# „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.“

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

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##### Aristarchos von Samos
griechischer Astronom, Vertreter des heliozentrischen Weltb…

## Ähnliche Zitate

### „Proposition 13. The straight line subtending the portion intercepted within the earth's shadow of the circumference of the circle in which the extremities of the diameter of the circle dividing the dark and the bright portions in the moon move is less than double of the diameter of the moon, but has to it a ratio greater than that which 88 has to 45; and it is less than 1/9th part of the diameter of the sun, but has to it a ratio greater than that which 22 has to 225. But it has to the straight line drawn from the centre of the sun at right angles to the axis and meeting the sides of the cone a ratio greater than that which 979 has to 10125.“

—  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 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

### „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

### „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

### „We are now in a position to prove the following propositions : —1. The distance of the sun from the earth is greater than eighteen times, but less than twenty times, the distance of the moon (from the earth); this follows from the hypothesis about the halved moon.2. The diameter of the sun has the same ratio (as aforesaid) to the diameter of the moon.3. The diameter of the sun has to the diameter of the earth a ratio greater than that which 19 has to 3, but less than that which 43 has to 6; this follows from the ratio thus discovered between the distances, the hypothesis about the shadow, and the hypothesis that the moon subtends one fifteenth part of a sign of the zodiac.“

—  Aristarchus of Samos ancient Greek astronomer and mathematician

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

### „Proposition 11. The diameter of the moon is less than 2/45ths, but greater than 1/30th of the distance of the centre of the moon from our eye.“

—  Aristarchus of Samos ancient Greek astronomer and mathematician

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

### „[Hypotheses]1. That the Moon receives its light from the sun.2. That the earth is in the relation of a point and centre to the sphere in which the moon moves.3. That, when the moon appears to us halved, the great circle which divides the dark and the bright portions of the moon is in the direction of our eye.4. That, when the moon appears to us halved, its distance from the sun is then less than a quadrant by one-thirtieth of a quadrant.5. That the breadth of the (earth's) shadow is (that) of two moons.6. That the moon subtends one fifteenth part of a sign of the zodiac.“

—  Aristarchus of Samos ancient Greek astronomer and mathematician

Note "is less than a quadrant..." is less than 90° by l/30th of 90° or 3°, and is therefore equal to 87°.
On the Sizes and Distances of the Sun and the Moon (c. 250 BC)

### „Proposition 1. Two equal spheres are comprehended by one and the same cylinder, and two unequal spheres by one and the same cone which has its vertex in the direction of the lesser sphere; and the straight line drawn through the centres of the spheres is at right angles to each of the circles in which the surface of the cylinder, or of the cone, touches the spheres.“

—  Aristarchus of Samos ancient Greek astronomer and mathematician

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

### „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)

### „Proposition 18. The earth is to the moon in a ratio greater than that which 1259712 has to 79507, but less than that which 216000 has to 6859.“

—  Aristarchus of Samos ancient Greek astronomer and mathematician

p, 125
On the Sizes and Distances of the Sun and the Moon (c. 250 BC)
Variante: Proposition 17. The diameter of the earth is to the diameter of the moon in a ratio greater than that which 108 has to 43, but less than that which 60 has to 19.

### „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

### „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

### „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)

### „As Hegel well knew, the ascent of reason has never followed a straight line.“

—  Paul A. Baran American Marxist economist 1909 - 1964

Quelle: The Political Economy Of Growth (1957), Chapter Eight, The Steep Ascent, p. 298

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

—  Friedensreich Hundertwasser Austrian artist 1928 - 2000

Mould Manifesto against Rationalism in Architecture (1958)

### „Nothing shows you the straight line from here to death like a list.“

—  Chuck Palahniuk, buch Survivor

Quelle: Survivor

### „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

### „I say that conceit is just as natural a thing to human minds as a centre is to a circle. But little-minded people's thoughts move in such small circles that five minutes' conversation gives you an arc long enough to determine their whole curve. An arc in the movement of a large intellect does not sensibly differ from a straight line. Even if it have the third vowel ['I', the first-person pronoun] as its centre, it does not soon betray it. The highest thought, that is, is the most seemingly impersonal; it does not obviously imply any individual centre.“

—  Oliver Wendell Holmes Poet, essayist, physician 1809 - 1894

The Autocrat of the Breakfast Table (1858)

### „Proposition 12. The diameter of the circle which divides the dark and the bright portions in the moon is less than the diameter of the moon, but has to it a ratio greater than that which 89 has to 90.“

—  Aristarchus of Samos ancient Greek astronomer and mathematician

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

### „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.