Two New Sciences

Geometric, but rather place the cause in the imperfection of the matter, which is subject to many alterations and imperfections. But here I do not know if I will be able, without stumbling into some note of arrogance, to say that not even resorting to the imperfections of matter, which are capable of contaminating the purest Mathematical demonstrations, suffices to excuse the disobedience of machines in the concrete to the same abstract and Ideal ones: nevertheless, I will say it, affirming that, abstracting all the imperfections of Matter, and supposing it most perfect and unalterable, and exempt from every accidental mutation, still the mere fact of being material makes it so that the larger machine, built of the same material and with the same proportions as the smaller one, will respond in all other conditions with exact symmetry to the smaller one, except in robustness and resistance against violent invasions: but the larger it is, the weaker it will be in proportion. And because I suppose the matter to be unalterable, that is, always the same, it is manifest that of it, as of an eternal and necessary property, demonstrations can be produced no less than the other neat and pure Mathematical ones. Therefore, Mr. Sagredo, revoke the opinion you held, and perhaps together with all others who have studied Mechanics, that machines and structures composed of the same materials with punctual observance of the same proportions among their parts must be equally, or to put it better, proportionally disposed to resist and to yield to external invasions and onslaughts: because it can be Geometrically demonstrated that the larger ones are always proportionally less resistant than the smaller ones: so that ultimately, not only for all artificial machines and structures, but for natural ones as well, there is a necessarily ascribed limit, beyond which neither art nor nature can pass: I mean pass by always observing the same proportions with the identity of the material.

Sagredo. I already feel my brain turning, and as if a cloud were suddenly opened by a flash of lightning, my mind is being overwhelmed by a momentary and unusual light, which beckons me from afar, and immediately confuses and hides foreign and indigested imaginations. And from what...