In the passage in question, a lecture _Della leggerezza,_ read to the Accademia della Crusca, Torricelli controverts, as based on mere appearances and not confirmed by facts and reasoning, Aristotle's definition in the _De coelo_: "heavy is that which has a natural property of going towards the centre." He remarks upon this: "The definitions of Physics differ from those of Mathematics in that the former are obliged to adapt and adjust themselves to the object defined, while the latter mathematical definitions are free and can be formed at the will of the geometrician who is defining. The reason is perfectly plain: the things defined in Physics do not come into being with the definition, they exist already by themselves and are found in nature previously. But the things defined by geometry, that is by the science of abstraction, have no existence in the universe of the world other than that which definition gives to them in the universe of intelligence. Thus whatever objects of Mathematics are defined, the same objects will come into existence simultaneously with the definition."[53] The arbitrary character of mathematics seems here to be clearly stated. But let us reserve our judgment and read on. "If I were to say, the circle is a plane figure with four equal sides and four right angles, this is not at all a false definition; but for the rest of my book I should have to mean, whenever I spoke of a circle, a certain figure which others have called a square. But if a man should say in Physics, 'the horse is a rational animal,' should we not be justified in calling him the horse? We must first look very carefully to see whether the horse is a rational animal or not and then define it as it is, in order that the physical definition may conform to the object and not be counted defective." Here we see that what appeared to be a profound thought has turned out to be a platitude; it is indifferent whether we call the bow the stern or the stern the bow, said Galileo, or, says Torricelli in his turn, whether we call a square a circle or a circle a square; while it does not seem to him an indifferent matter whether we call a horse a rational animal. But even this does not prevent him from admitting later some degree of arbitrariness in physical terminology, when he says, "since then it is not demonstrated that the intrinsic principle of downward motion exists upon the earth, I will accept this definition, if the tests will allow me, as the simple imposition of a name, and, replacing the verb 'to be' by the verb 'to be called,' I will adapt the definition to my own requirements thus: That is called heavy which descends to the centre. Whenever any one says, the earth is heavy, I will agree, but always with the interpretation that the word 'heavy' only signifies descending in a lighter medium."[54]