# Archimedes: Wikis

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Archimedes of Syracuse
(Greek: Ἀρχιμήδης)

Archimedes Thoughtful by Fetti (1620)
Born c. 287 BC
Syracuse, Sicily
Magna Graecia
Died c. 212 BC
Syracuse
Residence Syracuse, Sicily
Ethnicity Greek
Fields Mathematics, Physics, Engineering, Astronomy, Invention
Known for Archimedes' Principle, Archimedes' screw, Hydrostatics, Levers, Infinitesimals
.Archimedes of Syracuse (Greek: Ἀρχιμήδης; c. 287 BC – c. 212 BC) was a Greek mathematician, physicist, engineer, inventor, and astronomer.^ Archimedes          (287-212 BC).
• "Natural Magick" - "Glossery/Index - A" 19 January 2010 8:47 UTC homepages.tscnet.com [Source type: Original source]

^ Archimedes Archimedes was a mathematician and inventor from ancient Greece best known for his discovery of the relation between the surface and volume of a sphere and ...
• Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]

^ This gifted Greek mathematician and inventor once said, "Give me a place to stand and rest my lever on, and I can move the Earth."
• "Natural Magick" - "Glossery/Index - A" 19 January 2010 8:47 UTC homepages.tscnet.com [Source type: Original source]

.Although few details of his life are known, he is regarded as one of the leading scientists in classical antiquity.^ Although Newton should certainly be in the top 5 of any such list, if one thinks through this clearly, one has to conclude that Charles Darwin was mankind’s greatest scientist to date.
• Top 10 Most Influential Scientists - Listverse 19 January 2010 8:47 UTC listverse.com [Source type: General]

^ Archimedes of Syracuse Greek mathematician, scientist and inventor Archimedes regarded as one of the leading scientists and inventor of all time though there are very much a few details of his life mentioned.
• Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]

^ ARCHIMEDES - GREATEST SCIENTIST EVER? Math is the "queen of sciences," and Archimedes is widely regarded as one of the greatest mathematicians ever - perhaps the most influential of them all.
• Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]

.Among his advances in physics are the foundations of hydrostatics, statics and the explanation of the principle of the lever.^ He is known for his formulation of hydrostatic principle commonly known as "Archimedes Principle" and at the same time he is the first who recognize and used the power of lever.
• Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]

He is credited with designing innovative machines, including siege engines and the screw pump that bears his name. .Modern experiments have tested claims that Archimedes designed machines capable of lifting attacking ships out of the water and setting ships on fire using an array of mirrors.^ The physicist grabs a bucket and leaps towards the sink, fills the bucket with water and puts out the fire.
• Math Jokes and Archimedes - Jokes and Science 19 January 2010 8:47 UTC www.juliantrubin.com [Source type: Original source]

^ The engineer starts to calculate how much water it takes to put out the fire.
• Math Jokes and Archimedes - Jokes and Science 19 January 2010 8:47 UTC www.juliantrubin.com [Source type: Original source]

^ His invention of the water-screw, still in use in Egypt, for irrigation, draining marshy land and pumping out water from the bilges of ships.
• Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]

[1]
.Archimedes is generally considered to be the greatest mathematician of antiquity and one of the greatest of all time.^ In conclusion, Archimedes is well deserved to be named as one of the greatest mathematicians.
• Mathematical Database - Math Funland - Math Articles 19 January 2010 8:47 UTC www.mathdb.org [Source type: FILTERED WITH BAYES]

^ Also Archimedes is also considered one of the three greatest mathematicians ever, as with Newton and Gauss.
• Mathematical Database - Math Funland - Math Articles 19 January 2010 8:47 UTC www.mathdb.org [Source type: FILTERED WITH BAYES]

^ It was authored by one of the greatest mechanical minds in history: the legendary Archimedes , who knew a thing or two about spheres right down to his dying words...
• 7 Books We Lost to History That Would Have Changed the World | Cracked.com 19 January 2010 8:47 UTC www.cracked.com [Source type: General]

[2][3] .He used the method of exhaustion to calculate the area under the arc of a parabola with the summation of an infinite series, and gave a remarkably accurate approximation of pi.^ He used the method of exhaustion to calculate the area under the arc of a parabola with the summation of an infinite series, and gave a remarkably accurate approximation of Pi.
• Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]

^ The method of exhaustion gives us the formulae for calculating areas.
• Mathematical Database - Math Funland - Math Articles 19 January 2010 8:47 UTC www.mathdb.org [Source type: FILTERED WITH BAYES]

^ For example, he gave the approximations of and square roots of some large numbers, insights on the solutions of cubic equations and arithmetic series.
• Mathematical Database - Math Funland - Math Articles 19 January 2010 8:47 UTC www.mathdb.org [Source type: FILTERED WITH BAYES]

[4] .He also defined the spiral bearing his name, formulas for the volumes of surfaces of revolution and an ingenious system for expressing very large numbers.^ He also defined the spiral bearing his name, formulas for the volumes of surfaces of revolution and an ingenious system for expressing very large numbers.
• Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]

^ So, there are a > > lot of things that we know about very large numbers.
• #266 mathematics ends at about 10^500 Re: powerset - sci.logic | Google Groups 19 January 2010 8:47 UTC groups.google.com [Source type: Original source]

^ So, there are a > > > lot of things that we know about very large numbers.
• #266 mathematics ends at about 10^500 Re: powerset - sci.logic | Google Groups 19 January 2010 8:47 UTC groups.google.com [Source type: Original source]

.Archimedes died during the Siege of Syracuse when he was killed by a Roman soldier despite orders that he should not be harmed.^ The soldier was enraged by this, and killed Archimedes with his sword.
• Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]

^ General Marcellus was reportedly angered by the death of Archimedes, as he considered him a valuable scientific asset and had ordered that he not be harmed.
• Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]

^ BC during the Second Punic War, when Roman forces under General Marcus Claudius Marcellus captured the city of Syracuse after a two-year-long siege.
• Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]

.Cicero describes visiting the tomb of Archimedes, which was surmounted by a sphere inscribed within a cylinder.^ According to Plutarch (45-120 AD), Archimedes is said to have requested his friends and relations that, when he was dead, they would place over his tomb a sphere containing a cylinder, inscribing it with the ratio which the containing solid bears to the contained.
• Math Jokes and Archimedes - Jokes and Science 19 January 2010 8:47 UTC www.juliantrubin.com [Source type: Original source]

^ This is also reflected by the fact that in Statements 1 and 5 of "Spheres and Cylinders" Archimedes dealt with the equation a 2 : x = x : b .
• Mathematical Database - Math Funland - Math Articles 19 January 2010 8:47 UTC www.mathdb.org [Source type: FILTERED WITH BAYES]

^ Archimedes gave instructions that his tombstone should have displayed on it a diagram consisting of a sphere with a circumscribing cylinder.
• Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]

.Archimedes had proven that the sphere has two thirds of the volume and surface area of the cylinder (including the bases of the latter), and regarded this as the greatest of his mathematical achievements.^ He discovered the relation between the surface area and volume of a sphere and those of its circumscribing cylinder.
• "Natural Magick" - "Glossery/Index - A" 19 January 2010 8:47 UTC homepages.tscnet.com [Source type: Original source]

^ Archimedes had proved that the volume and surface area of the sphere are two thirds that of the cylinder including its bases.
• Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]

^ Volume of the cylinder = ´ Volume of the sphere .
• Mathematical Database - Math Funland - Math Articles 19 January 2010 8:47 UTC www.mathdb.org [Source type: FILTERED WITH BAYES]

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, while commentaries on the works of Archimedes written by Eutocius in the sixth century AD opened them to wider readership for the first time.^ A biography of Archimedes was written by his friend Heracleides but this work has been lost, leaving the details of his life obscure.
• Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]

^ Archimedes - we're back - Archimedes - The Open CAD After a lot of work, some news and no release, we're back on full speed (or almost) with Archimedes' new version.
• Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]

^ He is known for his formulation of hydrostatic principle commonly known as "Archimedes Principle" and at the same time he is the first who recognize and used the power of lever.
• Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]

.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,[5] 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.^ A biography of Archimedes was written by his friend Heracleides but this work has been lost, leaving the details of his life obscure.
• Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]

^ Archimedes - we're back - Archimedes - The Open CAD After a lot of work, some news and no release, we're back on full speed (or almost) with Archimedes' new version.
• Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]

^ ARCHIMEDES - GREATEST SCIENTIST EVER? Math is the "queen of sciences," and Archimedes is widely regarded as one of the greatest mathematicians ever - perhaps the most influential of them all.
• Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]

[6]

## Biography

This bronze statue of Archimedes is at the Archenhold Observatory in Berlin. It was sculpted by Gerhard Thieme and unveiled in 1972.
Archimedes was born c. .287 BC in the seaport city of Syracuse, Sicily, at that time a colony of Magna Graecia.^ BC in the seaport city of Syracuse, Sicily, at that time a colony of Magna Graecia.
• Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]

^ Archimedes (287 - 212 B.C.) was born at Syracuse of Sicily as a son of the astronomer Pheidias.
• Mathematical Database - Math Funland - Math Articles 19 January 2010 8:47 UTC www.mathdb.org [Source type: FILTERED WITH BAYES]

.The date of birth is based on a statement by the Byzantine Greek historian John Tzetzes that Archimedes lived for 75 years.^ The date of birth is based on a statement by the Byzantine Greek historian John Tzetzes that Archimedes lived for 75 years.
• Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]

[7] In The Sand Reckoner, Archimedes gives his father's name as Phidias, an astronomer about whom nothing is known. .Plutarch wrote in his Parallel Lives that Archimedes was related to King Hiero II, the ruler of Syracuse.^ Plutarch wrote in his Parallel Lives that Archimedes was related to King Hiero II, the ruler of Syracuse.
• Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]

^ Archimedes proposed the following problem when he visited Hieron, the King of Syracuse: .
• Mathematical Database - Math Funland - Math Articles 19 January 2010 8:47 UTC www.mathdb.org [Source type: FILTERED WITH BAYES]

^ It is said that Archimedes was a relative of Hieron, the king of Syracuse.
• Mathematical Database - Math Funland - Math Articles 19 January 2010 8:47 UTC www.mathdb.org [Source type: FILTERED WITH BAYES]

[8] .A biography of Archimedes was written by his friend Heracleides but this work has been lost, leaving the details of his life obscure.^ In 1906, J. L. Geiberg (1854 - 1928) found in Turkey a book containing a lot of Archimedes' works, including "The Methods", which was written by Archimedes to describe where his beautiful ideas came from.
• Mathematical Database - Math Funland - Math Articles 19 January 2010 8:47 UTC www.mathdb.org [Source type: FILTERED WITH BAYES]

^ Many works were written by Archimedes, including "On the Sphere and Cylinder", "On the Measurement of a Circle", "On Conoids and Spheroids", "On Spirals", "The Sandreckoner", "On Quadrature of the parabola", "Book of Lemmas" and "The Methods".
• Mathematical Database - Math Funland - Math Articles 19 January 2010 8:47 UTC www.mathdb.org [Source type: FILTERED WITH BAYES]

