The Pneumatics of Hero of Alexandria

some way help or hinder the intention of the operator, as Diognetus did; and at the same time he does not forget to be a mathematician, contemplating the proportion, number, magnitude, distance, order, figure, and the causes whence their effects full of wonder have their origin, and how they proceed from the miraculous property of the circular figure—a principle, as Aristotle said in the Mechanics, of all other miracles, for being composed of mobile and immobile, for containing within itself different contrarieties, but mainly the curved and the convex in one same line indivisible for width, and many others described there by him. Upon these are founded not only the reasons of all the most miraculous machines, but those of the machine of the world itself, being, as one reads in the Book of Wisdom, disposed with measure, number, and weight. So that not Ctesibius (as Vitruvius would have it) was the inventor of the Spiritual machines, not Vulcan, not Daedalus of the self-moving ones, as the ancients wanted, but the same master of this fabric of the world. From his work, just as Archimedes drew the example of his much-praised glass machine—where, no differently than one sees sometimes sculpted in a small ring the likeness of a very large Colossus, one saw wonderfully expressed in that narrow space the proportion, the order, and the motion with which this vast worldly mass was made and goes on maintaining itself—so others could draw from it various models of all the most stupendous machines that human thought could ever imagine. But let us come to declare some things necessary to be known in order to well understand what Hero says, and let us begin from the definition of the machine, which Vitruvius said was a perpetual and continued conjunction of matter, which has very great force in the movements of weights. But it seems that this definition is defective and lacking, and that he had regard only to machines that pull, that push, and that lift, without thinking that, saying it so, the Spiritual and self-moving ones remained entirely excluded. Therefore it would be perhaps better to say that it is an ingenious compound of proportionate things, apt to operate with violence, and this will comprehend all the species. It has been said that it is a compound; because a single wood, a single iron, a single rope does not constitute