Excerpt from Miscellanies, Vol. 5: Chiefly Academic
That Plato, as a mere theologian, was pro-eminent among eminent Greeks, is easy to receive on modern testimony. It will not be called in question by us here but as a mere theologian, he surely cannot be important to a Christian reasoner. He went to school in Oriental Philosophy, but had a deep taproot native to Greece. Thales and Pythagoras, not to refer to Empedocles, must have joined tradition and legend to active thought. Pythagoras also looked abroad for philosophy. Plato was deeply impressed by Pythagorean dogma, and exhibits a vehement ten deney to a priori methods, in contrast to Aristotle, to Socrates, and probably to Thales. Ipse dixit (the Master has said it), was sufficient with a Pythagorean. If Plato be supposed to speak in Platonic dialogues, he betrays a childish reverence for the letter of Finder and Simonides. But the passion for Geometry, the earliest of Sciences, peculiarly captivated him.
This was the first Science cultivated by Demonstration, which means, Complete Proof. Plato may have hoped that it would supersede the mere dogma of Pythagoreans. Much sound pro gress had been made in Geometry earlier than Socrates; but this sturdy thinker was alienated from all superhuman science -u'; Culpa'mo) by the mutual refutations of the too rapid speculators. The practical value of Geometry was well known in the Athens of Pericles; indeed the grossly false satire of Socrates in the Clouds of Aristophanes may indicate that the elements of Astronomy also were becoming a staple of education for aristo cratic youth. Certainly in the next generation Plato took up Geometry with enthusiasm, and with a panegyric which passed all bounds. He is said to have written up over his gate: Let no one enter, who is untaught in Geometry, as though it were indispensable to all who might seek instruction in his philosophy. To his followers accordingly the Science was indebted for some notable additions. Among them are named the celebrated problems of Trisecting an Angle, and what we now call Ex tracting the Cube Root, geometrically. To solve these by rule and compass certain new curves were imagined. The geometrical method of Analysis is ascribed to Plato himself.
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