[9] .It is unknown, for instance, whether he ever married or had children.^ It is unknown, for instance, whether he ever married or had children.
• Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]

.During his youth Archimedes may have studied in Alexandria, Egypt, where Conon of Samos and Eratosthenes of Cyrene were contemporaries.^ When he was learning at Alexandria, he made friends with Conon, Eratosthenes and many others.
• Mathematical Database - Math Funland - Math Articles 19 January 2010 8:47 UTC www.mathdb.org [Source type: FILTERED WITH BAYES]

^ He probably visited Egypt and studied at Alexandria at the school which Euclid had started there.
• Math Jokes and Archimedes - Jokes and Science 19 January 2010 8:47 UTC www.juliantrubin.com [Source type: Original source]

.He referred to Conon of Samos as his friend, while two of his works (The Method of Mechanical Theorems and the Cattle Problem) have introductions addressed to Eratosthenes.^ He referred to Conon of Samos as his friend, while two of his works (The Sand Reckoner and the Cattle Problem) have introductions addressed to Eratosthenes.
• Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]

^ During his youth Archimedes may have studied in Alexandria, Egypt, where Conon of Samos and Eratosthenes of Cyrene were contemporaries.
• Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]

[a]
Archimedes died c. .212 BC during the Second Punic War, when Roman forces under General Marcus Claudius Marcellus captured the city of Syracuse after a two-year-long siege.^ BC during the Second Punic War, when Roman forces under General Marcus Claudius Marcellus captured the city of Syracuse after a two-year-long siege.
• Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]

^ Galileo was eventually forced to recant his heliocentrism and spent the last years of his life under house arrest on orders of the Holy Inquisition.
• Top 10 Most Influential Scientists - Listverse 19 January 2010 8:47 UTC listverse.com [Source type: General]

^ A Roman soldier commanded him to come and meet General Marcellus but he declined, saying that he had to finish working on the problem.
• Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]

.According to the popular account given by Plutarch, Archimedes was contemplating a mathematical diagram when the city was captured.^ In the section 'Mathematical Achievements', the reader will be given a detailed discussion of Archimedes' books and achievements.
• Mathematical Database - Math Funland - Math Articles 19 January 2010 8:47 UTC www.mathdb.org [Source type: FILTERED WITH BAYES]

• Mathematical Database - Math Funland - Math Articles 19 January 2010 8:47 UTC www.mathdb.org [Source type: FILTERED WITH BAYES]

.A Roman soldier commanded him to come and meet General Marcellus but he declined, saying that he had to finish working on the problem.^ A Roman soldier commanded him to come and meet General Marcellus but he declined, saying that he had to finish working on the problem.
• Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]

^ General Marcellus was reportedly angered by the death of Archimedes, as he considered him a valuable scientific asset and had ordered that he not be harmed.
• Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]

^ Other thoughts of mine are the Roman soldier killed Archimedes most likely because he was pissed at him for building the siege engines that killed many of comrades.
• 7 Books We Lost to History That Would Have Changed the World | Cracked.com 19 January 2010 8:47 UTC www.cracked.com [Source type: General]

.The soldier was enraged by this, and killed Archimedes with his sword.^ The soldier was enraged by this, and killed Archimedes with his sword.
• Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]

^ Other thoughts of mine are the Roman soldier killed Archimedes most likely because he was pissed at him for building the siege engines that killed many of comrades.
• 7 Books We Lost to History That Would Have Changed the World | Cracked.com 19 January 2010 8:47 UTC www.cracked.com [Source type: General]

^ According to this story, Archimedes was carrying mathematical instruments, and was killed because the soldier thought that they were valuable items.
• Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]

.Plutarch also gives a lesser-known account of the death of Archimedes which suggests that he may have been killed while attempting to surrender to a Roman soldier.^ The soldier was enraged by this, and killed Archimedes with his sword.
• Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]

^ Plutarch also gives a lesser-known account of the death of Archimedes which suggests that he may have been killed while attempting to surrender to a Roman soldier.
• Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]

^ In The Sand Reckoner, Archimedes gives his father's name as Phidias, an astronomer about whom nothing is known.
• Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]

.According to this story, Archimedes was carrying mathematical instruments, and was killed because the soldier thought that they were valuable items.^ The soldier was enraged by this, and killed Archimedes with his sword.
• Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]

^ According to this story, Archimedes was carrying mathematical instruments, and was killed because the soldier thought that they were valuable items.
• Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]

^ Romanian soldiers got into Archimedes' camp secretly and killed him.
• Mathematical Database - Math Funland - Math Articles 19 January 2010 8:47 UTC www.mathdb.org [Source type: FILTERED WITH BAYES]

.General Marcellus was reportedly angered by the death of Archimedes, as he considered him a valuable scientific asset and had ordered that he not be harmed.^ General Marcellus was reportedly angered by the death of Archimedes, as he considered him a valuable scientific asset and had ordered that he not be harmed.
• Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]

^ Archimedes is generally considered to be the greatest mathematician of antiquity and one of the greatest of all time.
• Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]

^ I’d say pretty much all scientifically educated people would consider Einstein, Newton & Darwin as the top 3 (though not necessarily in that order).
• Top 10 Most Influential Scientists - Listverse 19 January 2010 8:47 UTC listverse.com [Source type: General]

[10]
.
A sphere has 2/3 the volume and surface area of its circumscribing cylinder.
^ He discovered the relation between the surface area and volume of a sphere and those of its circumscribing cylinder.
• "Natural Magick" - "Glossery/Index - A" 19 January 2010 8:47 UTC homepages.tscnet.com [Source type: Original source]

^ His real importance in mathematics, however, lies in his discovery of formulae for the areas and volumes of spheres, cylinders, parabolas, and other plane and solid figures.
• Math Jokes and Archimedes - Jokes and Science 19 January 2010 8:47 UTC www.juliantrubin.com [Source type: Original source]

A sphere and cylinder were placed on the tomb of Archimedes at his request.
.The last words attributed to Archimedes are "Do not disturb my circles" (Greek: μή μου τούς κύκλους τάραττε), a reference to the circles in the mathematical drawing that he was supposedly studying when disturbed by the Roman soldier.^ Other thoughts of mine are the Roman soldier killed Archimedes most likely because he was pissed at him for building the siege engines that killed many of comrades.
• 7 Books We Lost to History That Would Have Changed the World | Cracked.com 19 January 2010 8:47 UTC www.cracked.com [Source type: General]

^ He was killed at the siege of Syracuse by a Roman soldier whose challenge he ignored while immersed in a mathematical problem.
• Math Jokes and Archimedes - Jokes and Science 19 January 2010 8:47 UTC www.juliantrubin.com [Source type: Original source]

^ The next panel has the soldier going "Fuck your circles," and then he just goes nuts on Archimedes.
• 7 Books We Lost to History That Would Have Changed the World | Cracked.com 19 January 2010 8:47 UTC www.cracked.com [Source type: General]

.This quote is often given in Latin as "Noli turbare circulos meos," but there is no reliable evidence that Archimedes uttered these words and they do not appear in the account given by Plutarch.^ This quote is often given in Latin as "Noli turbare circulos meos", but there is no reliable evidence that Archimedes uttered these words and they do not appear in the account given by Plutarch.
• Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]

^ According to the popular account given by Plutarch, Archimedes was contemplating a mathematical diagram when the city was captured.
• Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]

^ Plutarch also gives a lesser-known account of the death of Archimedes which suggests that he may have been killed while attempting to surrender to a Roman soldier.
• Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]

[10]
.The tomb of Archimedes carried a sculpture illustrating his favorite mathematical proof, consisting of a sphere and a cylinder of the same height and diameter.^ The tomb of Archimedes carried a sculpture illustrating his favorite mathematical proof, consisting of a sphere and a cylinder of the same height and diameter.
• Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]

^ Archimedes gave instructions that his tombstone should have displayed on it a diagram consisting of a sphere with a circumscribing cylinder.
• Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]

^ He made a lot of greatest contribution in science, mathematics, astronomy, mechanics and engineering for his discovery of the relation between the surface and the volume of a sphere and its circumscribing cylinder.
• Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]

.Archimedes had proven that the volume and surface area of the sphere are two thirds that of the cylinder including its bases.^ Archimedes had proved that the volume and surface area of the sphere are two thirds that of the cylinder including its bases.
• Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]

^ He found the volume and surface area of a sphere.
• Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]

^ He made a lot of greatest contribution in science, mathematics, astronomy, mechanics and engineering for his discovery of the relation between the surface and the volume of a sphere and its circumscribing cylinder.
• Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]

.In 75 BC, 137 years after his death, the Roman orator Cicero was serving as quaestor in Sicily.^ In 75 BC, 137 years after his death, the Roman orator Cicero was serving as quaestor in Sicily.
• Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]

^ C H Edwards (see reference below) writes how Cicero, while serving as quaestor in Sicily, had Archimedes' tombstone restored, and adds "The Romans had so little interest in pure mathematics that this action by Cicero was probably the greatest single contribution of any Roman to the history of mathematics."
• Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]

.He had heard stories about the tomb of Archimedes, but none of the locals was able to give him the location.^ He had heard stories about the tomb of Archimedes, but none of the locals was able to give him the location.
• Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]

^ In The Sand Reckoner, Archimedes gives his father's name as Phidias, an astronomer about whom nothing is known.
• Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]

.Eventually he found the tomb near the Agrigentine gate in Syracuse, in a neglected condition and overgrown with bushes.^ Eventually he found the tomb near the Agrigentine gate in Syracuse, in a neglected condition and overgrown with bushes.
• Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]

.Cicero had the tomb cleaned up, and was able to see the carving and read some of the verses that had been added as an inscription.^ Cicero had the tomb cleaned up, and was able to see the carving and read some of the verses that had been added as an inscription.
• Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]

^ Euclid collected and rearranged all the known facts about geometry, up to his time, in step-by-step order and added some new propositions and proofs.
• Math Jokes and Archimedes - Jokes and Science 19 January 2010 8:47 UTC www.juliantrubin.com [Source type: Original source]

[11]
.The standard versions of the life of Archimedes were written long after his death by the historians of Ancient Rome.^ A biography of Archimedes was written by his friend Heracleides but this work has been lost, leaving the details of his life obscure.
• Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]

^ Archimedes Stuff Archimedes Stuff on eBay Life & Death of Archimedes of Syracuse Archimedes Stuff on eBay Book on the Spotlight on Archimedes more...
• Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]

^ Archimedes Stuff Archimedes Stuff on eBay Life & Death of Archimedes of Syracuse Archimedes Stuff on eBay Book on the Spotlight on Archimedes Archimedes' Discoveries .
• Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]

The account of the siege of Syracuse given by Polybius in his Universal History was written around seventy years after Archimedes' death, and was used subsequently as a source by Plutarch and Livy. It sheds little light on Archimedes as a person, and focuses on the war machines that he is said to have built in order to defend the city.[12]

