# Archimedes

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**Archimedes of Syracuse** (c. 287 BC – c. 212 BC) was a Greek mathematician, philosopher, scientist and engineer.

## Contents

## Quotes[edit]

- εὕρηκα [
*heureka*]**I have found it!**or**I have got it!**, commonly quoted as**Eureka!**- 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;

- δῶς μοι πᾶ στῶ καὶ τὰν γᾶν κινάσω. [
*Dos moi pa sto, kai tan gan kinaso.*]**Give me the place to stand, and I shall move the earth.**- 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. This and "**Give me a place to stand, and I shall move the world**" are the most commonly quoted translations.

- Said to be his assertion in demonstrating the principle of the lever; as quoted by Pappus of Alexandria,
- 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, 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*].

- This variant derives from an earlier source than Pappus:
- 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.
- Give me a lever and a place to stand and I will move the earth.

*Noli turbare circulos meos.*or*Noli tangere circulos meos.***Do not disturb my circles!**- 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"). 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.

*On Spirals* (225 B.C.)[edit]

- As translated by T. L. Heath,
*The Works of Archimedes*(1897) unless otherwise indicated.

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

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

*On the Equilibrium of Planes*[edit]

- or
*The Centres of Gravity of Planes* - as translated by T. L. Heath,
*The Works of Archimedes*(1897) unless otherwise indicated.

- 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.
- Book 1, Postulate 1.

- 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.
- Book 1, Proposition 4.

- Two magnitudes whether commensurable or incommensurable, balance at distances reciprocally proportional to the magnitudes.
- Book 1, Propositions 6 & 7, The Law of the Lever.

- The centre of gravity of any parallelogram lies on the straight line joining the middle points of opposite sides.
- Book 1, Proposition 9.

- The centre of gravity of a parallelogram is the point of intersection of its diagonals.
- Book 1, Proposition 10.

- In any triangle the centre of gravity lies on the straight line joining any angle to the middle point of the opposite side.
- Book 1, Proposition 13.

- 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.
- Book 1, Proposition 14.

*The Method of Mechanical Theorems*[edit]

- As quoteed in
*The Method of Archimedes, recently discovered by Heiberg: a supplement to the Works of Archimedes*(1912) Ed. T. L. Heath unless otherwise indicated.

- 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.**

- 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.**

- 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]...

- The centre of gravity of any cylinder is the point of bisection of the axis.
- Proposition presumed from previous work.

- The centre of gravity of any cone is [the point which divides its axis so that] the portion [adjacent to the vertex is] triple [of the portion adjacent to the base].
- Proposition presumed from previous work.

- 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
- Proprosition 4.

- 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.
- Proposition 6.

## Quotes about Archimedes[edit]

**The treatises are, without exception, monuments of mathematical exposition**; the gradual revelation of the plan of attack, the masterly ordering of the propositions, the stern elimination of everything not immediately relevant to the purpose, the finish of the whole, are so impressive in their perfection as to create a feeling akin to awe in the mind of the reader.- T. L. Heath,
*A History of Greek Mathematics II*(1931).

- T. L. Heath,

**Archimedes originally solved the problem of finding the solid content of a sphere before that of finding its surface, and he inferred the result of the latter problem from that of the former. ...another illustration of the fact that the order of propositions in the treatises of the Greek geometers as finally elaborated does not necessarily follow the order of discovery.**

- Archimedes was a brilliant inventor and a mathematician. He says to the people around him, "Don't just live in the lap of the gods. Don't be dominated by Mother Nature. You, as a man, can take control of your own destiny."
- "Ancient Einsteins,"
*Ancient Impossible*(S1E4, aired 27 July 2014, 10:53 P.M. Eastern Daylight Time).

- "Ancient Einsteins,"

- According to legend, nothing could get between him [Archimedes] and his work, and sometimes he would even forget to eat. Ideas would come to him at any moment, and he would scribble them on any available surface. Famously, he was in the bath when he discovered the laws of buoyancy, leading him to run naked through the streets shouting "Eureka!" …
*Eureka*means "I have found it," and it could be argued that Archimedes found out more than anyone else before or since.- "Ancient Einsteins,"
*Ancient Impossible*(S1E4, aired 27 July 2014, 10:53, 10:57 P.M. Eastern Daylight Time).

- "Ancient Einsteins,"

- Tragically for all of us, he [Archimedes] was cut down by a Roman soldier because he refused to stop working. … If Archimedes hadn't been killed before his time, what could have he achieved? The industrial revolution could have happened two thousand years earlier. He might have kick-started the modern age.
- "Ancient Einsteins,"
*Ancient Impossible*(S1E4, aired 27 July 2014, 10:57, 10:58 P.M. Eastern Daylight Time).

- "Ancient Einsteins,"

## External links[edit]

- Archimedes Home Page
- "Archimedes - The Greatest Scientist Ever?"
- "Archimedes of Syracuse"
- Archimedes'
*Book of Lemmas* - "Archimedes and the Rhombicuboctahedron" by Antonio Gutierrez
- Archimedes - The Golden Crown
- Archimedes'
*Quadrature Of The Parabola* - Archimedes'
*On The Measurement Of The Circle* *The Works Of Archimedes*- Works by Archimedes at Project Gutenberg
- NOVA program on Archimedes Palimpsest
- The Archimedes Palimpsest
- The Archimedes Palimpsest project at The Walters Art Museum in Baltimore, Maryland
- Archimedes and his Burning Mirrors, Reality or Fantasy?
- Squaring the circle History Topic at MacTutor
- Biography of Archimedes
- Archimedes - The Greek mathematician and his Eureka moments" on
*BBC 4*(25 January 2007) (requires RealPlayer).