TO LOUIS XIV,

THE ILLUSTRIOUS KING

OF FRANCE AND NAVARRE.

RENOWNED King, it is to France especially that we owe the rebirth and restoration of Geometry The author refers to the 17th-century "Scientific Revolution" and the recovery of classical Greek mathematical texts in this century. For from here arose those who first restored and brought back into the light this science, which had been lost in its greatest and better part, and as if buried away. Following in their footsteps, men of the most subtle intellect throughout all of Europe have since so refined it, that little now seems left by them for the industry of posterity; indeed, they have far surpassed the discoveries of the ancients. In this science, which I have always admired and loved most dearly, whenever I have applied my mind to it, I have set before myself for investigation those things above all others which, once discovered, might prove useful either for the conveniences of life or for the knowledge of Nature. Then, truly, I considered my labor best spent when I happened upon those matters in which utility [is joined] with the difficulty of discovery and some subtlety...