## Discoveries and inventions

### The Golden Crown

Archimedes may have used his principle of buoyancy to determine whether the golden crown was less dense than solid gold.
.The most widely known anecdote about Archimedes tells of how he invented a method for determining the volume of an object with an irregular shape.^ Although there was not much known about the value of the ratio between the circumference and diameter of a circle, and it was impossible to evaluate ratios using irrational numbers with the number system at that time, Archimedes was still able to point out the relationships between the volumes and areas of various geometric shapes.
• Mathematical Database - Math Funland - Math Articles 19 January 2010 8:47 UTC www.mathdb.org [Source type: FILTERED WITH BAYES]

.According to Vitruvius, a new crown in the shape of a laurel wreath had been made for King Hiero II, and Archimedes was asked to determine whether it was of solid gold, or whether silver had been added by a dishonest goldsmith.^ The Sicilian King, Archimedes was told, Ordered a crown from a large lump of gold, And though the weight of the gold was completely correct, The goldsmith's eye made the King suspect That he'd made up the weight with some cheaper metal And stolen some gold, that his debts he might settle.
• Math Jokes and Archimedes - Jokes and Science 19 January 2010 8:47 UTC www.juliantrubin.com [Source type: Original source]

[13] .Archimedes had to solve the problem without damaging the crown, so he could not melt it down into a regularly shaped body in order to calculate its density.^ Bohr’s work helped solve the problems classical physics could not explain about the nuclear model of the atom.
• Top 10 Most Influential Scientists - Listverse 19 January 2010 8:47 UTC listverse.com [Source type: General]

^ Experts on the history of mathematics believe that Archimedes himself could not solve this problem either because in 1965, with the help of computers, the answer was found to be of 206500 digits ([ 2 ], page 97 - 98).
• Mathematical Database - Math Funland - Math Articles 19 January 2010 8:47 UTC www.mathdb.org [Source type: FILTERED WITH BAYES]

^ In "On the Sphere and Cylinder", "On Measurement of a Circle", "On Quadrature of the parabola", "On Conoids and Spheroids" and "On Spirals", Archimedes often use the method of exhaustion to solve the problems.
• Mathematical Database - Math Funland - Math Articles 19 January 2010 8:47 UTC www.mathdb.org [Source type: FILTERED WITH BAYES]

While taking a bath, he noticed that the level of the water in the tub rose as he got in, and realized that this effect could be used to determine the volume of the crown. .For practical purposes water is incompressible,[14] so the submerged crown would displace an amount of water equal to its own volume.^ He found the upthrust, produced on a body's base*, To be equal in weight to the water displaced, And soon volumes and weights would make it quite plain What various metals the crown could contain, And so he could easily show to his Royalty The absolute proof of the goldsmith's disloyalty.
• Math Jokes and Archimedes - Jokes and Science 19 January 2010 8:47 UTC www.juliantrubin.com [Source type: Original source]

.By dividing the weight of the crown by the volume of water displaced, the density of the crown could be obtained.^ He found the upthrust, produced on a body's base*, To be equal in weight to the water displaced, And soon volumes and weights would make it quite plain What various metals the crown could contain, And so he could easily show to his Royalty The absolute proof of the goldsmith's disloyalty.
• Math Jokes and Archimedes - Jokes and Science 19 January 2010 8:47 UTC www.juliantrubin.com [Source type: Original source]

.This density would be lower than that of gold if cheaper and less dense metals had been added.^ It was discovered after Lord Rayleigh tried (1893) to measure the density of nitrogen gas accurately: he found that chemically-generated nitrogen gas was less dense than nitrogen separated from air, by a small but persistent amount.
• SBF Glossary: A/R to ARW 19 January 2010 8:47 UTC www.plexoft.com [Source type: FILTERED WITH BAYES]

Archimedes then took to the streets naked, so excited by his discovery that he had forgotten to dress, crying "Eureka!" (Greek: "εὕρηκα!," meaning "I have found it!")[15]
The story of the golden crown does not appear in the known works of Archimedes. .Moreover, the practicality of the method it describes has been called into question, due to the extreme accuracy with which one would have to measure the water displacement.^ In 1919, Goddard wrote a scientific article, "A Method of Reaching Extreme Altitudes," describing a high-altitude rocket; it was published in a Smithsonian report.
• Inventors and Inventions of Scientific Instruments: EnchantedLearning.com 19 January 2010 8:47 UTC www.enchantedlearning.com [Source type: FILTERED WITH BAYES]

^ THE NATURE OF LIGHT One of the main goals of physics is to develop plausible conceptual models, as they are called, in terms of which various physical phenomena can be described and explained.

[16] .Archimedes may have instead sought a solution that applied the principle known in hydrostatics as Archimedes' Principle, which he describes in his treatise On Floating Bodies.^ In popular tradition he is remembered for the construction of siege-engines against the Romans, the Archimedes' screw still used for raising water, and his cry of eureka ("I have found it') when he discovered the principle of the upthrust on a floating body.
• Math Jokes and Archimedes - Jokes and Science 19 January 2010 8:47 UTC www.juliantrubin.com [Source type: Original source]

^ Alexipharmacal    "...The same may be extracted out ot other Alexipharmacal bodies, which Princes may use at meals, instead of ordinary Salt ..."
• "Natural Magick" - "Glossery/Index - A" 19 January 2010 8:47 UTC homepages.tscnet.com [Source type: Original source]

This principle states that a body immersed in a fluid experiences a buoyant force equal to the weight of the fluid it displaces.[17] Using this principle, it would have been possible to compare the density of the golden crown to that of solid gold by balancing the crown on a scale with a gold reference sample, then immersing the apparatus in water. .If the crown was less dense than gold, it would displace more water due to its larger volume, and thus experience a greater buoyant force than the reference sample.^ Overtime was expensive, sure, but at a certain point that became less important than the fact that slower construction meant later and therefore more expensive outlays.
• SBF Glossary: A/R to ARW 19 January 2010 8:47 UTC www.plexoft.com [Source type: FILTERED WITH BAYES]

^ We have discovered prime numbers that are far larger than 10^500, and those would be primes in the Incognitum.
• #266 mathematics ends at about 10^500 Re: powerset - sci.logic | Google Groups 19 January 2010 8:47 UTC groups.google.com [Source type: Original source]

^ In fact, if one assumed that the size of their charge was equal to that of a hydrogen ion in electrolysis (a proposition that was verified by experiment later) their mass was less than 1/1000 of the mass of a hydrogen atom.

This difference in buoyancy would cause the scale to tip accordingly. Galileo considered it "probable that this method is the same that Archimedes followed, since, besides being very accurate, it is based on demonstrations found by Archimedes himself."[18]

### The Archimedes Screw

The Archimedes screw can raise water efficiently.
.A large part of Archimedes' work in engineering arose from fulfilling the needs of his home city of Syracuse.^ His problems arose largely from the fact that he was an eccentric who was unable to work with (and consequently to learn from) other people, and the increasing unreality of his ideas shows it.” .
• Top 10 Most Influential Scientists - Listverse 19 January 2010 8:47 UTC listverse.com [Source type: General]

^ To remove this misperception, in his only work on arithmetic, "Arithmetic on Sand Grains", Archimedes proposed a new way to denote large numbers and calculated the number of sand grains in the world.
• Mathematical Database - Math Funland - Math Articles 19 January 2010 8:47 UTC www.mathdb.org [Source type: FILTERED WITH BAYES]

^ Of course it is hard to compare ancient and more recent breakthroughs, but Archimedes’ work would have more total impact as he also laid the foundations of physics and mathematical engineering.
• Top 10 Most Influential Scientists - Listverse 19 January 2010 8:47 UTC listverse.com [Source type: General]

.The Greek writer Athenaeus of Naucratis described how King Hieron II commissioned Archimedes to design a huge ship, the Syracusia, which could be used for luxury travel, carrying supplies, and as a naval warship.^ Archimedes proposed the following problem when he visited Hieron, the King of Syracuse: .
• Mathematical Database - Math Funland - Math Articles 19 January 2010 8:47 UTC www.mathdb.org [Source type: FILTERED WITH BAYES]

^ And that King Ptolomey built a tower in Pharos, where he set a glass, that he could see for six hundred miles, see by it the enemy ships, that invaded his country and plundered it ..."
• "Natural Magick" - "Glossery/Index - A" 19 January 2010 8:47 UTC homepages.tscnet.com [Source type: Original source]

^ It is said that Archimedes was a relative of Hieron, the king of Syracuse.
• Mathematical Database - Math Funland - Math Articles 19 January 2010 8:47 UTC www.mathdb.org [Source type: FILTERED WITH BAYES]

The Syracusia is said to have been the largest ship built in classical antiquity.[19] According to Athenaeus, it was capable of carrying 600 people and included garden decorations, a gymnasium and a temple dedicated to the goddess Aphrodite among its facilities. Since a ship of this size would leak a considerable amount of water through the hull, the Archimedes screw was purportedly developed in order to remove the bilge water. .Archimedes' machine was a device with a revolving screw-shaped blade inside a cylinder.^ Archimedes invented the water screw, a device for raising water using an encased screw open at both ends.
• Inventors and Inventions of Scientific Instruments: EnchantedLearning.com 19 January 2010 8:47 UTC www.enchantedlearning.com [Source type: FILTERED WITH BAYES]

.It was turned by hand, and could also be used to transfer water from a low-lying body of water into irrigation canals.^ Hot to use your “marketer’s eye” to spot the hidden value in websites—and turn them into cold, hard cash in your pocket...

^ It was first turned into reality in 1953 by Charles Townes (1915 - ) and his students, using radiation of about l cm wavelength emitted and absorbed by ammonia molecules.

.The Archimedes screw is still in use today for pumping liquids and granulated solids such as coal and grain.^ Roman times and is still in use today.

^ The Archimedes screw is still in use today.
• Inventors and Inventions of Scientific Instruments: EnchantedLearning.com 19 January 2010 8:47 UTC www.enchantedlearning.com [Source type: FILTERED WITH BAYES]

^ Archimedes invented the water screw, a device for raising water using an encased screw open at both ends.
• Inventors and Inventions of Scientific Instruments: EnchantedLearning.com 19 January 2010 8:47 UTC www.enchantedlearning.com [Source type: FILTERED WITH BAYES]

.The Archimedes screw described in Roman times by Vitruvius may have been an improvement on a screw pump that was used to irrigate the Hanging Gardens of Babylon.^ Roman times and is still in use today.

