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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 Phædrus of Plato: A Dialogue Concerning Beauty and Love; An Essay on the Beautiful, from the Greek of Plotinus; The Philosophical and Mathematical Commentaries of Proclus on the First Book of Euclid's Elements, and his Life by Marinus. With a preliminary Dissertation on the Platonic Doctrine of Ideas.
Proclus Lycius (/ ˈ p r ɒ k l ə s l aɪ ˈ s i ə s /; 8 February 412 – 17 April 485), called Proclus the Successor (Ancient Greek: Πρόκλος ὁ Διάδοχος, Próklos ho Diádokhos), was a Greek Neoplatonist philosopher, one of the last major classical philosophers of late antiquity.
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 last book (Book XIII) of the Euclid's Elements, which is probably derived from the work of Theaetetus, is devoted to constructing the Platonic solids and describing their properties; Andreas Speiser has advocated the view that the construction of the 5 regular solids is the chief goal of the deductive system canonized in the Elements. [2]
Euclid's Elements. Theon's edition of the Elements was the only known version until François Peyrard discovered an older copy of the Elements in the Vatican Library in 1808. [ 8 ] Comparison of the two versions show that Theon's edition attempts to remove difficulties that might be felt by learners in studying the text. [ 9 ]
Plutarch elaborated on this phrase in his essay Πῶς Πλάτων ἔλεγε τὸν θεὸν ἀεί γεωμετρεῖν "What is Plato's meaning when he says that God always applies geometry". [2] Based on the phrase of Plato, above, a present-day mnemonic for π (pi) was derived: Ἀεὶ ὁ θεὸς ὁ μέγας ...