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Erwachen

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Melissa Ratsch

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“In Euclid's Elements we meet the concept which later plays a significant role in the development of science. The concept is called the "division of a line in extreme and mean ratio" (DEMR). ...the concept occurs in two forms. The first is formulated in Proposition 11 of Book II. ...why did Euclid introduce different forms... which we can find in Books II, VI and XIII? ...Only three types of regular polygons can be faces of the Platonic solids: the equilateral triangle... the square... and the regular pentagon. In order to construct the Platonic solids... we must build the two-dimensional faces... It is for this purpose that Euclid introduced the golden ratio... (Proposition II.11)... By using the "golden" isosceles triangle...we can construct the regular pentagon... Then only one step remains to construct the dodecahedron... which for Plato is one of the most important regular polyhedra symbolizing the universal harmony in his cosmology.”

HarmonyPlatoGeometryEuclidGolden RatioPlatonic Solids
Book:"GOLDEN" NON-EUCLIDEAN GEOMETRY, THE: HILBERT'S FOURTH PROBLEM, "GOLDEN" DYNAMICAL SYSTEMS, AND THE FINE-STRUCTURE CONSTANT
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“In fifth–sixth-century Athens, philosophy appears more and more as a systematic whole, its study guided by a canon of authoritative works, including both Aristotle and Plato. The peak of the philosophical curriculum is no longer metaphysics, but theology, i.e.,a philosophical discourse about the divine principles, whose sources lie first and foremost in the revelations of late paganism and then in Plato’s dialogues, allegorically interpreted as conveying his theological doctrine. […] Both the Platonic Theology and the Elements of Theology begin with the One, the First Principle. Departing from Plotinus, who was convinced that the suprasensible causes were but three – the One-Good, Intellect, and Soul – the two Proclean works expound the procession of multiplicity from the One as the derivation of a series of intermediate principles, first between the One and the intelligible being, then between the intelligible being and the divine Intellect (and intellects), and then between the divine Intellect and the divine Soul (and souls). For Proclus, an entire hierarchy of divine principles lies both outside the visible universe and within it, and the human soul, fallen into the world of coming-to-be and passing away, can return to the First Principle only through the “appropriate mediations.” [...] Philosophy, insofar as it celebrates the truly divine principles of the visible cosmos, is prayer.”

PhilosophyPhilosophicalTheologyPlatonismNeo PlatonismProclus
Book:The Cambridge Companion to Arabic Philosophy
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“Aelin's hand wavered slightly over his wound. "What's your shield made of, then?" Fenrys tried and failed to shrug. But Gavriel muttered from where he worked on the still-whimpering pirate, "Arrogance." Aelin snorted, but didn't dare take her eyes off Fenrys's injury as she said, "So you do have sense of humor, Gavriel." The Lion of Doranelle gave a wary smile over his shoulder. The rare-sighted, restrained twin to Aedion's own flashing grins. Aelin had called him Uncle Kitty-Cat all of one time before Aedion had snarled viciously enough to make her think carefully before using the term again. Gavriel, to his credit, had merely given Aelin a long-suffereing sigh that seemed to be used only when she or Fenrys were around. "That sense of humor only appears about once every century," Fenrys rasped, "so you'd better hope you Settle, or else that's the last time you'll see it.”

Aelin Ashryver GalathyniusGavrielAedion AshryverFenrys
Book:Empire of Storms
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