The Book of Mechanics

Nicolaus Tartalea and others followed in the little book On Weights) has also attempted to demonstrate this same proposition and has used several means to show it; nevertheless, the name of "demonstration" can fit no proof of his. Since his arguments are composed scarcely from probabilities and those things which in no way bring necessity, and perhaps not even from probabilities. Since in mathematics the most exquisite demonstrations are required, and therefore it does not seem to me that that Jordanus is to be counted among the mechanicians. Wherefore, we must flee to Archimedes if we desire to learn the mechanical foundations and the true principles of this science, who (in my judgment) looked primarily to this, that he might hand down mechanical elements; as Pappus also feels in the eighth book of his Mathematical Collections, which is indeed easily discerned from the division and progress of these books.

OF THE DIVISION OF THESE BOOKS.

For this treatise is divided first into two books, into postulates and theorems; the theorems, however, are subdivided into two sections, of which the first contains the first eight theorems; the remaining theorems pertain to the other. Which can indeed still be divided into two other parts, namely, into the theorems examined in the first book, and into those which the second book contemplates. We establish this division of these books, however, because Archimedes, in the first place (omitting the postulates, which ought to hold the first place), treated some things common in the first eight theorems; the scope of which is to find that primary mechanical foundation, namely, that gravity is to gravity as distance is to distance, conversely. To demonstrate which, he premises five theorems, which gradually lead us into the knowledge of the demonstration of the aforementioned foundation. At which place it is to be noted above all, namely, that that foundation, and also the first eight theorems, are common to both planes and solids, and Archimedes demonstrates them indiscriminately for both. For if anyone thought otherwise,