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The Elements (Ancient Greek: Στοιχεῖα Stoikheîa) is a mathematical treatise consisting of 13 books attributed to the ancient Greek mathematician Euclid c. 300 BC. It is a collection of definitions, postulates, propositions (theorems and constructions), and mathematical proofs of the propositions.
Euclid (/ ˈ j uː k l ɪ d /; Ancient Greek: Εὐκλείδης; fl. 300 BC) was an ancient Greek mathematician active as a geometer and logician. [2] Considered the "father of geometry", [3] he is chiefly known for the Elements treatise, which established the foundations of geometry that largely dominated the field until the early 19th century.
The Republic (Ancient Greek: Πολιτεία, romanized: Politeia; Latin: De Republica) [1] is a Socratic dialogue, authored by Plato around 375 BC, concerning justice (dikaiosúnē), the order and character of the just city-state, and the just man. [2]
Papyrus Oxyrhynchus 29 (P. Oxy. 29) is a fragment of the second book of the Elements of Euclid in Greek. It was discovered by Grenfell and Hunt in 1897 in Oxyrhynchus. The fragment was originally dated to the end of the third century or the beginning of the fourth century, although more recent scholarship suggests a date of 75–125 CE.
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Euclid himself wrote six dialogues—the Lamprias, the Aeschines, the Phoenix, the Crito, the Alcibiades, and the Amatory dialogue—but none survive. According to its prologue, the ostensibly Platonic dialogue Theaetetus was originally a Euclidean work. The main extant source on his views is the brief summary by Diogenes Laërtius. [10]
The Ring of Gyges / ˈ dʒ aɪ ˌ dʒ iː z / (Ancient Greek: Γύγου Δακτύλιος, Gúgou Daktúlios, Attic Greek pronunciation: [ˈɡyːˌɡoː dakˈtylios]) is a hypothetical magic ring mentioned by the philosopher Plato in Book 2 of his Republic (2:359a–2:360d). [1] It grants its owner the power to become invisible at will.
The debate over the extent to which Plato's portrayal of Socrates represents the actual Socrates's ideas is known as the Socratic problem. [62] [63] The Death of Socrates, by Jacques-Louis David (1787) Plato expressed his ideas through dialogues, that is, written works purporting to describe conversations between different individuals.