Euclid ( c. 325-265 BC ), of Alexandria, probably a student of one of Plato ’ s students, wrote a treatise in 13 books ( chapters ), titled The Elements of Geometry, in which he presented geometry in an ideal axiomatic form, which came to be known as Euclidean geometry.

The antecedents of Western politics can be traced back to the Socratic political philosophers, Plato ( 427 – 347 BC ), Xenophon ( c. 430 – 354 BC ), and Aristotle (" The Father of Political Science ") ( 384 – 322 BC ).

Platonic realism is a philosophical term usually used to refer to the idea of realism regarding the existence of universals or abstract objects after the Greek philosopher Plato ( c. 427 – c.

Plato ( c. 427 – c.

* Arcesilaus, Greek philosopher, who has become the sixth head of the Greek Academy founded by Plato ( b. c. 316 BC )

* Plato, Greek philosopher ( d. c. 347 BC )

* Plato, Greek philosopher and founder of the Academy in Athens ( b. c. 427 BC )

Moreover, the term ' dialectic ' owes much of its prestige to its role in the philosophies of Socrates and Plato, in the Greek Classical period ( 4 – 5 c. BCE ).

In the Gorgias, Plato ( c. 400 BC ) wrote that souls were judged after death and those who received punishment were sent to Tartarus.

According to Plato ( c. 427 BC ), Rhadamanthus, Aeacus and Minos were the judges of the dead and chose who went to Tartarus.

Plato, Seneca, and Aristotle in a medieval manuscript illustration ( c. 1325 – 35 )

In the Protagoras of Plato, ( dramatic date c. 430 BC ), Prodicus is mentioned as having previously arrived in Athens.

Plato ( c. 427 – c. 347 BC ) placed the Sun second in order after the Moon.

The Greek phrase was used by Plato ( 360 BC ), and by Irenæus ( c. AD 196 ).

:: < sup > ¹a </ sup > page 774 Plato ( c. 427-348 BC )

Literary historians commonly suppose that in the West Plato ( c. 437 BC – c. 347 BC ) introduced the systematic use of dialogue as an independent literary form: they point to his earliest experiment with the genre in the Laches.

* Karl Scheele, Plato and Johann Arndt, Ein Vortrag, & c., 1857

The Symposium () is a philosophical text by Plato dated c. 385 – 380 BC.

The exact date of the Sacred Band's creation and whether it was created before or after the Symposium of Plato ( c. 424 – 347 BC ) and the similarly titled Symposium by his rival Xenophon ( c. 430 – 354 BC ), has also long been debated.

The word `` mimesis '' ( `` imitation '' ) is usually associated with Plato and Aristotle.

For Plato, `` imitation '' is twice removed from reality, being a poor copy of physical appearance, which in itself is a poor copy of ideal essence.

Aristotle also tended to stratify all aspects of human nature and activity into levels of excellence and, like Plato, he put the pure and unimpassioned intellect on the top level.

The Poetics, in affirming that all human arts are `` modes of imitation '', gives a more serious role to artistic mimesis than did Plato.

For both Plato and Aristotle artistic mimesis, in contrast to the power of dialectic, is relatively incapable of expressing the character of fundamental reality.

In much the same way, we recognize the importance of Shakespeare's familarity with Plutarch and Montaigne, of Shelley's study of Plato's dialogues, and of Coleridge's enthusiastic plundering of the writings of many philosophers and theologians from Plato to Schelling and William Godwin, through which so many abstract ideas were brought to the attention of English men of letters.

Altogether, the list will give us considerable variety in attitudes and some typical ones, for these critics range all the way from censors to those who consider art above ethics, all the way from Plato to Poe.

Plato and Aristotle agree on some vital literary issues.

While Aristotle censors literature only for the young, Plato would banish all poets from his ideal state.

Even more important, in his Poetics, Aristotle differs somewhat from Plato when he moves in the direction of treating literature as a unique thing, separate and apart from its causes and its effects.

All through The Republic, Plato attends to the way art relates to the general life and ultimately to a good life for his citizens.

Plato is, at times, just as suspicious of the poets themselves as he is of their work.

Plato feels that man has two competing aspects, his rational faculty and his irrational.

His whole objection, indeed, seems to rise out of a deep conviction that the poets do have great power to influence, but Plato seldom pays any attention to what might be called the poem itself.

While Plato finally allows a few acceptable hymns to the gods and famous men, still he clearly leaves the way open for further discussion of the issue.

Both sides claimed that Plato and Aristotle supported their cause.

Those who wanted to close the theaters, for example, pointed to Plato's Republic and those who wished to keep them open called on the Plato of the Ion to testify in their behalf.

But contrary to Whitehead, philosophy is not a synonym for Plato.

Aristotle (, Aristotélēs ) ( 384 BC – 322 BC ) was a Greek philosopher and polymath, a student of Plato and teacher of Alexander the Great.

Together with Plato and Socrates ( Plato's teacher ), Aristotle is one of the most important founding figures in Western philosophy.

The traditional story about his departure reports that he was disappointed with the direction the academy took after control passed to Plato's nephew Speusippus upon his death, although it is possible that he feared anti-Macedonian sentiments and left before Plato had died.

However, Plato reports that syntax was devised before him, by Prodicus of Ceos, who was concerned by the correct use of words.

Even Plato had difficulties with logic ; although he had a reasonable conception of a deductive system, he could never actually construct one and relied instead on his dialectic.

Plato believed that deduction would simply follow from premises, hence he focused on maintaining solid premises so that the conclusion would logically follow.

Consequently, Plato realized that a method for obtaining conclusions would be most beneficial.