# „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

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

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### „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

### „If two equal weights have not the same centre of gravity, the centre of gravity of both taken together is at the middle point of the line joining their centres of gravity.“

—  Archimedes, buch On the Equilibrium of Planes

Book 1, Proposition 4.
On the Equilibrium of Planes

### „The centre of gravity of a parallelogram is the point of intersection of its diagonals.“

—  Archimedes, buch On the Equilibrium of Planes

Book 1, Proposition 10.
On the Equilibrium of Planes

### „It follows at once from the last proposition that the centre of gravity of any triangle is at the intersection of the lines drawn from any two angles to the middle points of the opposite sides respectively.“

—  Archimedes, buch On the Equilibrium of Planes

Book 1, Proposition 14.
On the Equilibrium of Planes

### „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 centre of gravity of any cylinder is the point of bisection of the axis.“

—  Archimedes, buch The Method of Mechanical Theorems

Proposition presumed from previous work.
The Method of Mechanical Theorems

### „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 cone is [the point which divides its axis so that] the portion [adjacent to the vertex is] triple“

—  Archimedes, buch The Method of Mechanical Theorems

of the portion adjacent to the base
Proposition presumed from previous work.
The Method of Mechanical Theorems

### „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"

### „If the earth were not round, heavy bodies would not tend from every side in a straight line towards the center of the earth, but to different points from different sides.“

—  Johannes Kepler, buch Astronomia nova

As quoted by Bryant, ibid.
Astronomia nova (1609)

### „Opinion is like a pendulum and obeys the same law. If it goes past the centre of gravity on one side, it must go a like distance on the other; and it is only after a certain time that it finds the true point at which it can remain at rest.“

—  Arthur Schopenhauer, buch Parerga und Paralipomena

Vol. 2 "Further Psychological Observations" as translated in Essays and Aphorisms (1970), as translated by R. J. Hollingdale
Parerga and Paralipomena (1851), Counsels and Maxims

### „We hang on to every line,And walk straight down the middle of it.“

—  Kate Bush British recording artist; singer, songwriter, musician and record producer 1958

Song lyrics, The Sensual World (1989)

### „Take two opposites, connect the dots, and you have a straight line.“

—  Yahia Lababidi 1973

Signposts to Elsewhere (2008)

### „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)

### „In the preceding section attention was called to the fact that every point p of the straight line produces a separation of the same into two portions such that every point of one portion lies to the left of every point of the other. I find the essence of continuity in the converse, i. e., in the following principle:"If all points of the straight line fall into two classes such that every point of the first class lies to the left of every point of the second class, then there exists one and only one point which produces this division of all points into two classes, this severing of the straight line into two portions."…every one will at once grant the truth of this statement; the majority of my readers will be very much disappointed in learning that by this commonplace remark the secret of continuity is to be revealed.“

—  Richard Dedekind German mathematician 1831 - 1916

Stetigkeit und irrationale Zahlen (1872)

### „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).

### „Grasping spatial gestalts as figures is mathematizing of space. Arranging the properties of a parallelogram such that a particular one pops up to base the others on it in order to arrive at a definition of parallelogram, that is mathematizing the conceptual field of the parallelogram.“

—  Hans Freudenthal Dutch mathematician 1905 - 1990

Quelle: Mathematics as an Educational Task (1973), p. 133

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

—  Morris Kline American mathematician 1908 - 1992

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.