„Archytas of Tarentum found the two mean proportionals by a very striking construction in three dimensions, which shows that solid geometry, in the hands of Archytas at least, was already well advanced. The construction was usually called mechanical, which it no doubt was in form, though in reality it was in the highest degree theoretical. It consisted in determining a point in space as the intersection of three surfaces: (a) a cylinder, (b) a cone, (c) an "anchor-ring" with internal radius = 0.“

Achimedes (1920)

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Thomas Heath
englischer Mathematikhistoriker 1861 - 1940

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„The truth is that other systems of geometry are possible, yet after all, these other systems are not spaces but other methods of space measurements. There is one space only, though we may conceive of many different manifolds, which are contrivances or ideal constructions invented for the purpose of determining space.“

—  Paul Carus American philosopher 1852 - 1919

Science, Vol. 18 (1903), p. 106, as reported in Memorabilia Mathematica; or, The Philomath's Quotation-Book https://archive.org/stream/memorabiliamathe00moriiala#page/81/mode/2up, (1914), by Robert Edouard Moritz, p. 352

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„The bodies of which the world is composed are solids, and therefore have three dimensions. Now, three is the most perfect number,—it is the first of numbers, for of one we do not speak as a number, of two we say both, but three is the first number of which we say all.“

—  Aristotle Classical Greek philosopher, student of Plato and founder of Western philosophy -384 - -321 v.Chr

Moreover, it has a beginning, a middle, and an end.
I. 1. as translated by William Whewell and as quoted by Florian Cajori, A History of Physics in its Elementary Branches (1899) as Aristotle's proof that the world is perfect.
On the Heavens

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„At the highest level of satori from which people return, the point of consciousness becomes a surface or a solid which extends throughout the whole known universe.“

—  John Lilly American physician 1915 - 2001

Tanks for the Memories : Floatation Tank Talks (1995)<!-- . Nevada City, CA: Gateways -->
Kontext: At the highest level of satori from which people return, the point of consciousness becomes a surface or a solid which extends throughout the whole known universe. This used to be called fusion with the Universal Mind or God. In more modern terms you have done a mathematical transformation in which your centre of consciousness has ceased to be a travelling point and has become a surface or solid of consciousness... It was in this state that I experienced "myself" as melded and intertwined with hundreds of billions of other beings in a thin sheet of consciousness that was distributed around the galaxy. A "membrane".

„It was Pythagoras who discovered that the 5th and the octave of a note could be produced on the same string by stopping at 2⁄3 and ½ of its length respectively. Harmony therefore depends on a numerical proportion. It was this discovery, according to Hankel, which led Pythagoras to his philosophy of number. It is probable at least that the name harmonical proportion was due to it, since1:½ :: (1-½):(2⁄3-½).Iamblichus says that this proportion was called ύπ eναντία originally and that Archytas and Hippasus first called it harmonic.“

—  James Gow (scholar) scholar 1854 - 1923

Nicomachus gives another reason for the name, viz. that a cube being of 3 equal dimensions, was the pattern &#940;&rho;&mu;&omicron;&nu;&#943;&alpha;: and having 12 edges, 8 corners, 6 faces, it gave its name to harmonic proportion, since:<center>12:6 :: 12-8:8-6</center>
Footnote, citing Vide Cantor, Vorles [Vorlesüngen über Geschichte der Mathematik ?] p 152. Nesselmann p. 214 n. Hankel. p. 105 sqq.
A Short History of Greek Mathematics (1884)

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„It seems a little paradoxical to construct a configuration space with the coordinates of points which do not exist.“

—  Louis de Broglie French physicist 1892 - 1987

La nouvelle dynamique des quanta (1928), translation by [Bacciagaluppi, G., Valentini, A., Quantum Theory at the Crossroads: Reconsidering the 1927 Solvay Conference, Cambridge University Press, 2009, 0521814219, 380]

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