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ONE:It has been said that the Greeks only worshipped beauty; that they cultivated morality from the aesthetic side; that58 virtue was with them a question, not of duty, but of taste. Some very strong texts might be quoted in support of this judgment. For example, we find Isocrates saying, in his encomium on Helen, that ��Beauty is the first of all things in majesty, and honour, and divineness. It is easy to see its power: there are many things which have no share of courage, or wisdom, or justice, which yet will be found honoured above things which have each of these, but nothing which is devoid of beauty is prized; all things are scorned which have not been given their part of that attribute; the admiration for virtue itself comes to this, that of all manifestations of life virtue is the most beautiful.��44 And Aristotle distinguishes the highest courage as willingness to die for the καλ?ν. So also Plato describes philosophy as a love ��that leads one from fair forms to fair practices, and from fair practices to fair notions, until from fair notions he arrives at the notion of absolute beauty, and at last knows what the essence of beauty is. And this is that life beyond all others which man should live in the contemplation of beauty absolute.��45 Now, first of all, we must observe that, while loveliness has been worshipped by many others, none have conceived it under a form so worthy of worship as the Greeks. Beauty with them was neither little, nor fragile, nor voluptuous; the soul��s energies were not relaxed but exalted by its contemplation; there was in it an element of austere and commanding dignity. The Argive H��r��, though revealed to us only through a softened Italian copy, has more divinity in her countenance than any Madonna of them all; and the Melian Aphrodit�� is distinguished by majesty of form not less than by purity and sweetness of expression. This beauty was the unreserved information of matter by mind, the visible rendering of absolute power, wisdom, and goodness. Therefore, what a Greek wor59shipped was the perpetual and ever-present energising of mind; but he forgot that beauty can only exist as a combination of spirit with sense; and, after detaching the higher element, he continued to call it by names and clothe it in attributes proper to its earthly manifestations alone. Yet such an extension of the aesthetic sentiment involved no weakening of the moral fibre. A service comprehending all idealisms in one demanded the self-effacement of a laborious preparation and the self-restraint of a gradual achievement. They who pitched the goal of their aspiration so high, knew that the paths leading up to it were rough, and steep, and long; they felt that perfect workmanship and perfect taste, being supremely precious, must be supremely difficult as well; χαλεπ? τ? καλ? they said, the beautiful is hard��hard to judge, hard to win, and hard to keep. He who has passed through that stern discipline need tremble at no other task; nor has duty anything to fear from a companionship whose ultimate requirements are coincident with her own, and the abandonment of which for a joyless asceticism can only lead to the reappearance as an invading army of forces that should have been cherished as indispensable allies. TWO:By assuming this or any other well-proved example, and estimating larger or smaller shafts by keeping their diameters as the cube root of the power to be transmitted, the distance between bearings as the diameter, and the speed inverse as the diameter, the reader will find his calculations to agree approximately with the modern practice of our best engineers. This is not mentioned to give proportions for shafts, so much as to call attention to accidental strains, such as winding belts, and to call attention to a marked discrepancy between actual practice and such proportions as would be given by what has been called the measured or determinable strains to which shafts are subjected.The famous theses of Gorgias were quoted in a former chapter as an illustration of the tactics pursued by Greek Humanism in its controversy with physical science. They must be noticed again in the present connexion, on account of their bearing on the development of scepticism, and as having inaugurated a method of reasoning often employed in subsequent attacks, directed, not against the whole of knowledge, but against particular parts of it. The scepticism of Protagoras rested on the assumption that there is an external reality from the reaction of which with mind all our perceptions proceed. Neither of these two factors can be known apart from the other, and as both are in a constant flux, our knowledge of the resulting compound at one time does not show what it has been or will be at another time. But Gorgias altogether denied the existence of any objective reality; and he attempted to disprove it by an analytical instead of a synthetic argument, laying down a series of disjunctive propositions, and upsetting the different alternatives in succession. Existence must be either something or nothing, or both together; and if something, it must be either finite or infinite, or both, and either one or many, or both. His argument against an infinite existence is altogether futile; but it serves to illustrate the undeveloped state of reflection at that period. The eternity of the world is confounded with its unlimited extension in space: and this hypothesis, again, is met by the transparent quibble that the world, not being in any one place, must be nowhere or not at all. And the alternative that the world has not always existed is refuted by the unproved assumption, which, apparently, no Greek philosopher ever thought of disputing, that nothing can begin without being caused by something else. Still, however contemptible such reasonings may seem,131 it is obvious that in them we have the first crude form of the famous antinomies by which Kant long afterwards sought to prove the impossibility of a world existing in space and time apart from a percipient subject, and which have since been used to establish in a more general way the unknowability of existence as such. It will also be observed that the sceptical arguments respectively derived from the relativity of thought and from the contradictions inherent in its ultimate products are run together by modern agnostics. But no reason that we can remember has ever been given to show that an idea is necessarily subjective because it is self-contradictory.

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