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Archimedes Quotes

Archimedes of Syracuse was a Greek mathematician, physicist, engineer, inventor, and astronomer. Although few details of his life are known, he is regarded as one of the leading scientists in classical antiquity. Generally considered the greatest mathematician of antiquity and one of the greatest of all time, Archimedes anticipated modern calculus and analysis by applying concepts of infinitesimals and the method of exhaustion to derive and rigorously prove a range of geometrical theorems, including the area of a circle, the surface area and volume of a sphere, and the area under a parabola.Other mathematical achievements include deriving an accurate approximation of pi, defining and investigating the spiral bearing his name, and creating a system using exponentiation for expressing very large numbers. He was also one of the first to apply mathematics to physical phenomena, founding hydrostatics and statics, including an explanation of the principle of the lever. He is credited with designing innovative machines, such as his screw pump, compound pulleys, and defensive war machines to protect his native Syracuse from invasion.

Archimedes died during the Siege of Syracuse when he was killed by a Roman soldier despite orders that he should not be harmed. Cicero describes visiting the tomb of Archimedes, which was surmounted by a sphere and a cylinder, which Archimedes had requested be placed on his tomb to represent his mathematical discoveries.

Unlike his inventions, the mathematical writings of Archimedes were little known in antiquity. Mathematicians from Alexandria read and quoted him, but the first comprehensive compilation was not made until c. 530 AD by Isidore of Miletus in Byzantine Constantinople, while commentaries on the works of Archimedes written by Eutocius in the sixth century AD opened them to wider readership for the first time. The relatively few copies of Archimedes' written work that survived through the Middle Ages were an influential source of ideas for scientists during the Renaissance, while the discovery in 1906 of previously unknown works by Archimedes in the Archimedes Palimpsest has provided new insights into how he obtained mathematical results. Wikipedia  

✵ 287 BC – 212 BC
Archimedes photo

Works
On Spirals
Archimedes
Archimedes: 20   quotes 22   likes

Famous Archimedes Quotes

“Equal weights at equal distances are in equilibrium and equal weights at unequal distances are not in equilibrium but incline towards the weight which is at the greater distance.”

Archimedes book On the Equilibrium of Planes

Book 1, Postulate 1.
On the Equilibrium of Planes

“I have found it! or I have got it!, commonly quoted as Eureka!”

Archimedes

What he exclaimed as he ran naked from his bath, realizing that by measuring the displacement of water an object produced, compared to its weight, he could measure its density (and thus determine the proportion of gold that was used in making a king's crown); as quoted by Vitruvius Pollio in De Architectura, ix.215;

“Those who claim to discover everything but produce no proofs of the same may be confuted as having actually pretended to discover the impossible.”

Archimedes book On Spirals

On Spirals (225 B.C.)

“Two magnitudes whether commensurable or incommensurable, balance at distances reciprocally proportional to the magnitudes.”

Archimedes book On the Equilibrium of Planes

Book 1, Propositions 6 & 7, The Law of the Lever.
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 1½ times the cone which has the same base and the same axis as the segment”

Archimedes book The Method of Mechanical Theorems

Proprosition 4.
The Method of Mechanical Theorems

Archimedes Quotes

“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

“Give me the place to stand, and I shall move the earth.”

Archimedes

δῶς[No omega+perispomene doric form per e.g. LSJ, March 2017] μοι πᾶ στῶ καὶ τὰν γᾶν κινάσω.
Dôs moi pâ stô, kaì tàn gân kinásō.
Said to be his assertion in demonstrating the principle of the lever; as quoted by Pappus of Alexandria, Synagoge, Book VIII, c. AD 340; also found in Chiliades (12th century) by John Tzetzes, II.130 http://books.google.com/books?id=dG0GAAAAQAAJ&pg=PA46. This and "Give me a place to stand, and I shall move the world" are the most commonly quoted translations.
Variant translations:
Give me a place to stand and with a lever I will move the whole world.
This variant derives from an earlier source than Pappus: The Library of History of Diodorus Siculus, Fragments of Book XXVI http://penelope.uchicago.edu/Thayer/E/Roman/Texts/Diodorus_Siculus/26*.html, as translated by F. R. Walton, in Loeb Classical Library (1957) Vol. XI. In Doric Greek this may have originally been Πᾷ βῶ, καὶ χαριστίωνι τὰν γᾶν κινήσω πᾶσαν [Pā bō, kai kharistiōni tan gān kinēsō [variant kinasō] pāsan].
Give me a lever and a place to stand and I will move the earth.
Give me a fulcrum, and I shall move the world.
Give me a firm spot on which to stand, and I shall move the earth.

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

Archimedes book On the Equilibrium of Planes

Book 1, Proposition 10.
On the Equilibrium of Planes

“I am persuaded that it [The Method of Mechanical Theorems] will be of no little service to mathematics; for I apprehend that some, either of my contemporaries or of my successors, will, by means of the method when once established, be able to discover other theorems in addition, which have not yet occurred to me.”

Archimedes book The Method of Mechanical Theorems

The Method of Mechanical Theorems

Mathematics

“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 book On the Equilibrium of Planes

Book 1, Proposition 14.
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 book On the Equilibrium of Planes

Book 1, Proposition 13.
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 book The Method of Mechanical Theorems

Proposition 6.
The Method of Mechanical Theorems

Way

“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

“Do not disturb my circles!”
Noli turbare circulos meos. or Noli tangere circulos meos.

Archimedes

Original form: "noli … istum disturbare" ("Do not … disturb that (sand)") — Valerius Maximus, Memorable Doings and Sayings, Book VIII.7.ext.7 (See Chris Rorres (Courant Institute of Mathematical Sciences) – "Death of Archimedesː Sources" http://www.math.nyu.edu/~crorres/Archimedes/Death/Histories.html). This quote survives only in its Latin version or translation. In modern era, it was paraphrased as Noli turbare circulos meos and then translated to Katharevousa Greek as "μὴ μου τοὺς κύκλους τάραττε".
Reportedly his last words, said to a Roman soldier who, despite being given orders not to, killed Archimedes during the conquest of Syracuse; as quoted in World Literature: An Anthology of Human Experience (1947) by Arthur Christy, p. 655.

“I thought fit to… explain in detail in the same book the peculiarity of a certain method, by which it will be possible… to investigate some of the problems in mathematics by means of mechanics. This procedure is… no less useful even for the proof of the theorems themselves; for certain things first became clear to me by a mechanical method, although they had to be demonstrated by geometry afterwards… But it is of course easier, when we have previously acquired, by the method, some knowledge of the questions, to supply the proof than it is to find it without any previous knowledge.”

Archimedes book The Method of Mechanical Theorems

The Method of Mechanical Theorems

Books , Mathematics , Question , Knowledge

“How many theorems in geometry which have seemed at first impracticable are in time successfully worked out!”

Archimedes book On Spirals

On Spirals (225 B.C.)

Time

“First then I will set out the very first theorem which became known to me by means of mechanics, namely that
Any segment of a section of a right angled cone (i. e., a parabola) is four-thirds of the triangle which has the same base and equal height,
and after this I will give each of the other theorems investigated by the same method. Then at the end of the book I will give the geometrical [proofs of the propositions]…”

Archimedes book The Method of Mechanical Theorems

The Method of Mechanical Theorems

Books

“The centre of gravity of any cylinder is the point of bisection of the axis.”

Archimedes book The Method of Mechanical Theorems

Proposition presumed from previous work.
The Method of Mechanical Theorems

“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 book On the Equilibrium of Planes

Book 1, Proposition 4.
On the Equilibrium of Planes

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