The Book of Mechanics

immediately we will conceive that it cannot only not be of equal weight, but that the plane D tends downward. And this for no other reason than that, since D is greater than E, we immediately conceive that D is also heavier than E. Therefore, to consider planes with gravity is not at all alien to reason. Wherefore, we have judged that both titles—namely, "Of Equal-Weight Planes" or "Centers of Gravity of Planes"—are to be admitted. But since Archimedes inscribed his second book with the simple term "Of Equal-Weight Planes" (as if embracing everything at once), we therefore judge that both the first and the second book ought to be inscribed "Of Equal-Weight Planes." And we do so the more willingly, since Eutocius himself, the commentator of these books, has referred to these books by this name alone, "Of Equal-Weight Planes," and all others who name these books of Archimedes refer to them by this title regarding equal-weight planes. Furthermore, this title seems to me more fitting to the work, since Archimedes at the beginning treats of some things that exist in common to both solids and planes, although the rest are to be referred only to planes. In all of which he treats of a matter most useful and conducive to very many things. For from those things which we are taught by Archimedes in these books, we can arrive at the knowledge of many things. This is easily evident in the first place by the example of Archimedes himself, for by this method, in his book On the Quadrature of the Parabola, by comparing planes placed on a balance, he discovered the quadrature of the parabola by wondrous artifice. Next, from the knowledge of the centers of gravity of planes, we are led to the knowledge of the centers of gravity of solids. Finally, this doctrine which Archimedes provides for us in these books is so profitable that I do not fear to affirm that there is no theorem, nor any problem pertaining to mechanical matters, which in its speculation does not assume a peculiar foundation from those things which Archimedes discourses upon in these books. Just as (to omit others for the time being) is clear from that common proposition stating that weight is to weight as distance is to distance, conversely, from which they are suspended—which is most excellently demonstrated by him in the first book. And although Jordanus Nemorarius (whom