^ The Archimedes screw is still in use today.
• Inventors and Inventions of Scientific Instruments: EnchantedLearning.com 19 January 2010 8:47 UTC www.enchantedlearning.com [Source type: FILTERED WITH BAYES]

^ Brass , often used, and let it melt six or sever times, that it may be pure and cleansed.
• "Natural Magick" - "Glossery/Index - A" 19 January 2010 8:47 UTC homepages.tscnet.com [Source type: Original source]

[20][21][22]

### The Claw of Archimedes

.The Claw of Archimedes is a weapon that he is said to have designed in order to defend the city of Syracuse.^ It is said that Archimedes was a relative of Hieron, the king of Syracuse.
• Mathematical Database - Math Funland - Math Articles 19 January 2010 8:47 UTC www.mathdb.org [Source type: FILTERED WITH BAYES]

Also known as "the ship shaker," the claw consisted of a crane-like arm from which a large metal grappling hook was suspended. .When the claw was dropped onto an attacking ship the arm would swing upwards, lifting the ship out of the water and possibly sinking it.^ Draw it with a gentle fire, it will Distil out by drops after the water..."
• "Natural Magick" - "Glossery/Index - A" 19 January 2010 8:47 UTC homepages.tscnet.com [Source type: Original source]

.There have been modern experiments to test the feasibility of the claw, and in 2005 a television documentary entitled Superweapons of the Ancient World built a version of the claw and concluded that it was a workable device.^ There was a misperception among some ancient Greeks that the number of sand grains in the world was infinite and the number could not be represented by a number.
• Mathematical Database - Math Funland - Math Articles 19 January 2010 8:47 UTC www.mathdb.org [Source type: FILTERED WITH BAYES]

[23][24]

### The Archimedes Heat Ray – myth or reality?

Archimedes may have used mirrors acting collectively as a parabolic reflector to burn ships attacking Syracuse.
.The 2nd century AD author Lucian wrote that during the Siege of Syracuse (c. 214–212 BC), Archimedes destroyed enemy ships with fire.^ Archimedes (287 - 212 B.C.) was born at Syracuse of Sicily as a son of the astronomer Pheidias.
• Mathematical Database - Math Funland - Math Articles 19 January 2010 8:47 UTC www.mathdb.org [Source type: FILTERED WITH BAYES]

^ Heron lived during the first century AD and is sometimes called Hero.
• Inventors and Inventions of Scientific Instruments: EnchantedLearning.com 19 January 2010 8:47 UTC www.enchantedlearning.com [Source type: FILTERED WITH BAYES]

^ Levers were first described about 260 BC by the ancient Greek mathematician Archimedes (287-212 BC).
• Inventors and Inventions of Scientific Instruments: EnchantedLearning.com 19 January 2010 8:47 UTC www.enchantedlearning.com [Source type: FILTERED WITH BAYES]

.Centuries later, Anthemius of Tralles mentions burning-glasses as Archimedes' weapon.^ We read that Archimedes at Syracuse with burning glasses defeated the forces of the Romans.
• "Natural Magick" - "Glossery/Index - A" 19 January 2010 8:47 UTC homepages.tscnet.com [Source type: Original source]

[25] .The device, sometimes called the "Archimedes heat ray", was used to focus sunlight onto approaching ships, causing them to catch fire.^ GEIGER COUNTER The Geiger counter (sometimes called the Geiger-Muller counter) is a device that detects ionizing radioactivity (including gamma rays and X-rays) - it counts the radioactive particle that pass through the device.
• Inventors and Inventions of Scientific Instruments: EnchantedLearning.com 19 January 2010 8:47 UTC www.enchantedlearning.com [Source type: FILTERED WITH BAYES]

^ Archimedes invented the water screw, a device for raising water using an encased screw open at both ends.
• Inventors and Inventions of Scientific Instruments: EnchantedLearning.com 19 January 2010 8:47 UTC www.enchantedlearning.com [Source type: FILTERED WITH BAYES]

This purported weapon has been the subject of ongoing debate about its credibility since the Renaissance. René Descartes rejected it as false, while modern researchers have attempted to recreate the effect using only the means that would have been available to Archimedes.[26] It has been suggested that a large array of highly polished bronze or copper shields acting as mirrors could have been employed to focus sunlight onto a ship. This would have used the principle of the parabolic reflector in a manner similar to a solar furnace.
A test of the Archimedes heat ray was carried out in 1973 by the Greek scientist Ioannis Sakkas. The experiment took place at the Skaramagas naval base outside Athens. On this occasion 70 mirrors were used, each with a copper coating and a size of around five by three feet (1.5 by 1 m). The mirrors were pointed at a plywood mock-up of a Roman warship at a distance of around 160 feet (50 m). When the mirrors were focused accurately, the ship burst into flames within a few seconds. The plywood ship had a coating of tar paint, which may have aided combustion.[27]
.In October 2005 a group of students from the Massachusetts Institute of Technology carried out an experiment with 127 one-foot (30 cm) square mirror tiles, focused on a mock-up wooden ship at a range of around 100 feet (30 m).^ The males are about one tenth the size of the females (which range in length from 5 to 30 cm).
• SBF Glossary: A/R to ARW 19 January 2010 8:47 UTC www.plexoft.com [Source type: FILTERED WITH BAYES]

^ THE NATURE OF PHYSICS THE NATURE OF PHYSICS A. P. French Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA   INTRODUCTION The world is full of experiences that cry out for explanations.

Flames broke out on a patch of the ship, but only after the sky had been cloudless and the ship had remained stationary for around ten minutes. It was concluded that the device was a feasible weapon under these conditions. The MIT group repeated the experiment for the television show MythBusters, using a wooden fishing boat in San Francisco as the target. Again some charring occurred, along with a small amount of flame. In order to catch fire, wood needs to reach its flash point, which is around 300 degrees Celsius (570 °F).[28]
.When MythBusters broadcast the result of the San Francisco experiment in January 2006, the claim was placed in the category of "busted" (or failed) because of the length of time and the ideal weather conditions required for combustion to occur.^ The experiment can be done under such conditions that only one photon passes through the apparatus at a time.

^ I mention this not for the sake of the particular result, but because it points to another essential feature of physics -- the dependence on direct observation or experiment.

It was also pointed out that since Syracuse faces the sea towards the east, the Roman fleet would have had to attack during the morning for optimal gathering of light by the mirrors. .MythBusters also pointed out that conventional weaponry, such as flaming arrows or bolts from a catapult, would have been a far easier way of setting a ship on fire at short distances.^ PM Phillyastro @iamfry: the point of this article is that if western civilization had not lost the knowledge that these books contain, we would be far ahead of where we are in technology right now.
• 7 Books We Lost to History That Would Have Changed the World | Cracked.com 19 January 2010 8:47 UTC www.cracked.com [Source type: General]

^ PM greenprince Love the look of Ab urbe condita libri, by Livy..would made Ancient History, back in High School way easier!
• 7 Books We Lost to History That Would Have Changed the World | Cracked.com 19 January 2010 8:47 UTC www.cracked.com [Source type: General]

^ I think he's a blowhard too but you're going way too far out of your way.
• 7 Books We Lost to History That Would Have Changed the World | Cracked.com 19 January 2010 8:47 UTC www.cracked.com [Source type: General]

[1]

### Other discoveries and inventions

.While Archimedes did not invent the lever, he wrote the earliest known rigorous explanation of the principle involved.^ And he did – today we still feel his impact through a lever spanning 2200+ years of Archimedes-inspired science.
• Top 10 Most Influential Scientists - Listverse 19 January 2010 8:47 UTC listverse.com [Source type: General]

^ The best example is perhaps the lever, the principle of which was recognized by Archimedes about 250 B.C.: "...unequal weights are in equilibrium only when they are inversely proportional to the arms from which they are suspended."

According to Pappus of Alexandria, his work on levers caused him to remark: "Give me a place to stand on, and I will move the Earth." (Greek: δῶς μοι πᾶ στῶ καὶ τὰν γᾶν κινάσω)[29] Plutarch describes how Archimedes designed block-and-tackle pulley systems, allowing sailors to use the principle of leverage to lift objects that would otherwise have been too heavy to move.[30] .Archimedes has also been credited with improving the power and accuracy of the catapult, and with inventing the odometer during the First Punic War.^ The first scientist to recognize and use the power of the lever was Archimedes .
• "Natural Magick" - "Glossery/Index - A" 19 January 2010 8:47 UTC homepages.tscnet.com [Source type: Original source]

The odometer was described as a cart with a gear mechanism that dropped a ball into a container after each mile traveled.[31]
.Cicero (106–43 BC) mentions Archimedes briefly in his dialogue De re publica, which portrays a fictional conversation taking place in 129 BC. After the capture of Syracuse c. 212 BC, General Marcus Claudius Marcellus is said to have taken back to Rome two mechanisms used as aids in astronomy, which showed the motion of the Sun, Moon and five planets.^ Archimedes (287 - 212 B.C.) was born at Syracuse of Sicily as a son of the astronomer Pheidias.
• Mathematical Database - Math Funland - Math Articles 19 January 2010 8:47 UTC www.mathdb.org [Source type: FILTERED WITH BAYES]

^ It was authored by one of the greatest mechanical minds in history: the legendary Archimedes , who knew a thing or two about spheres right down to his dying words...
• 7 Books We Lost to History That Would Have Changed the World | Cracked.com 19 January 2010 8:47 UTC www.cracked.com [Source type: General]

^ And Hermes the learned, said, t hat the sun and the moon are the life of all things living...
• "Natural Magick" - "Glossery/Index - A" 19 January 2010 8:47 UTC homepages.tscnet.com [Source type: Original source]

Cicero mentions similar mechanisms designed by Thales of Miletus and Eudoxus of Cnidus. .The dialogue says that Marcellus kept one of the devices as his only personal loot from Syracuse, and donated the other to the Temple of Virtue in Rome.^ For, say they, the Atoms that flew out of the Iron , and meet in the Loadstone in one figure, so that they easily embrace one the other..."
• "Natural Magick" - "Glossery/Index - A" 19 January 2010 8:47 UTC homepages.tscnet.com [Source type: Original source]

^ Herodotus says, that Artabazus and Timoxenus did this, when one would declare anything to the other..."
• "Natural Magick" - "Glossery/Index - A" 19 January 2010 8:47 UTC homepages.tscnet.com [Source type: Original source]

^ What A Commonsense Person Would Do: A person full of commonsense would say: (a) since physics has no infinities then let us only do Mathematics to the largest (smallest) numbers that physics needs to use.
• #266 mathematics ends at about 10^500 Re: powerset - sci.logic | Google Groups 19 January 2010 8:47 UTC groups.google.com [Source type: Original source]

Marcellus' mechanism was demonstrated, according to Cicero, by Gaius Sulpicius Gallus to Lucius Furius Philus, who described it thus:
Hanc sphaeram Gallus cum moveret, fiebat ut soli luna totidem conversionibus in aere illo quot diebus in ipso caelo succederet, ex quo et in caelo sphaera solis fieret eadem illa defectio, et incideret luna tum in eam metam quae esset umbra terrae, cum sol e regione. — When Gallus moved the globe, it happened that the Moon followed the Sun by as many turns on that bronze contrivance as in the sky itself, from which also in the sky the Sun's globe became to have that same eclipse, and the Moon came then to that position which was its shadow on the Earth, when the Sun was in line.[32][33]
This is a description of a planetarium or orrery. .Pappus of Alexandria stated that Archimedes had written a manuscript (now lost) on the construction of these mechanisms entitled On Sphere-Making.^ It was authored by one of the greatest mechanical minds in history: the legendary Archimedes , who knew a thing or two about spheres right down to his dying words...
• 7 Books We Lost to History That Would Have Changed the World | Cracked.com 19 January 2010 8:47 UTC www.cracked.com [Source type: General]

