# „To avoid any assertion about the infinitude of the straight line, Euclid says a line segment“

Quelle: Mathematical Thought from Ancient to Modern Times (1972), p. 175
Kontext: To avoid any assertion about the infinitude of the straight line, Euclid says a line segment (he uses the word "line" in this sense) can be extended as far as necessary. Unwillingness to involve the infinitely large is seen also in Euclid's statement of the parallel axiom. Instead of considering two lines that extend to infinity and giving a direct condition or assumption under which parallel lines might exist, his parallel axiom gives a condition under which two lines will meet at some finite point.

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##### Morris Kline
US-amerikanischer Mathematiker 1908 - 1992

## Ähnliche Zitate

### „Today we live in a chaos of straight lines, in a jungle of straight lines. If you do not believe this, take the trouble to count the straight lines which surround you. Then you will understand, for you will never finish counting.“

—  Friedensreich Hundertwasser Austrian artist 1928 - 2000

Mould Manifesto against Rationalism in Architecture (1958)

### „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

### „The materialists say, it is by means of a series of straight lines more or less perfect that one imagines the perfect straight line as an ideal limit. That is right, but the progression in itself necessarily contains what is infinite; it is in relation to the perfect straight line that one can say that such and such a straight line is less twisted than some other. … Either one conceives the infinite or one does not conceive at all.“

—  Simone Weil French philosopher, Christian mystic, and social activist 1909 - 1943

Quelle: Lectures on Philosophy (1959), p. 87

### „The straight line belongs to Man. The curved line belongs to God.“

—  Antoni Gaudí Catalan architect 1852 - 1926

The real author seems to be Pierre Albert-Birot https://books.google.com/books?id=3Ul51CwjUOcC&pg=PA290&dq=%22the+curved+line+that+belongs+let%27s+say+to+God+and+the+straight+line+that+belongs+to+man%22&hl=de&sa=X&redir_esc=y#v=onepage&q=%22the%20curved%20line%20that%20belongs%20let%27s%20say%20to%20God%20and%20the%20straight%20line%20that%20belongs%20to%20man%22&f=false.
Attributed

### „The straight line is godless and immoral.“

—  Friedensreich Hundertwasser Austrian artist 1928 - 2000

Mould Manifesto against Rationalism in Architecture (1958)

### „Euclid defines the angle as an inclination of lines…he meant halflines, because otherwise he would not be able to distinguish adjacent angles from each other… Euclid does not know zero angles, nor straight and bigger than straight angles…Euclid takes the liberty of adding angles beyond two and even four right angles; the result cannot be angles according to the original definitions…Nevertheless one feels that Euclid’s angle concept is consistent.“

—  Hans Freudenthal Dutch mathematician 1905 - 1990

Quelle: Mathematics as an Educational Task (1973), p. 476-477

### „In any triangle the centre of gravity lies on the straight line joining any angle to the middle point of the opposite side.“

—  Archimedes, buch On the Equilibrium of Planes

Book 1, Proposition 13.
On the Equilibrium of Planes

### „This makes you think in straight lines. And if today doesn't happen in straight lines -- think of your own experience -- why should the past have?“

—  James Burke (science historian) British broadcaster, science historian, author, and television producer 1936

