„The centre of gravity of any hemisphere [is on the straight line which] is its axis, and divides the said straight line in such a way that the portion of it adjacent to the surface of the hemisphere has to the remaining portion the ratio which 5 has to 3.“

—  Archimedes, buch The Method of Mechanical Theorems

Proposition 6.
The Method of Mechanical Theorems

Letzte Aktualisierung 22. Mai 2020. Geschichte
Archimedes Foto
antiker griechischer Mathematiker, Physiker und Ingenieur -287 - -212 v.Chr

Ähnliche Zitate

Nicole Oresme Foto
John Wyndham Foto
Samuel Beckett Foto

„I did my best to go in a circle, hoping in this way to go in a straight line.“

—  Samuel Beckett, buch Molloy

Molloy (1951)
Kontext: Having heard, or more probably read somewhere, in the days when I thought I would be well advised to educate myself, or amuse myself, or stupefy myself, or kill time, that when a man in a forest thinks he is going forward in a straight line, in reality he is going in a circle, I did my best to go in a circle, hoping in this way to go in a straight line. For I stopped being half-witted and became sly, whenever I took the trouble … and if I did not go in a rigorously straight line, with my system of going in a circle, at least I did not go in a circle, and that was something.

Cassandra Clare Foto
Michael Collins (Irish leader) Foto
Hans Reichenbach Foto

„It is remarkable that this generalization of plane geometry to surface geometry is identical with that generalization of geometry which originated from the analysis of the axiom of parallels. …the construction of non-Euclidean geometries could have been equally well based upon the elimination of other axioms. It was perhaps due to an intuitive feeling for theoretical fruitfulness that the criticism always centered around the axiom of parallels. For in this way the axiomatic basis was created for that extension of geometry in which the metric appears as an independent variable. Once the significance of the metric as the characteristic feature of the plane has been recognized from the viewpoint of Gauss' plane theory, it is easy to point out, conversely, its connection with the axiom of parallels. The property of the straight line as being the shortest connection between two points can be transferred to curved surfaces, and leads to the concept of straightest line; on the surface of the sphere the great circles play the role of the shortest line of connection… analogous to that of the straight line on the plane. Yet while the great circles as "straight lines" share the most important property with those of the plane, they are distinct from the latter with respect to the axiom of the parallels: all great circles of the sphere intersect and therefore there are no parallels among these "straight lines". …If this idea is carried through, and all axioms are formulated on the understanding that by "straight lines" are meant the great circles of the sphere and by "plane" is meant the surface of the sphere, it turns out that this system of elements satisfies the system of axioms within two dimensions which is nearly identical in all of it statements with the axiomatic system of Euclidean geometry; the only exception is the formulation of the axiom of the parallels.“

—  Hans Reichenbach American philosopher 1891 - 1953

The geometry of the spherical surface can be viewed as the realization of a two-dimensional non-Euclidean geometry: the denial of the axiom of the parallels singles out that generalization of geometry which occurs in the transition from the plane to the curve surface.
The Philosophy of Space and Time (1928, tr. 1957)

Augustus De Morgan Foto

„Experience has convinced me that the proper way of teaching is to bring together that which is simple from all quarters, and, if I may use such a phrase, to draw upon the surface of the subject a proper mean between the line of closest connexion and the line of easiest deduction.“

—  Augustus De Morgan British mathematician, philosopher and university teacher (1806-1871) 1806 - 1871

This was the method followed by Euclid, who, fortunately for us, never dreamed of a geometry of triangles, as distinguished from a geometry of circles, or a separate application of the arithmetics of addition and subtraction; but made one help out the other as he best could.
The Differential and Integral Calculus (1836)

Alvin C. York Foto

„The major suggested we go down a gully, but I knew that was the wrong way. And I told him we were not going down any gully. We were going straight through the German front line trenches back to the American lines.“

—  Alvin C. York United States Army Medal of Honor recipient 1887 - 1964

Account of 8 October 1918.
Kontext: The major suggested we go down a gully, but I knew that was the wrong way. And I told him we were not going down any gully. We were going straight through the German front line trenches back to the American lines.
It was their second line that I had captured. We sure did get a long way behind the German trenches! And so I marched them straight at that old German front line trench. And some more machine guns swung around and began to spit at us. I told the major to blow his whistle or I would take off his head and theirs too. So he blew his whistle and they all surrendered — all except one. I made the major order him to surrender twice. But he wouldn't. And I had to touch him off. I hated to do it. But I couldn't afford to take any chances and so I had to let him have it.

Paul Carus Foto
E. W. Hobson Foto
Hans Reichenbach Foto

„The surfaces of three-dimensional space are distinguished from each other not only by their curvature but also by certain more general properties. A spherical surface, for instance, differs from a plane not only by its roundness but also by its finiteness. Finiteness is a holistic property. The sphere as a whole has a character different from that of a plane. A spherical surface made from rubber, such as a balloon, can be twisted so that its geometry changes…. but it cannot be distorted in such a way as that it will cover a plane. All surfaces obtained by distortion of the rubber sphere possess the same holistic properties; they are closed and finite. The plane as a whole has the property of being open; its straight lines are not closed. This feature is mathematically expressed as follows. Every surface can be mapped upon another one by the coordination of each point of one surface to a point of the other surface, as illustrated by the projection of a shadow picture by light rays. For surfaces with the same holistic properties it is possible to carry through this transformation uniquely and continuously in all points. Uniquely means: one and only one point of one surface corresponds to a given point of the other surface, and vice versa. Continuously means: neighborhood relations in infinitesimal domains are preserved; no tearing of the surface or shifting of relative positions of points occur at any place. For surfaces with different holistic properties, such a transformation can be carried through locally, but there is no single transformation for the whole surface.“

—  Hans Reichenbach American philosopher 1891 - 1953

The Philosophy of Space and Time (1928, tr. 1957)

Northrop Frye Foto

„The wise man looks for the invisible line between the "is" and the "is not" which is the way through“

—  Northrop Frye Canadian literary critic and literary theorist 1912 - 1991

"Quotes", Late Notebooks, 1982–1990: Architecture of the Spiritual World (2002)
Kontext: Man is born lost in a forest. If he is obsessed by the thereness of the forest, he stays lost and goes in circles; if he assumes the forest is not there, he keeps bumping into trees. The wise man looks for the invisible line between the "is" and the "is not" which is the way through. The street in the city, the highway in the desert, the pathway of the planets through the labyrinth of the stars, are parallel forms. (1:111)

Carl Sagan Foto
Abby Stein Foto

„There is no straight way to not being straight. We (Queer individuals) all have different stories.“

—  Abby Stein Trans activist, speaker, and educator 1991

Speech at Nyack Library, May 15, 2016. https://www.youtube.com/watch?v=PHXHcf47LJk&list=PLGAOZDy50dxnuaem8ls2U6285DxR9_jH9

Li Bai Foto

„Flying waters descending straight three thousand feet,
Till I think the Milky Way has tumbled from the ninth height of Heaven.“

—  Li Bai Chinese poet of the Tang dynasty poetry period 701 - 762

"Viewing the Waterfall at Mount Lu" (望庐山瀑布), trans. Burton Watson
Original: (zh-TW) 飛流直下三千尺,疑是銀河落九天。

Theo van Doesburg Foto
Albert Schweitzer Foto
Ernest Hemingway Foto

„Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam egestas wisi a erat. Morbi imperdiet, mauris ac auctor dictum.“