• 7 Books We Lost to History That Would Have Changed the World | Cracked.com 19 January 2010 8:47 UTC www.cracked.com [Source type: General]

^ On Sphere-Making , by Archimedes .
• 7 Books We Lost to History That Would Have Changed the World | Cracked.com 19 January 2010 8:47 UTC www.cracked.com [Source type: General]

.Modern research in this area has been focused on the Antikythera mechanism, another device from classical antiquity that was probably designed for the same purpose.^ Here's another modern classic that'll change the world.
• 7 Books We Lost to History That Would Have Changed the World | Cracked.com 19 January 2010 8:47 UTC www.cracked.com [Source type: General]

Constructing mechanisms of this kind would have required a sophisticated knowledge of differential gearing. This was once thought to have been beyond the range of the technology available in ancient times, but the discovery of the Antikythera mechanism in 1902 has confirmed that devices of this kind were known to the ancient Greeks.[34][35]

## Mathematics

.While he is often regarded as a designer of mechanical devices, Archimedes also made contributions to the field of mathematics.^ Niels Bohr was a Danish physicist who made fundamental contributions to understanding atomic structure and quantum mechanics, for which he received the Nobel Prize in Physics in 1922.
• Top 10 Most Influential Scientists - Listverse 19 January 2010 8:47 UTC listverse.com [Source type: General]

^ With the Turing test, meanwhile, he made a significant and characteristically provocative contribution to the debate regarding artificial intelligence: whether it will ever be possible to say that a machine is conscious and can think.
• Top 10 Most Influential Scientists - Listverse 19 January 2010 8:47 UTC listverse.com [Source type: General]

^ It was incredibly difficult to categorize them in a top 10 list as they all had astounding contributions to their respective fields, and I made numerous changes to the order as I compiled the list.
• Top 10 Most Influential Scientists - Listverse 19 January 2010 8:47 UTC listverse.com [Source type: General]

Plutarch wrote: "He placed his whole affection and ambition in those purer speculations where there can be no reference to the vulgar needs of life."[36]
Archimedes used the method of exhaustion to approximate the value of π.
.Archimedes was able to use infinitesimals in a way that is similar to modern integral calculus.^ Firstly; where is ARCHIMEDES? Archimedes was the first to introduce infinitesimals which is the foundation of calculus.
• Top 10 Most Influential Scientists - Listverse 19 January 2010 8:47 UTC listverse.com [Source type: General]

Through proof by contradiction (reductio ad absurdum), he could give answers to problems to an arbitrary degree of accuracy, while specifying the limits within which the answer lay. This technique is known as the method of exhaustion, and he employed it to approximate the value of π (pi). He did this by drawing a larger polygon outside a circle and a smaller polygon inside the circle. As the number of sides of the polygon increases, it becomes a more accurate approximation of a circle. When the polygons had 96 sides each, he calculated the lengths of their sides and showed that the value of π lay between 317 (approximately 3.1429) and 31071 (approximately 3.1408), consistent with its actual value of approximately 3.1416. He also proved that the area of a circle was equal to π multiplied by the square of the radius of the circle. .In On the Sphere and Cylinder, Archimedes postulates that any magnitude when added to itself enough times will exceed any given magnitude.^ AM Inspector_Anys I missed the part where Plato was a physicist, or that a deity-riddled epic isn't "religious" unless enough people at a given time think the deity/deities are "real".
• 7 Books We Lost to History That Would Have Changed the World | Cracked.com 19 January 2010 8:47 UTC www.cracked.com [Source type: General]

^ AM iamfry I missed the part where Plato was a physicist, or that a deity-riddled epic isn't "religious" unless enough people at a given time think the deity/deities are "real".
• 7 Books We Lost to History That Would Have Changed the World | Cracked.com 19 January 2010 8:47 UTC www.cracked.com [Source type: General]

This is the Archimedean property of real numbers.[37]
In Measurement of a Circle, Archimedes gives the value of the square root of 3 as lying between 265153 (approximately 1.7320261) and 1351780 (approximately 1.7320512). .The actual value is approximately 1.7320508, making this a very accurate estimate.^ I have flipped websites in the past for a very cool profit but using your system I was able to actually make more money in 2 flips than I made in 7 flips previously.

He introduced this result without offering any explanation of the method used to obtain it. This aspect of the work of Archimedes caused John Wallis to remark that he was: "as it were of set purpose to have covered up the traces of his investigation as if he had grudged posterity the secret of his method of inquiry while he wished to extort from them assent to his results."[38]
As proven by Archimedes, the area of the parabolic segment in the upper figure is equal to 4/3 that of the inscribed triangle in the lower figure.
In The Quadrature of the Parabola, Archimedes proved that the area enclosed by a parabola and a straight line is 43 times the area of a corresponding inscribed triangle as shown in the figure at right. He expressed the solution to the problem as an infinite geometric series with the common ratio 14:
$\sum_{n=0}^\infty 4^{-n} = 1 + 4^{-1} + 4^{-2} + 4^{-3} + \cdots = {4\over 3}. \;$
If the first term in this series is the area of the triangle, then the second is the sum of the areas of two triangles whose bases are the two smaller secant lines, and so on. This proof uses a variation of the series 1/4 + 1/16 + 1/64 + 1/256 + · · · which sums to 13.
.In The Sand Reckoner, Archimedes set out to calculate the number of grains of sand that the universe could contain.^ He devised a number of techniques for breaking German ciphers, including the method of the bombe, an electromechanical machine that could find settings for the Enigma machine.
• Top 10 Most Influential Scientists - Listverse 19 January 2010 8:47 UTC listverse.com [Source type: General]

In doing so, he challenged the notion that the number of grains of sand was too large to be counted. He wrote: "There are some, King Gelo (Gelo II, son of Hiero II), who think that the number of the sand is infinite in multitude; and I mean by the sand not only that which exists about Syracuse and the rest of Sicily but also that which is found in every region whether inhabited or uninhabited." To solve the problem, Archimedes devised a system of counting based on the myriad. .The word is from the Greek μυριάς murias, for the number 10,000. He proposed a number system using powers of a myriad of myriads (100 million) and concluded that the number of grains of sand required to fill the universe would be 8 vigintillion, or 8 × 1063.^ You've seen my 6-figure profits, and now you're about to own the exact system I used to fill my bank accounts.

^ Castilian, as now pronounced in most of Spain, does have the Þ sound, but like Italian generally uses a Roman letter tee for any theta in a Greek loan word.
• SBF Glossary: A/R to ARW 19 January 2010 8:47 UTC www.plexoft.com [Source type: FILTERED WITH BAYES]

^ One wonders if we would be any better collectively if we all the had the equivalent brain-power and insight of the 10 cited in this topic.
• Top 10 Most Influential Scientists - Listverse 19 January 2010 8:47 UTC listverse.com [Source type: General]

[39]

## Writings

.The works of Archimedes were written in Doric Greek, the dialect of ancient Syracuse.^ Of course it is hard to compare ancient and more recent breakthroughs, but Archimedes’ work would have more total impact as he also laid the foundations of physics and mathematical engineering.
• Top 10 Most Influential Scientists - Listverse 19 January 2010 8:47 UTC listverse.com [Source type: General]

^ His two main works, written in Greek, are De natura animalium (On the Nature of Animals) and Varia historia (Miscellany).
• "Natural Magick" - "Glossery/Index - A" 19 January 2010 8:47 UTC homepages.tscnet.com [Source type: Original source]

[40] .The written work of Archimedes has not survived as well as that of Euclid, and seven of his treatises are known to have existed only through references made to them by other authors.^ Math made only a fleeting attempt to incorporate duality such as in the regular-polyhedra of a duality relationship of sides with angles with other properties.
• #266 mathematics ends at about 10^500 Re: powerset - sci.logic | Google Groups 19 January 2010 8:47 UTC groups.google.com [Source type: Original source]

^ There will be room for broad interdisciplinary thematic discussions by various authors as well as for detailed interpretations of individual, or groups of, documents and pieces of other evidence.
• SBF Glossary: A/R to ARW 19 January 2010 8:47 UTC www.plexoft.com [Source type: FILTERED WITH BAYES]

^ Averroes composed 38 treatises on the various works of Aristotle , as well as original tracts on astronomy, physics, and medicine.
• "Natural Magick" - "Glossery/Index - A" 19 January 2010 8:47 UTC homepages.tscnet.com [Source type: Original source]

Pappus of Alexandria mentions On Sphere-Making and another work on polyhedra, while Theon of Alexandria quotes a remark about refraction from the now-lost Catoptrica.[b] During his lifetime, Archimedes made his work known through correspondence with the mathematicians in Alexandria. The writings of Archimedes were collected by the Byzantine architect Isidore of Miletus (c. 530 AD), while commentaries on the works of Archimedes written by Eutocius in the sixth century AD helped to bring his work a wider audience. .Archimedes' work was translated into Arabic by Thābit ibn Qurra (836–901 AD), and Latin by Gerard of Cremona (c. 1114–1187 AD).^ Jerome, who knew Hebrew, usually translated the epithet directly into a corresponding Latin epithet -- Dominus Exercituum.
• SBF Glossary: A/R to ARW 19 January 2010 8:47 UTC www.plexoft.com [Source type: FILTERED WITH BAYES]

.During the Renaissance, the Editio Princeps (First Edition) was published in Basel in 1544 by Johann Herwagen with the works of Archimedes in Greek and Latin.^ From what I've read, Homer was considered something like the ghetto version of epic Greek works" Totally irrelevant if Homer was not the influential person during his time.
• 7 Books We Lost to History That Would Have Changed the World | Cracked.com 19 January 2010 8:47 UTC www.cracked.com [Source type: General]

[41] .Around the year 1586 Galileo Galilei invented a hydrostatic balance for weighing metals in air and water after apparently being inspired by the work of Archimedes.^ And he did – today we still feel his impact through a lever spanning 2200+ years of Archimedes-inspired science.
• Top 10 Most Influential Scientists - Listverse 19 January 2010 8:47 UTC listverse.com [Source type: General]

^ Over the years since then, we have extended the work of Galileo and Newton ....
• Archimedes to Hawking: Laws of Science and the Great Minds Behind Them 19 January 2010 8:47 UTC sprott.physics.wisc.edu [Source type: Original source]

[42]

### Surviving works

Archimedes is said to have remarked about the lever: Give me a place to stand on, and I will move the Earth.
• On the Equilibrium of Planes (two volumes)
The first book is in fifteen propositions with seven postulates, while the second book is in ten propositions. In this work Archimedes explains the Law of the Lever, stating, "Magnitudes are in equilibrium at distances reciprocally proportional to their weights."
Archimedes uses the principles derived to calculate the areas and centers of gravity of various geometric figures including triangles, parallelograms and parabolas.[43]
This is a short work consisting of three propositions. It is written in the form of a correspondence with Dositheus of Pelusium, who was a student of Conon of Samos. In Proposition II, Archimedes shows that the value of π (pi) is greater than 22371 and less than 227. The latter figure was used as an approximation of π throughout the Middle Ages and is still used today when only a rough figure is required.
This work of 28 propositions is also addressed to Dositheus. The treatise defines what is now called the Archimedean spiral. It is the locus of points corresponding to the locations over time of a point moving away from a fixed point with a constant speed along a line which rotates with constant angular velocity. Equivalently, in polar coordinates (r, θ) it can be described by the equation
$\, r=a+b heta$
with real numbers a and b. .This is an early example of a mechanical curve (a curve traced by a moving point) considered by a Greek mathematician.^ This gifted Greek mathematician and inventor once said, "Give me a place to stand and rest my lever on, and I can move the Earth."
• "Natural Magick" - "Glossery/Index - A" 19 January 2010 8:47 UTC homepages.tscnet.com [Source type: Original source]