Connections (1979), 10 - Yesterday, Tomorrow and You
Kontext: The question is in what way are the triggers around us likely to operate to cause things to change -- for better or worse. And, is there anything we can learn from the way that happened before, so we can teach ourselves to look for and recognize the signs of change? The trouble is, that's not easy when you have been taught as I was, for example, that things in the past happened in straight-forward lines. I mean, take one oversimple example of what I'm talking about: the idea of putting the past into packaged units -- subjects, like agriculture. The minute you look at this apparently clear-cut view of things, you see the holes. I mean, look at the tractor. Oh sure, it worked in the fields, but is it a part of the history of agriculture or a dozen other things? The steam engine, the electric spark, petroleum development, rubber technology. It's a countrified car. And, the fertilizer that follows; it doesn't follow! That came from as much as anything else from a fellow trying to make artificial diamonds. And here's another old favorite: Eureka! Great Inventors You know, the lonely genius in the garage with a lightbulb that goes ping in his head. Well, if you've seen anything of this series, you'll know what a wrong approach to things that is. None of these guys did anything by themselves; they borrowed from other people's work. And how can you say when a golden age of anything started and stopped? The age of steam certainly wasn't started by James Watt; nor did the fellow whose engine he was trying to repair -- Newcomen, nor did his predecessor Savorey, nor did his predecessor Papert. And Papert was only doing what he was doing because they had trouble draining the mines. You see what I'm trying to say? This makes you think in straight lines. And if today doesn't happen in straight lines -- think of your own experience -- why should the past have? That's part of what this series has tried to show: that the past zig-zagged along -- just like the present does -- with nobody knowing what's coming next. Only we do it more complicatedly, and it's because our lives are that much more complex than theirs were that it's worth bothering about the past. Because if you don't know how you got somewhere, you don't know where you are. And we are at the end of a journey -- the journey from the past.

### „The attempt to avoid a direct affirmation about infinite parallel straight lines caused Euclid to phrase the parallel axiom in a rather complicated way. He realized that, so worded, this axiom lacked the self-sufficiency of the other nine axioms, and there is good reason to believe that he avoided using it until he had to. Many Greeks tried to find substitute axioms for the parallel axiom or to prove it on the basis of the other nine. …Simplicius“

—  Morris Kline American mathematician 1908 - 1992

Quelle: Mathematical Thought from Ancient to Modern Times (1972), p. 177
Kontext: The attempt to avoid a direct affirmation about infinite parallel straight lines caused Euclid to phrase the parallel axiom in a rather complicated way. He realized that, so worded, this axiom lacked the self-sufficiency of the other nine axioms, and there is good reason to believe that he avoided using it until he had to. Many Greeks tried to find substitute axioms for the parallel axiom or to prove it on the basis of the other nine.... Simplicius cites others who worked on the problem and says further that people "in ancient times" objected to the use of the parallel postulate.

### „Human knowledge is not (or does not follow) a straight line, but a curve, which endlessly approximates a series of circles, a spiral. Any fragment, segment, section of this curve can be transformed (transformed one-sidedly) into an independent, complete, straight line, which then (if one does not see the wood for the trees) leads into the quagmire, into clerical obscurantism (where it is anchored by the class interests of the ruling classes).“

—  Vladimir Lenin Russian politician, led the October Revolution 1870 - 1924

### „My formula for happiness: a Yes, a No, a straight line, a goal.“

—  Friedrich Nietzsche German philosopher, poet, composer, cultural critic, and classical philologist 1844 - 1900

### „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

### „The growth of love is not a straight line, but a series of hills and valleys.“

—  Madeleine L'Engle American writer 1918 - 2007

Quelle: Two-Part Invention: The Story of a Marriage

### „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

### „A circle is a round straight line with a hole in the middle.“

—  Mark Twain American author and humorist 1835 - 1910

Quoting a schoolchild in "English as She Is Taught"

### „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)

### „Everything in the universe goes by indirection. There are no straight lines.“

—  Ralph Waldo Emerson American philosopher, essayist, and poet 1803 - 1882

### „Proposition 14. The straight line joined from the centre of the earth to the centre of the moon has to the straight line cut off from the axis towards the centre of the moon by the straight line subtending the (circumference) within the earth's shadow a ratio greater than that which 675 has to 1.“

—  Aristarchus of Samos ancient Greek astronomer and mathematician

p, 125
On the Sizes and Distances of the Sun and the Moon (c. 250 BC)

### „The centre of gravity of any parallelogram lies on the straight line joining the middle points of opposite sides.“

—  Archimedes, buch On the Equilibrium of Planes

Book 1, Proposition 9.
On the Equilibrium of Planes

### „Somedays the line I walk turns out to be straight -Other days the line tends to deviate.“

—  Ani DiFranco musician and activist 1970

In or Out
Song lyrics