# „Parallel lines have a common end point at an infinite distance.“

Brouillion project (1639) as quoted by Harold Scott MacDonald Coxeter, Projective Geometry (1987)

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##### Gérard Desargues
französischer Mathematiker 1591 - 1661

## Ähnliche Zitate

### „When no point of a line is at a finite distance, the line itself is at an infinite distance.“

—  Girard Desargues French mathematician and engineer 1591 - 1661

Brouillion project (1639) as quoted by Harold Scott MacDonald Coxeter, Projective Geometry (1987)

### „In the field of non-Euclidean geometry, Riemann… began by calling attention to a distinction that seems obvious once it is pointed out: the distinction between an unbounded straight line and an infinite line. The distinction between unboundedness and infiniteness is readily illustrated. A circle is an unbounded figure in that it never comes to an end, and yet it is of finite length. On the other hand, the usual Euclidean concept of a straight line is also unbounded in that it never reaches an end but is of infinite length.…he proposed to replace the infiniteness of the Euclidean straight line by the condition that it is merely unbounded. He also proposed to adopt a new parallel axiom… In brief, there are no parallel lines. This … had been tried… in conjunction with the infiniteness of the straight line and had led to contradictions. However… Riemann found that he could construct another consistent non-Euclidean geometry.“

—  Morris Kline American mathematician 1908 - 1992

Quelle: Mathematical Thought from Ancient to Modern Times (1972), p. 454

### „A straight line is not the shortest distance between two points.“

—  Madeleine L'Engle American writer 1918 - 2007

Quelle: A Wrinkle in Time: With Related Readings

### „In philosophy, as in politics, the longest distance between two points is a straight line.“

—  Will Durant American historian, philosopher and writer 1885 - 1981

Quelle: The Story of Philosophy: The Lives and Opinions of the World's Greatest Philosophers

### „The straight line is regarded as the shortest distance between two people, as if they were points.“

—  Theodor W. Adorno, buch Minima Moralia

Nun gilt für die kürzeste Verbindung zwischen zwei Personen die Gerade, so als ob sie Punkte wären.
E. Jephcott, trans. (1974), § 20
Minima Moralia (1951)

### „The Now, that indivisible point which studs the length of infinite lineWhose ends are nowhere, is thine all, the puny all thou callest thine.“

—  Richard Francis Burton British explorer, geographer, translator, writer, soldier, orientalist, cartographer, ethnologist, spy, linguist, poet,… 1821 - 1890

The Kasîdah of Hâjî Abdû El-Yezdî (1870)
Kontext: And hold Humanity one man, whose universal agony
Still strains and strives to gain the goal, where agonies shall cease to be.
Believe in all things; none believe; judge not nor warp by "Facts" the thought;
See clear, hear clear, tho' life may seem Mâyâ and Mirage, Dream and Naught.
Abjure the Why and seek the How: the God and gods enthroned on high,
Are silent all, are silent still; nor hear thy voice, nor deign reply.
The Now, that indivisible point which studs the length of infinite line
Whose ends are nowhere, is thine all, the puny all thou callest thine.

### „As lines, so loves oblique may wellThemselves in every angle greet;But ours so truly parallel,Though infinite, can never meet.“

—  Andrew Marvell English metaphysical poet and politician 1621 - 1678

Stanza 7.
The Definition of Love (1650-1652)

### „The concept of the infinitely small is involved in the relation of points to a line or the relation of the discrete to the continuous, and Zeno's paradoxes may have caused the Greeks to shy away from this subject.“

—  Morris Kline American mathematician 1908 - 1992

Quelle: Mathematical Thought from Ancient to Modern Times (1972), p. 175

### „In s (in which 180° = \pi [radians]). Further, each full line (great circle) is of finite length 2 \pi R, and any two full lines meet in two points—there are no parallels!“

—  Howard P. Robertson American mathematician and physicist 1903 - 1961

Geometry as a Branch of Physics (1949)