^ Apollonius of Perga     Apollonius of Perga, a Greek mathematician of the 3d and early 2d centuries BC, was known as the Great Geometer.
• "Natural Magick" - "Glossery/Index - A" 19 January 2010 8:47 UTC homepages.tscnet.com [Source type: Original source]

• On the Sphere and the Cylinder (two volumes)
In this treatise addressed to Dositheus, Archimedes obtains the result of which he was most proud, namely the relationship between a sphere and a circumscribed cylinder of the same height and diameter. .The volume is 43πr3 for the sphere, and 2πr3 for the cylinder.^ He discovered the relation between the surface area and volume of a sphere and those of its circumscribing cylinder.
• "Natural Magick" - "Glossery/Index - A" 19 January 2010 8:47 UTC homepages.tscnet.com [Source type: Original source]

.The surface area is 4πr2 for the sphere, and 6πr2 for the cylinder (including its two bases), where r is the radius of the sphere and cylinder.^ He discovered the relation between the surface area and volume of a sphere and those of its circumscribing cylinder.
• "Natural Magick" - "Glossery/Index - A" 19 January 2010 8:47 UTC homepages.tscnet.com [Source type: Original source]

.The sphere has a volume and surface area two-thirds that of the cylinder.^ He discovered the relation between the surface area and volume of a sphere and those of its circumscribing cylinder.
• "Natural Magick" - "Glossery/Index - A" 19 January 2010 8:47 UTC homepages.tscnet.com [Source type: Original source]

A sculpted sphere and cylinder were placed on the tomb of Archimedes at his request.
• On Conoids and Spheroids
This is a work in 32 propositions addressed to Dositheus. In this treatise Archimedes calculates the areas and volumes of sections of cones, spheres, and paraboloids.
• On Floating Bodies (two volumes)
In the first part of this treatise, Archimedes spells out the law of equilibrium of fluids, and proves that water will adopt a spherical form around a center of gravity. This may have been an attempt at explaining the theory of contemporary Greek astronomers such as Eratosthenes that the Earth is round. The fluids described by Archimedes are not self-gravitating, since he assumes the existence of a point towards which all things fall in order to derive the spherical shape.
In the second part, he calculates the equilibrium positions of sections of paraboloids. This was probably an idealization of the shapes of ships' hulls. Some of his sections float with the base under water and the summit above water, similar to the way that icebergs float. Archimedes' principle of buoyancy is given in the work, stated as follows:
Any body wholly or partially immersed in a fluid experiences an upthrust equal to, but opposite in sense to, the weight of the fluid displaced.
In this work of 24 propositions addressed to Dositheus, Archimedes proves by two methods that the area enclosed by a parabola and a straight line is 4/3 multiplied by the area of a triangle with equal base and height. He achieves this by calculating the value of a geometric series that sums to infinity with the ratio 14.
This is a dissection puzzle similar to a Tangram, and the treatise describing it was found in more complete form in the Archimedes Palimpsest. Archimedes calculates the areas of the 14 pieces which can be assembled to form a square. Research published by Dr. Reviel Netz of Stanford University in 2003 argued that Archimedes was attempting to determine how many ways the pieces could be assembled into the shape of a square. Dr. Netz calculates that the pieces can be made into a square 17,152 ways.[44] The number of arrangements is 536 when solutions that are equivalent by rotation and reflection have been excluded.[45] The puzzle represents an example of an early problem in combinatorics.
The origin of the puzzle's name is unclear, and it has been suggested that it is taken from the Ancient Greek word for throat or gullet, stomachos (στόμαχος).[46] Ausonius refers to the puzzle as Ostomachion, a Greek compound word formed from the roots of ὀστέον (osteon, bone) and μάχη (machē - fight). The puzzle is also known as the Loculus of Archimedes or Archimedes' Box.[47]
This work was discovered by Gotthold Ephraim Lessing in a Greek manuscript consisting of a poem of 44 lines, in the Herzog August Library in Wolfenbüttel, Germany in 1773. It is addressed to Eratosthenes and the mathematicians in Alexandria. Archimedes challenges them to count the numbers of cattle in the Herd of the Sun by solving a number of simultaneous Diophantine equations. .There is a more difficult version of the problem in which some of the answers are required to be square numbers.^ Here, Physics would say that there is no more physics beyond the numbers of the Planck Units.
• #266 mathematics ends at about 10^500 Re: powerset - sci.logic | Google Groups 19 January 2010 8:47 UTC groups.google.com [Source type: Original source]

.This version of the problem was first solved by A. Amthor[48] in 1880, and the answer is a very large number, approximately 7.760271 × 10206,544.^ So, there are a > > lot of things that we know about very large numbers.
• #266 mathematics ends at about 10^500 Re: powerset - sci.logic | Google Groups 19 January 2010 8:47 UTC groups.google.com [Source type: Original source]

^ So, there are a > > > lot of things that we know about very large numbers.
• #266 mathematics ends at about 10^500 Re: powerset - sci.logic | Google Groups 19 January 2010 8:47 UTC groups.google.com [Source type: Original source]

^ So, there are a lot of things that we know about very large numbers.
• #266 mathematics ends at about 10^500 Re: powerset - sci.logic | Google Groups 19 January 2010 8:47 UTC groups.google.com [Source type: Original source]

[49]
In this treatise, Archimedes counts the number of grains of sand that will fit inside the universe. This book mentions the heliocentric theory of the .solar system proposed by Aristarchus of Samos, as well as contemporary ideas about the size of the Earth and the distance between various celestial bodies.^ Newton showed that the motions of objects on Earth and of celestial bodies are governed by the same set of natural laws by demonstrating the consistency between Kepler’s laws of planetary motion and his theory of gravitation, thus removing the last doubts about heliocentrism and advancing the scientific revolution.
• Top 10 Most Influential Scientists - Listverse 19 January 2010 8:47 UTC listverse.com [Source type: General]

.By using a system of numbers based on powers of the myriad, Archimedes concludes that the number of grains of sand required to fill the universe is 8 × 1063 in modern notation.^ Sure, I admit that infinity exists, for example the infinitude of primes exists, but once I go beyond the number 10^500, I can no longer use Aristotlean Logic that mathematics is based upon and must use Physics logic which is nonlinear.
• #266 mathematics ends at about 10^500 Re: powerset - sci.logic | Google Groups 19 January 2010 8:47 UTC groups.google.com [Source type: Original source]

^ Can modern day mathematicians accept the idea that their subject ends at a large finite number of 10^500?
• #266 mathematics ends at about 10^500 Re: powerset - sci.logic | Google Groups 19 January 2010 8:47 UTC groups.google.com [Source type: Original source]

^ The first scientist to recognize and use the power of the lever was Archimedes .
• "Natural Magick" - "Glossery/Index - A" 19 January 2010 8:47 UTC homepages.tscnet.com [Source type: Original source]

The introductory letter states that Archimedes' father was an astronomer named Phidias. The Sand Reckoner or Psammites is the only surviving work in which Archimedes discusses his views on astronomy.[50]
This treatise was thought lost until the discovery of the .Archimedes Palimpsest in 1906. In this work Archimedes uses infinitesimals, and shows how breaking up a figure into an infinite number of infinitely small parts can be used to determine its area or volume.^ But don't expect mathematicians to give up work on the existing > infinite structures.
• #266 mathematics ends at about 10^500 Re: powerset - sci.logic | Google Groups 19 January 2010 8:47 UTC groups.google.com [Source type: Original source]

^ Specifically: To subtilize, as the humors of the body, or to break them into finer parts.
• "Natural Magick" - "Glossery/Index - A" 19 January 2010 8:47 UTC homepages.tscnet.com [Source type: Original source]

^ Find messages by this author Archimedes Plutonium wrote: > If all numbers were finite numbers, then the set of all primes is not > infinite, because > every Finite number has a successor.
• #266 mathematics ends at about 10^500 Re: powerset - sci.logic | Google Groups 19 January 2010 8:47 UTC groups.google.com [Source type: Original source]

Archimedes may have considered this method lacking in formal rigor, so he also used the method of exhaustion to derive the results. .As with The Cattle Problem, The Method of Mechanical Theorems was written in the form of a letter to Eratosthenes in Alexandria.^ Alphabet   Alphabet - The letters of a language arranged in the customary order; the series of letters or signs which form the elements of written language.
• "Natural Magick" - "Glossery/Index - A" 19 January 2010 8:47 UTC homepages.tscnet.com [Source type: Original source]

### Apocryphal works

Archimedes' Book of Lemmas or Liber Assumptorum is a treatise with fifteen propositions on the nature of circles. The earliest known copy of the text is in Arabic. .The scholars T. L. Heath and Marshall Clagett argued that it cannot have been written by Archimedes in its current form, since it quotes Archimedes, suggesting modification by another author.^ Find messages by this author On Jan 6, 12:33pm, Archimedes Plutonium - Hide quoted text - - Show quoted text - .
• #266 mathematics ends at about 10^500 Re: powerset - sci.logic | Google Groups 19 January 2010 8:47 UTC groups.google.com [Source type: Original source]

^ Martin Gardner, author of The Colossal Book of Mathematics "The incomparable Clifford Pickover has written another rich science narrative that at once informs and entertains.
• Archimedes to Hawking: Laws of Science and the Great Minds Behind Them 19 January 2010 8:47 UTC sprott.physics.wisc.edu [Source type: Original source]

^ Find messages by this author On Jan 4, 11:27pm, Archimedes Plutonium - Hide quoted text - - Show quoted text - .
• #266 mathematics ends at about 10^500 Re: powerset - sci.logic | Google Groups 19 January 2010 8:47 UTC groups.google.com [Source type: Original source]

The Lemmas may be based on an earlier work by Archimedes that is now lost.[51]
It has also been claimed that Heron's formula for calculating the area of a triangle from the length of its sides was known to Archimedes.[c] However, the first reliable reference to the formula is given by Heron of Alexandria in the 1st century AD.[52]

