# „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

Letzte Aktualisierung 22. Mai 2020. Geschichte
##### Archimedes4
antiker griechischer Mathematiker, Physiker und Ingenieur -287 - -212 v.Chr

## Ähnliche Zitate

### „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 3. The circle in the moon which divides the dark and the bright portions is least when the cone comprehending both the sun and the moon has its vertex at 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)

### „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)

### „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

### „Proposition 8. When the sun is totally eclipsed, the sun and the moon are then comprehended by one and the same cone which has its vertex at 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)

### „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

### „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

### „Any segment of a right-angled conoid (i. e., a paraboloid of revolution) cut off by a plane at right angles to the axis is 1&frac12; times the cone which has the same base and the same axis as the segment“

—  Archimedes, buch The Method of Mechanical Theorems

Proprosition 4.
The Method of Mechanical Theorems

### „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

### „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)

### „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 sword is the axis of the world and grandeur cannot be divided.“

—  Charles de Gaulle eighteenth President of the French Republic 1890 - 1970

L'épée est l'axe du monde et la grandeur ne se divise pas.
in Vers l’armée de métier.
Writings

### „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

### „[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)

### „Your rights reach down where all owners meet, in Hell'sPointed exclusive conclave, at earth’s centre(Your spun farm's root still on that axis dwells);And up, through galaxies, a growing sector.“

—  William Empson English literary critic and poet 1906 - 1984

"Legal Fiction", line 9; cited from John Haffenden (ed.) The Complete Poems (London: Allen Lane, 2000) p. 37.
The Complete Poems

### „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)

### „In its most general form and from the point of view of physics, love is the internal, affectively apprehended, aspect of the affinity which links and draws together the elements of the world, centre to centre.“

—  Pierre Teilhard De Chardin French philosopher and Jesuit priest 1881 - 1955

This is how it has been understood by the great philosophers from Plato, the poet, to Nicolas of Cusa and other representatives of frigid scholasticism. Once this definition has been accepted, it gives rise to a series of important consequences. Love is power of producing inter-centric relationship. It is present, therefore (at least in a rudimentary state), in all the natural centres, living and pre-living, which make up the world; and it represents, too, the most profound, most direct, and most creative form of inter-action that it is possible to conceive between those centres. Love, in fact, is the expression and the agent of universal synthesis.
pp. 70–71 https://archive.org/stream/ActivationOfEnergy/Activation_of_Energy#page/n65/mode/2up
Activation of Energy (1976)

### „They say gravity is the centre of attraction; I rather think that noise is. Nothing so soon assembles the inhabitants of a house as a loud and sudden noise : …“

—  Letitia Elizabeth Landon English poet and novelist 1802 - 1838

Heath's book of Beauty, 1833 (1832)

### „Proposition 4. The circle which divides the dark and the bright portions in the moon is not perceptibly different from a great circle in the moon.“

—  Aristarchus of Samos ancient Greek astronomer and mathematician

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