“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 , book The Method of Mechanical Theorems

Proposition 6.
The Method of Mechanical Theorems

Adopted from Wikiquote. Last update June 3, 2021. History

Help us to complete the source, original and additional information

Do you have more details about the quote "The centre of gravity of any hemisphere [is on the straight line which] is its axis, and divides the said straight line…" by Archimedes?
Archimedes photo
Archimedes 20
Greek mathematician, physicist, engineer, inventor, and ast… -287–-212 BC

Related quotes

Archimedes photo

“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 book The Method of Mechanical Theorems

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

Aristarchus of Samos photo

“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)

Aristarchus of Samos photo

“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)

Archimedes photo

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

Archimedes book On the Equilibrium of Planes

Book 1, Proposition 9.
On the Equilibrium of Planes

Archimedes photo

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

Archimedes book On the Equilibrium of Planes

Book 1, Proposition 13.
On the Equilibrium of Planes

Aristarchus of Samos photo

“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)

Aristarchus of Samos photo

“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)

Aristarchus of Samos photo

“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)

Richard Dedekind photo

“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 (1831–1916) German mathematician

Stetigkeit und irrationale Zahlen (1872)

Friedensreich Hundertwasser photo

“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 (1928–2000) Austrian artist

Mould Manifesto against Rationalism in Architecture (1958)

Related topics