## Archimedes Palimpsest

Stomachion is a dissection puzzle in the Archimedes Palimpsest.
The foremost document containing the work of Archimedes is the Archimedes Palimpsest. In 1906, the Danish professor Johan Ludvig Heiberg visited Constantinople and examined a 174-page goatskin parchment of prayers written in the 13th century AD. He discovered that it was a palimpsest, a document with text that had been written over an erased older work. Palimpsests were created by scraping the ink from existing works and reusing them, which was a common practice in the Middle Ages as vellum was expensive. The older works in the palimpsest were identified by scholars as 10th century AD copies of previously unknown treatises by Archimedes.[53] The parchment spent hundreds of years in a monastery library in Constantinople before being sold to a private collector in the 1920s. On October 29, 1998 it was sold at auction to an anonymous buyer for $2 million at Christie's in New York.[54] .The palimpsest holds seven treatises, including the only surviving copy of On Floating Bodies in the original Greek.^ Of the 90 or so plays Aeschylus wrote, only seven have survived in complete form, among them the 'Oresteia' trilogy, 'The Seven against Thebes' and 'Prometheus Bound'. • "Natural Magick" - "Glossery/Index - A" 19 January 2010 8:47 UTC homepages.tscnet.com [Source type: Original source] It is the only known source of The Method of Mechanical Theorems, referred to by Suidas and thought to have been lost forever. Stomachion was also discovered in the palimpsest, with a more complete analysis of the puzzle than had been found in previous texts. The palimpsest is now stored at the Walters Art Museum in Baltimore, Maryland, where it has been subjected to a range of modern tests including the use of ultraviolet and x-ray light to read the overwritten text.[55] The treatises in the Archimedes Palimpsest are: On the Equilibrium of Planes, On Spirals, Measurement of a Circle, On the Sphere and the Cylinder, On Floating Bodies, The Method of Mechanical Theorems and Stomachion. ## Legacy The Fields Medal carries a portrait of Archimedes. There is a crater on the Moon named Archimedes (29.7° N, 4.0° W) in his honor, as well as a lunar mountain range, the Montes Archimedes (25.3° N, 4.6° W).[56] The asteroid 3600 Archimedes is named after him.[57] The Fields Medal for outstanding achievement in mathematics carries a portrait of Archimedes, along with his proof concerning the sphere and the cylinder. The inscription around the head of Archimedes is a quote attributed to him which reads in Latin: "Transire suum pectus mundoque potiri" (Rise above oneself and grasp the world).[58] .Archimedes has appeared on postage stamps issued by East Germany (1973), Greece (1983), Italy (1983), Nicaragua (1971), San Marino (1982), and Spain (1963).^ Nicaragua Postage Stamp List . • Archimedes to Hawking: Laws of Science and the Great Minds Behind Them 19 January 2010 8:47 UTC sprott.physics.wisc.edu [Source type: Original source] ^ Nicaragua postage stamps, 496-497 . • Archimedes to Hawking: Laws of Science and the Great Minds Behind Them 19 January 2010 8:47 UTC sprott.physics.wisc.edu [Source type: Original source] [59] The exclamation of Eureka! attributed to Archimedes is the state motto of California. In this instance the word refers to the discovery of gold near Sutter's Mill in 1848 which sparked the California Gold Rush.[60] A movement for civic engagement targeting universal access to health care in the US state of Oregon has been named the "Archimedes Movement," headed by former Oregon Governor John Kitzhaber.[61] ## See also ## Notes and references ### Notes a. ^ In the preface to On Spirals addressed to Dositheus of Pelusium, Archimedes says that "many years have elapsed since Conon's death." Conon of Samos lived c. 280–220 BC, suggesting that Archimedes may have been an older man when writing some of his works. .b. ^ The treatises by Archimedes known to exist only through references in the works of other authors are: On Sphere-Making and a work on polyhedra mentioned by Pappus of Alexandria; Catoptrica, a work on optics mentioned by Theon of Alexandria; Principles, addressed to Zeuxippus and explaining the number system used in The Sand Reckoner; On Balances and Levers; On Centers of Gravity; On the Calendar.^ Throughout, he includes fascinating, little-known tidbits relating to the law or lawgiver, and he provides cross-references to other laws or equations mentioned in the book. • Archimedes to Hawking: Laws of Science and the Great Minds Behind Them 19 January 2010 8:47 UTC sprott.physics.wisc.edu [Source type: Original source] ^ It was authored by one of the greatest mechanical minds in history: the legendary Archimedes , who knew a thing or two about spheres right down to his dying words... • 7 Books We Lost to History That Would Have Changed the World | Cracked.com 19 January 2010 8:47 UTC www.cracked.com [Source type: General] ^ The only reason we know the books exist at all is that other books from the time reference them (including some Cliffs Notes-style summaries) but that's it. • 7 Books We Lost to History That Would Have Changed the World | Cracked.com 19 January 2010 8:47 UTC www.cracked.com [Source type: General] Of the surviving works by Archimedes, T. L. Heath offers the following suggestion as to the order in which they were written: On the Equilibrium of Planes I, The Quadrature of the Parabola, On the Equilibrium of Planes II, On the Sphere and the Cylinder I, II, On Spirals, On Conoids and Spheroids, On Floating Bodies I, II, On the Measurement of a Circle, The Sand Reckoner. .c. ^ Boyer, Carl Benjamin A History of Mathematics (1991) ISBN 0471543977 "Arabic scholars inform us that the familiar area formula for a triangle in terms of its three sides, usually known as Heron's formula — k = √(s(s − a)(s − b)(s − c)), where s is the semiperimeter — was known to Archimedes several centuries before Heron lived.^ In this book, I discuss landmark laws of nature that were discovered over several centuries and whose ramifications have profoundly altered our everyday lives and understanding of the universe. • Archimedes to Hawking: Laws of Science and the Great Minds Behind Them 19 January 2010 8:47 UTC sprott.physics.wisc.edu [Source type: Original source] Arabic scholars also attribute to Archimedes the 'theorem on the broken chord' … Archimedes is reported by the Arabs to have given several proofs of the theorem." ### References 1. ^ a b "Archimedes Death Ray: Testing with MythBusters". MIT. Retrieved 2007-07-23. 2. ^ Calinger, Ronald (1999). A Contextual History of Mathematics. Prentice-Hall. pp. 150. ISBN 0-02-318285-7. "Shortly after Euclid, compiler of the definitive textbook, came Archimedes of Syracuse (ca. 287 212 BC), the most original and profound mathematician of antiquity." 3. ^ "Archimedes of Syracuse". The MacTutor History of Mathematics archive. January 1999. Retrieved 2008-06-09. 4. ^ O'Connor, J.J. and Robertson, E.F. (February 1996). "A history of calculus". University of St Andrews. Retrieved 2007-08-07. 5. ^ Bursill-Hall, Piers. "Galileo, Archimedes, and Renaissance engineers". sciencelive with the University of Cambridge. Retrieved 2007-08-07. 6. ^ 7. ^ T. L. Heath, Works of Archimedes, 1897 8. ^ 9. ^ O'Connor, J.J. and Robertson, E.F.. "Archimedes of Syracuse". University of St Andrews. Retrieved 2007-01-02. 10. ^ a b Rorres, Chris. "Death of Archimedes: Sources". Courant Institute of Mathematical Sciences. Retrieved 2007-01-02. 11. ^ Rorres, Chris. "Tomb of Archimedes: Sources". Courant Institute of Mathematical Sciences. Retrieved 2007-01-02. 12. ^ Rorres, Chris. "Siege of Syracuse". Courant Institute of Mathematical Sciences. Retrieved 2007-07-23. 13. ^ 14. ^ 15. ^ HyperPhysics. "Buoyancy". Georgia State University. Retrieved 2007-07-23. 16. ^ Rorres, Chris. "The Golden Crown". Drexel University. Retrieved 2009-03-24. 17. ^ Carroll, Bradley W. "Archimedes' Principle". Weber State University. Retrieved 2007-07-23. 18. ^ Rorres, Chris. "The Golden Crown: Galileo's Balance". Drexel University. Retrieved 2009-03-24. 19. ^ Casson, Lionel (1971). Ships and Seamanship in the Ancient World. Princeton University Press. ISBN 0691035369. 20. ^ Dalley, Stephanie. Oleson, John Peter. "Sennacherib, Archimedes, and the Water Screw: The Context of Invention in the Ancient World". Technology and Culture Volume 44, Number 1, January 2003 (PDF). Retrieved 2007-07-23. 21. ^ Rorres, Chris. "Archimedes screw - Optimal Design". Courant Institute of Mathematical Sciences. Retrieved 2007-07-23. 22. ^ 23. ^ Rorres, Chris. "Archimedes' Claw - Illustrations and Animations - a range of possible designs for the claw". Courant Institute of Mathematical Sciences. Retrieved 2007-07-23. 24. ^ Carroll, Bradley W. "Archimedes' Claw - watch an animation". Weber State University. Retrieved 2007-08-12. 25. ^ Hippias, 2 (cf. Galen, On temperaments 3.2, who mentions pyreia, "torches"); Anthemius of Tralles, On miraculous engines 153 [Westerman]. 26. ^ John Wesley. "A Compendium of Natural Philosophy (1810) Chapter XII, Burning Glasses". Online text at Wesley Center for Applied Theology. Retrieved 2007-09-14. 27. ^ "Archimedes' Weapon". Time Magazine. November 26, 1973. Retrieved 2007-08-12. 28. ^ Bonsor, Kevin. "How Wildfires Work". HowStuffWorks. Retrieved 2007-07-23. 29. ^ Quoted by Pappus of Alexandria in Synagoge, Book VIII 30. ^ Dougherty, F. C.; Macari, J.; Okamoto, C.. "Pulleys". Society of Women Engineers. Retrieved 2007-07-23. 31. ^ "Ancient Greek Scientists: Hero of Alexandria". Technology Museum of Thessaloniki. Retrieved 2007-09-14. 32. ^ Cicero. "De re publica 1.xiv §21". thelatinlibrary.com. Retrieved 2007-07-23. 33. ^ 34. ^ Rorres, Chris. "Spheres and Planetaria". Courant Institute of Mathematical Sciences. Retrieved 2007-07-23. 35. ^ "Ancient Moon 'computer' revisited". BBC News. November 29, 2006. Retrieved 2007-07-23. 36. ^ Plutarch. "Extract from Parallel Lives". fulltextarchive.com. Retrieved 2009-08-10. 37. ^ R.W. Kaye. "Archimedean ordered fields". web.mat.bham.ac.uk. Retrieved 2009-11-07. 38. ^ Quoted in T. L. Heath, Works of Archimedes, Dover Publications, ISBN 0-486-42084-1. 39. ^ Carroll, Bradley W. "The Sand Reckoner". Weber State University. Retrieved 2007-07-23. 40. ^ Encyclopedia of ancient Greece By Nigel Guy Wilson Page 77 ISBN 0794502253 (2006) 41. ^ "Editions of Archimedes' Work". Brown University Library. Retrieved 2007-07-23. 42. ^ Van Helden, Al. "The Galileo Project: Hydrostatic Balance". Rice University. Retrieved 2007-09-14. 43. ^ Heath,T.L.. "The Works of Archimedes (1897). The unabridged work in PDF form (19 MB)". Archive.org. Retrieved 2007-10-14. 44. ^ Kolata, Gina (December 14, 2003). "In Archimedes' Puzzle, a New Eureka Moment". The New York Times. Retrieved 2007-07-23. 45. ^ Ed Pegg Jr. (November 17, 2003). "The Loculus of Archimedes, Solved". Mathematical Association of America. Retrieved 2008-05-18. 46. ^ Rorres, Chris. "Archimedes' Stomachion". Courant Institute of Mathematical Sciences. Retrieved 2007-09-14. 47. ^ "Graeco Roman Puzzles". Gianni A. Sarcone and Marie J. Waeber. Retrieved 2008-05-09. 48. ^ B. Krumbiegel, A. Amthor, Das Problema Bovinum des Archimedes, Historisch-literarische Abteilung der Zeitschrift Für Mathematik und Physik 25 (1880) 121-136, 153-171. 49. ^ Calkins, Keith G. "Archimedes' Problema Bovinum". Andrews University. Retrieved 2007-09-14. 50. ^ 51. ^ 52. ^ O'Connor, J.J. and Robertson, E.F. (April 1999). "Heron of Alexandria". University of St Andrews. Retrieved 2010-02-17. 53. ^ Miller, Mary K. (March 2007). "Reading Between the Lines". Smithsonian Magazine. Retrieved 2008-01-24. 54. ^ "Rare work by Archimedes sells for$2 million". CNN. October 29, 1998. Retrieved 2008-01-15.
55. ^ "X-rays reveal Archimedes' secrets". BBC News. August 2, 2006. Retrieved 2007-07-23.
56. ^ Friedlander, Jay and Williams, Dave. "Oblique view of Archimedes crater on the Moon". NASA. Retrieved 2007-09-13.
57. ^ "Planetary Data System". NASA. Retrieved 2007-09-13.
58. ^ "Fields Medal". International Mathematical Union. Retrieved 2007-07-23.
59. ^ Rorres, Chris. "Stamps of Archimedes". Courant Institute of Mathematical Sciences. Retrieved 2007-08-25.
60. ^ "California Symbols". California State Capitol Museum. Retrieved 2007-09-14.
61. ^

