing like this, I believe, commonly occurs. But this will be our task at another time. For the rest, to return to the present matters, I willingly acknowledge the imperfection of this first attempt; I hope, however…

…something nevertheless has been achieved: the nature of indivisibles illustrated; the reason for cohesion now first detected; a physico-geometric construction of curves from straight lines and of every kind of curved bodies from rectilinear surfaces set forth; a Hypothesis brought forward from which all phenomena of nature can be mechanically explained. Indeed, I have even shown what that magnetic matter is, to whose rotation around the earth I recently learned the most ingenious Auzout suspected the Verticity [magnetic orientation] should be ascribed, after his Theory of Concrete Motion was already published, although he did not explain what sort of matter it was. With this detected, he himself, Auzout, does not despair that a constant hypothesis for magnetic variation and Longitudes can be found. Finally, if nothing else, at least these are the seeds of thoughts not to be regretted. I shall perhaps pursue them more happily sometime when there is more leisure, and I shall be encouraged to perfect other labors undertaken for the sake of the public good, if you, and those like you, favor these beginnings, such as they are, with auspicious omens.