Quotes about Plato
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What is philosophy? This is a notoriously difficult question. One of the easiest ways of answering it is to say that philosophy is what philosophers do, and then point to the writings of Plato, Aristotle, Descartes, Hume, Kant, Russell, Wittgenstein, Sartre, and other famous philosophers. However, this answer is unlikely to be of much use to you if you are just beginning the subject, as you probably won't have read anything by these writers. Menaechmus, a pupil of Eudoxus, and a contemporary of Plato, found the two mean proportionals by means of conic sections, in two ways, (α) by the intersection of two parabolas, the equations of which in Cartesian co-ordinates would be x2=ay, y2=bx, and (β) by the intersection of a parabola and a rectangular hyperbola, the corresponding equations being x2=ay, and xy=ab respectively. It would appear that it was in the effort to solve this problem that Menaechmus discovered the conic sections, which are called, in an epigram by Eratosthenes, "the triads of Menaechmus".