Two New Sciences

you have said, it seems to me that it should follow that it would be an impossible thing to build two structures of the same material that are similar and unequal, and among themselves equally proportionally resistant; and if this is so, it will also be impossible to find even two rods of the same wood similar in robustness and value, but unequal in size.

Salviati. It is so, Mr. Sagredo. And to better assure ourselves that we agree in the same concept, I say that if we reduce a wooden rod to such length and thickness that, fixed, for example, in a wall at right angles, that is, parallel to the horizon, it is reduced to the ultimate length that it can support, so that lengthened a hair more, it would break, burdened by its own weight, this will be unique in the world: so that, being for example its length one hundred times its thickness, no other rod of the same material could be found that, being one hundred times its thickness in length, is, like that one, precisely able to support itself and nothing more: but all the larger ones will weaken, and the smaller ones will be capable of supporting something else in addition to their own weight. And this, which I say about the state of supporting itself, let it be understood as said of every other constitution, and thus if one joist can support the weight of ten equal joists, a beam similar to it will by no means be able to support the weight of ten of its equals. But let Your Lordship and Mr. Simplicio notice how true conclusions, although at first glance they seem improbable, once pointed out a little, shed the garments that concealed them, and naked and simple, they make a joyful display of their secrets. Who does not see how a horse falling from a height of three or four braccia cubits/arms-lengths will break its bones, but a dog from such a height, and a cat from one of eight or ten, will not be harmed at all, just as a cricket would not from a tower, nor an ant precipitating from the lunar sphere? Small children remain unhurt in falls where adults break their shins or heads. And as the smallest animals are proportionally more robust and strong than the larger ones, so the smaller plants sustain themselves better: and I already believe that both of you understand that an Oak two hundred braccia high...