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In The Republic (509d–510a), Socrates describes the divided line to Glaucon this way: . Now take a line which has been cut into two unequal parts, and divide each of them again in the same proportion, [1] and suppose the two main divisions to answer, one to the visible and the other to the intelligible, and then compare the subdivisions in respect of their clearness and want of clearness ...
Meno, in a collection of Plato's Dialogues at Standard Ebooks; Approaching Plato: A Guide to the Early and Middle Dialogues; Guides to the Socratic Dialogues: Plato's Meno. A beginner's guide to the Meno; Plato's Meno: Contretemps in the Classroom; Meno 82b-85d A Visual Representation of the Geometry in Socrates' Interrogation of the Slave
Plato's allegory of the cave by Jan Saenredam, according to Cornelis van Haarlem, 1604, Albertina, Vienna. Plato's allegory of the cave is an allegory presented by the Greek philosopher Plato in his work Republic (514a–520a, Book VII) to compare "the effect of education (παιδεία) and the lack of it on our nature".
Platonic division may refer to: The Analogy of the Divided Line, Plato's schematic representation of all possible metaphysics, epistemology, and ethics on four hierarchical levels in the Republic, Book 6; Plato's tripartite theory of soul, Plato's partitioned organization of the Soul as presented in the Phaedo and the Republic
In philosophy, Plato's epistemology is a theory of knowledge developed by the Greek philosopher Plato and his followers.. Platonic epistemology holds that knowledge of Platonic Ideas is innate, so that learning is the development of ideas buried deep in the soul, often under the midwife-like guidance of an interrogator.
These views come from the heavily geometric straight-edge-and-compass viewpoint of the Greeks: just as lines drawn in a geometric problem are measured in proportion to the first arbitrarily drawn line, so too are the numbers on a number line measured in proportion to the arbitrary first "number" or "one". [citation needed]
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Plato (c. 428–348 BC), the founder of the Platonic Academy, mentions mathematics in several of his dialogues. [22] While not considered a mathematician, Plato seems to have been influenced by Pythagorean ideas about number and believed that the elements of matter could be broken down into geometric solids. [ 23 ]