### „These formulae [in (1) and (2) above] may be shown to be valid for a circle or a triangle in the hyperbolic plane… for which K < 0. Accordingly here the perimeter and area of a circle are greater, and the sum of the three angles of a triangle are less, than the corresponding quantities in the Euclidean plane. It can also be shown that each full line is of infinite length, that through a given point outside a given line an infinity of full lines may be drawn which do not meet the given line (the two lines bounding the family are said to be "parallel" to the given line), and that two full lines which meet do so in but one point.“

—  Howard P. Robertson American mathematician and physicist 1903 - 1961

Geometry as a Branch of Physics (1949)

### „Should there really be suns in the whole infinite space, they can be at approximately the same distance from one another, or distributed over galaxies, hence would be in infinite quantities, and consequently the whole sky should be as bright as the sun. Clearly, each line which can conceivably be drawn from our eye will necessarily end on one of the stars and each point on the sky would send us starlight, that is, sunlight.“

—  Heinrich Wilhelm Matthäus Olbers German physician and astronomer 1758 - 1840

Sind wirklich im ganzen unendlichen Raum Sonnen vorhanden, sie mögen nun in ungefähr gleichen Abständen von einander, oder in Milchstrassen-Systeme vertheilt sein, so wird ihre Menge unendlich, und da müsste der ganze Himmel ebenso hell sein, wie die Sonne. Denn jede Linie, die ich mir von unserm Auge gezogen denken kann, wird nothwendig auf irgend einen Fixstern treffen, und also müßte uns jeder Punkt am Himmel Fixsternlicht, also Sonnenlicht zusenden.
Olbers' paradox, expressed in [Ueber die Durchsichtigkeit des Weltraums, Astronomisches Jahrbuch für das Jahr 1826, J. Bode. Berlin, Späthen 1823, 110-121]

### „Our lives may be separate, but they run in the same direction, like parallel lines.“

—  Milan Kundera, buch Die unerträgliche Leichtigkeit des Seins

Quelle: The Unbearable Lightness of Being

### „I don't speechify. I know the shortest distance between two points is a straight line. And that's what I ask. But they get mad at the straight line. I just want to ask a tough question.“

—  Helen Thomas American author and journalist 1920 - 2013

Interview by Adam Holdorf for Real Change News, (18 March 2004).

### „In right knowledge the study of man must proceed on parallel lines with the study of the world, and the study of the world must run parallel with the study of man.“

—  G. I. Gurdjieff influential spiritual teacher, Armenian philosopher, composer and writer 1866 - 1949

In Search of the Miraculous (1949)

### „There’s a magic in the distance, where the sea-line meets the sky.“

—  Alfred Noyes English poet 1880 - 1958

Forty Singing Seamen
Poems (1906)

### „Distance in a straight line has no mystery. The mystery is in the sphere.“

—  Thomas Mann German novelist, and 1929 Nobel Prize laureate 1875 - 1955

### „Following straight lines shortens distances, and also life.“

—  Antonio Porchia Italian Argentinian poet 1885 - 1968

El ir derecho acorta las distancias, y también la vida.
Voces (1943)

### „The Infinite has to be a relative concept. Go any distance: an infinite space means that there is more to be explored.“

—  Joseph Silk British-American astronomer 1942

The Infinite Cosmos, Page 1

### „You do not reach the sublime by degrees; the distance between it and the merely beautiful is infinite.“

—  Anne Louise Germaine de Staël, buch Corinne

Bk. 4, ch. 3
Corinne (1807)

### „Closely related to the problem of the parallel postulate is the problem of whether physical space is infinite. Euclid assumes“

—  Morris Kline American mathematician 1908 - 1992

Quelle: Mathematical Thought from Ancient to Modern Times (1972), p. 177
Kontext: Closely related to the problem of the parallel postulate is the problem of whether physical space is infinite. Euclid assumes in Postulate 2 that a straight-line segment can be extended as far as necessary; he uses this fact, but only to find a larger finite length—for example in Book I, Propositions 11, 16, and 20. For these proofs Heron gave new proofs that avoided extending the lines, in order to meet the objection of anyone who would deny that the space was available for the extension.