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THREE:Nor was this all. Laws and justice once established would65 require to have their origin accounted for, and, according to the usual genealogical method of the early Greeks, would be described as children of the gods, who would thus be interested in their welfare, and would avenge their violation—a stage of reflection already reached in the Works and Days of Hesiod.In making notes, as much as possible of what is written should be condensed into brief formul?, a form of expression which is fast becoming the written language of machine shops. Reading formul? is in a great degree a matter of habit, like studying mechanical drawings; that which at the beginning is a maze of complexity, after a time becomes intelligible and clear at a glance.

THREE:It was from mathematical science that the light of certainty first broke. Socrates had not encouraged the study of mathematics, either pure or applied; nor, if we may judge from some disparaging allusions to Hippias and his lectures in the Protagoras, did Plato at first regard it with any particular favour. He may have acquired some notions of arithmetic and geometry at school; but the intimate acquaintance with, and deep interest in them, manifested throughout his later works, probably dates from his visits to Italy, Sicily, Cyrênê, and Egypt. In each of these places the exact sciences were cultivated with more assiduity than at Athens; in southern Italy they had been brought into close connexion with philosophy by a system of mystical interpretation. The glory of discovering their true speculative significance was reserved for Plato. Just as he had detected a profound analogy between the Socratic scepticism and the Heracleitean flux, so also, by another vivid intuition, he saw in the definitions and demonstrations of geometry a type of true reasoning, a particular application of the Socratic logic. Thus the two studies were brought into fruitful reaction, the one gaining a wider applicability, and the other an exacter method of proof. The mathematical spirit ultimately proved211 too strong for Plato, and petrified his philosophy into a lifeless formalism; but no extraneous influence helped so much to bring about the complete maturity of his constructive powers, in no direction has he more profoundly influenced the thought of later ages.

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