# „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

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##### Archimedes4
antiker griechischer Mathematiker, Physiker und Ingenieur -287 - -212 v.Chr

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### „Every measurable thing except numbers is imagined in the manner of a continuous quantity. Therefore, for the mensuration of such a thing, it is necessary that points, lines, and surfaces, or their properties, be imagined. For in them… measure or ratio is initially found… Therefore, every intensity which can be acquired successively ought to be imagined by a straight line perpendicularly erected on some point of the space or subject of the intensible thing, e. g., a quality… And since the quantity or ratio of lines is better known and is more readily conceived by us—nay the line is in the first species of continua, therefore such intensity ought to be imagined by lines… Therefore, equal intensities are designated by equal lines, a double intensity by a double line, and always in the same way if one proceeds proportionally.“

—  Nicole Oresme French philosopher 1323 - 1382

Tractatus de Configurationibus et Qualitatibus et Motuum (c. 1350)

### „You can't drive a flock of sheep to market in a dead straight line, but there are ways of getting 'em there.“

—  John Wyndham, buch The Day of the Triffids

The Day of the Triffids (1951), ch 10 - p.179

### „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.

### „History, the way the teachers liked it, was a racetrack, a straight shot from start to finish line; life itself was more of a maze.“

—  Cassandra Clare American author 1973

Quelle: The Evil We Love

### „How could one argue with a man who was always drawing lines and circles to explain the position; who, one day, drew a diagram [here Michael illustrated with pen and paper] saying 'take a point A, draw a straight line to point B, now three-fourths of the way up the line take a point C. The straight line AB is the road to the Republic; C is where we have got to along the road, we canot move any further along the straight road to our goal B; take a point out there, D [off the line AB]. Now if we bend the line a bit from C to D then we can bend it a little further, to another point E and if we can bend it to CE that will get us around Cathal Brugha which is what we want!“

How could you talk to a man like that?
Referring to Eamon de Valera in conversation with Michael Hayes, at the debates over the Anglo-Irish Treaty in 1921
Michael Hayes Papers, P53/299, UCDA
Quoted in Doherty, Gabriel and Keogh, Dermot (2006). Michael Collins and the Making of the Irish State. Mercier Press, p. 153.

### „Like drawing a straight line – you draw a straight line and it's crooked and you draw another straight line on top of it and it's crooked a different way and then you draw another one and eventually you have a very rich thing on your hands which is not a straight line. If you can do that the it seems to me you are doing more than most people. The thing is, it is very difficult to know oneself whether one is doing that or not, whether you mean what you do; and there is the other problem of the way you do it and whether sometimes you do more than you mean or you do less than you mean. It's very good if you can establish a language where it's clear that that is what you are doing – that you do what you mean to do.“

—  Jasper Johns American artist 1930

interview at John's studio, Billy Klüver, March 1963, as quoted in Jasper Johns, Writings, sketchbook Notes, Interviews, ed. Kirk Varnedoe, Moma New York, 1996, p. 85
1960s

### „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)

### „The Dude just pounded his way in a straight line, convinced that the lion was a figment of his imagination and that the vampire ahead of him was just Grendel's deformed mutant brother.“

—  Ilona Andrews American husband-and-wife novelist duo

### „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)

### „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.

### „Infinity is the land of mathematical hocus pocus. There Zero the magician is king. When Zero divides any number he changes it without regard to its magnitude into the infinitely small [great? ], and inversely, when divided by any number he begets the infinitely great [small? ]. In this domain the circumference of the circle becomes a straight line, and then the circle can be squared. Here all ranks are abolished, for Zero reduces everything to the same level one way or another. Happy is the kingdom where Zero rules!“

—  Paul Carus American philosopher 1852 - 1919

"Logical and Mathematical Thought?" in The Monist, Vol. 20 (1909-1910), p. 69

### „A new point is determined in Euclidean Geometry exclusively in one of the three following ways:Having given four points A, B, C, D, not all incident on the same straight line, then(1) Whenever a point P exists which is incident both on (A, B) and on (C, D), that point is regarded as determinate.(2) Whenever a point P exists which is incident both on the straight line (A, B) and on the circle C(D), that point is regarded as determinate.(3) Whenever a point P exists which is incident on both the circles A(B), C(D), that point is regarded as determinate.The cardinal points of any figure determined by a Euclidean construction are always found by means of a finite number of successive applications of some or all of these rules (1), (2) and (3). Whenever one of these rules is applied it must be shown that it does not fail to determine the point. Euclid's own treatment is sometimes defective as regards this requisite.In order to make the practical constructions which correspond to these three Euclidean modes of determination, correponding to (1) the ruler is required, corresponding to (2) both ruler and compass, and corresponding to (3) the compass only.…it is possible to develop Euclidean Geometry with a more restricted set of postulations. For example it can be shewn that all Euclidean constructions can be carried out by means of (3) alone…“

—  E. W. Hobson British mathematician 1856 - 1933

Quelle: Squaring the Circle (1913), pp. 7-8

### „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)

### „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)

### „There is no way to tell whether the patterns extracted by the right hemisphere are real or imagined without subjecting them to left-hemisphere scrutiny. On the other hand, mere critical thinking, without creative and intuitive insights, without the search for new patterns, is sterile and doomed. To solve complex problems in changing circumstances requires the activity of both cerebral hemispheres: the path to the future lies through the corpus callosum.“

—  Carl Sagan American astrophysicist, cosmologist, author and science educator 1934 - 1996

Quelle: The Dragons of Eden (1977), Chapter 7, “Lovers and Madmen” (pp. 190-191)

### „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
2016

### „For – to say a few words on technique – whereas the curved line was used predominantly for reasons of beauty, (Phidias, Michelangelo, Raphael, Rubens) it has been used more and more economically for reasons of truth (Millet, Claude Monet, Paul Cézanne) until it will end as the straight line for reasons of Love. This will enable the art of the future to create an international form; a form understandable to all and vital enough to the expression of a general feeling of love in a monumental way. Such is the future.“

—  Theo van Doesburg Dutch architect, painter, draughtsman and writer 1883 - 1931

Quote from 'Onafhankelijke bespiegelingen over de kunst', by Theo van Doesburg, in the Dutch journal De Avondpost 23 January 1916
1912 – 1919

### „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。

### „Faith which refuses to face indisputable facts is but little faith. Truth is always gain, however hard it is to accommodate ourselves to it. To linger in any kind of untruth proves to be a departure from the straight way of faith.“

—  Albert Schweitzer French-German physician, theologian, musician and philosopher 1875 - 1965

Quelle: The Spiritual Life (1947), p. 290

### „Value fulfillment itself is most difficult to describe, for it combines the nature of a loving presence - a presence with the innate knowledge of its own divine complexity - with a creative ability of infinite proportions that seeks to bring to fulfillment even the slightest, most distant portion of its own inverted complexity. Translated into simpler terms, each portion of energy is endowed with an inbuilt reach of creativity that seeks to fulfill its own potentials in all possible variations - and in such a way that such a development also furthers the creative potentials of each other portion of reality.“

—  Jane Roberts American Writer 1929 - 1984

Session 884, Page 138
Dreams, Evolution and Value Fulfillment, Volume One (1986)