• Boyer, Carl Benjamin (1991). A History of Mathematics. New York: Wiley. ISBN 0-471-54397-7.
• Dijksterhuis, E.J. (1987). Archimedes. Princeton University Press, Princeton. ISBN 0-691-08421-1.  Republished translation of the 1938 study of Archimedes and his works by an historian of science.
• Gow, Mary (2005). Archimedes: Mathematical Genius of the Ancient World. Enslow Publishers, Inc. ISBN 0-7660-2502-0.
• Hasan, Heather (2005). Archimedes: The Father of Mathematics. Rosen Central. ISBN 978-1404207745.
• Heath, T.L. (1897). Works of Archimedes. Dover Publications. ISBN 0-486-42084-1.  Complete works of Archimedes in English.
• Netz, Reviel and Noel, William (2007). The Archimedes Codex. Orion Publishing Group. ISBN 0-297-64547-1.
• Pickover, Clifford A. (2008). .Archimedes to Hawking: Laws of Science and the Great Minds Behind Them.^ Pickover examines more than 40 great laws, providing brief and cogent introductions to the science behind the laws as well as engaging biographies of such scientists as Newton, Faraday, Ohm, Curie, and Planck.
• Archimedes to Hawking: Laws of Science and the Great Minds Behind Them 19 January 2010 8:47 UTC sprott.physics.wisc.edu [Source type: Original source]

^ Laws of Science and the Great Minds Behind Them 22 Centuries of Discovery Do We Discover or Invent Laws?
• Archimedes to Hawking: Laws of Science and the Great Minds Behind Them 19 January 2010 8:47 UTC sprott.physics.wisc.edu [Source type: Original source]

^ Archimedes to Hawking: Laws of Science and the Great Minds Behind Them Return to Cliff Pickover's main web page .
• Archimedes to Hawking: Laws of Science and the Great Minds Behind Them 19 January 2010 8:47 UTC sprott.physics.wisc.edu [Source type: Original source]

.^ Clifford A. Pickover , Oxford University Press ( Buy at Amazon.Com ) Book Praise .
• Archimedes to Hawking: Laws of Science and the Great Minds Behind Them 19 January 2010 8:47 UTC sprott.physics.wisc.edu [Source type: Original source]

ISBN 978-0195336115.

• Simms, Dennis L. (1995). Archimedes the Engineer. Continuum International Publishing Group Ltd. ISBN 0-720-12284-8.
• Stein, Sherman (1999). Archimedes: What Did He Do Besides Cry Eureka?. Mathematical Association of America. ISBN 0-88385-718-9.

## The Works of Archimedes online

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# Quotes

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### From Wikiquote

Give me a place to stand, and I shall move the world.
.Archimedes of Syracuse (c. 287 BCc. 212 BC) was a Greek mathematician, philosopher, scientist and engineer.^ BC) Greek mathematician of the Alexandrian school.
• Math Jokes and Archimedes - Jokes and Science 19 January 2010 8:47 UTC www.juliantrubin.com [Source type: Original source]

^ BC) Greek mathematician, born in Syracuse.
• Math Jokes and Archimedes - Jokes and Science 19 January 2010 8:47 UTC www.juliantrubin.com [Source type: Original source]

^ Levers were first described about 260 BC by the ancient Greek mathematician Archimedes (287-212 BC).
• Inventors and Inventions of Scientific Instruments: EnchantedLearning.com 19 January 2010 8:47 UTC www.enchantedlearning.com [Source type: FILTERED WITH BAYES]

## Sourced

• εύρηκα. (Eureka!) .
• I have found it! or I have got it!
• 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;
• δος μοι που στω και κινω την γην (Dos moi pou sto kai kino taen gaen)
• Doric Greek: Δός μοι πᾶ στῶ καὶ τὰν γᾶν κινάσω
• 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.
• Variant translations:
• Give me a place to stand, and I shall move the world.
• Give me a fulcrum, and I shall move the world.
• Give me a stick long enough and a pivot and I shall move the world.
• Μη μου τους κύκλους τάραττε!^ This gifted Greek mathematician and inventor once said, "Give me a place to stand and rest my lever on, and I can move the Earth."
• "Natural Magick" - "Glossery/Index - A" 19 January 2010 8:47 UTC homepages.tscnet.com [Source type: Original source]

^ Vitruvius Pollio De Architectura 1912 .

^ (Dos moi pou sto kai kino taen gaen) Doric Greek: δος μοι π' αν στω και τα γαν κινάσω Translations: "Give me the place to stand, and I shall move the earth."
• PowerPedia:Archimedes - PESWiki 19 January 2010 8:47 UTC peswiki.com [Source type: FILTERED WITH BAYES]

(Me mou tous kyklous taratte!) .
• Noli turbare circulos meos. or Noli tangere circulos meos. (Latin translations)
• Do not disturb my circles!
• 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.^ Archimedes was killed by a Roman soldier during the sack of Syracuse during the Second Punic War , despite orders from the Roman general Marcellus that he was not to be harmed.
• PowerPedia:Archimedes - PESWiki 19 January 2010 8:47 UTC peswiki.com [Source type: FILTERED WITH BAYES]

^ The last words attributed to Archimedes are "Do not disturb my circles", a reference to the circles in the mathematical drawing that he was supposedly studying when disturbed by the Roman soldier.
• Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]

^ The soldier was enraged by this, and killed Archimedes with his sword.
• Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]

655

.
• 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.^ Mathematics is physics without purpose.
• Math Jokes and Archimedes - Jokes and Science 19 January 2010 8:47 UTC www.juliantrubin.com [Source type: Original source]

• T. L. Heath, in A History of Greek Mathematics II (1931)

# 1911 encyclopedia

Up to date as of January 14, 2010

### From LoveToKnow 1911

.ARCHIMEDES (c. 287 -212 B.C.), Greek mathematician and inventor, was born at Syracuse, in Sicily.^ Archimedes was born in the city of Syracuse on the island of Sicily in 287 BC. He was the son of an astronomer and mathematician named Phidias.

^ Called Archimedes of Syracuse Born 287 BC in Syracuse , Sicily Died 212 BC in Syracuse , Sicily A Greek mathematician who invented what is now known as Archimedean Screw and made enough advances in geometry and other branches of mathematics that school children curse his name to this day.
• Archimedes@Everything2.com 19 January 2010 8:47 UTC everything2.com [Source type: Original source]
• Archimedes@Everything2.com 19 January 2010 8:47 UTC www.everything2.com [Source type: Original source]

^ Plutarch, a Greek historian, had stated in ‘Parallel Lives’ that Archimedes was related to King Hiero II, the ruler of Syracuse.
• Archimedes Biography - Archimedes Childhood, Greek Scientist & Mathematician Archimedes Profile 16 October 2009 3:15 UTC lifestyle.iloveindia.com [Source type: FILTERED WITH BAYES]

.He was the son of Pheidias, an astronomer, and was on intimate terms with, if not related to, Hiero, king of Syracuse, and Gelo his son.^ He was the son of Pheidias , an astronomer, and was on intimate terms with, if not related to, Hiero , king of Syracuse, and Gelo his son.

^ He was the son of Pheidias, an astronomer, and was on intimate terms with, if not related to, Hiero, king of Syracuse, and Gelo his son.
• Archimedes 19 January 2010 8:47 UTC www.nndb.com [Source type: FILTERED WITH BAYES]

^ He may also have been related to Hieron, King of Syracuse, and his son Gelon.

.He studied at Alexandria and doubtless met there Conon of Samos, whom he admired as a mathematician and cherished as a friend, and to whom he was in the habit of communicating his discoveries before publication.^ It is also assumed that while in Alexandria Archimedes became friends with the Conon of Samos and with Eratosthenes.
• Archimedes The Life and Work of Archimedes 19 January 2010 8:47 UTC www.redstoneprojects.com [Source type: FILTERED WITH BAYES]

^ He studied at Alexandria and doubtless met there Conon of Samos, whom he admired as a mathematician and cherished as a friend, and to whom he was in the habit of communicating his discoveries before publication.
• Archimedes 19 January 2010 8:47 UTC www.nndb.com [Source type: FILTERED WITH BAYES]

^ He studied at Alexandria and doubtless met there Conon of Samos , whom he admired as a mathematician and cherished as a friend, and to whom he was in the habit of communicating his discoveries before publication.

.On his return to his native city he devoted himself to mathematical research.^ On his return to his native city he devoted himself to mathematical research.
• Archimedes 19 January 2010 8:47 UTC www.nndb.com [Source type: FILTERED WITH BAYES]
• Archimedes - LoveToKnow 1911 19 January 2010 8:47 UTC www.1911encyclopedia.org [Source type: FILTERED WITH BAYES]

^ After studying at the Alexandrian Museum in Egypt under successors of the mathematician Euclid, he returned to his native city.

^ Upon his return to Syracuse from Egypt, Archimedes devoted his life to the study of mathematics.
• Archimedes The Life and Work of Archimedes 19 January 2010 8:47 UTC www.redstoneprojects.com [Source type: FILTERED WITH BAYES]

.He himself set no value on the ingenious mechanical contrivances which made him famous, regarding them as beneath the dignity of pure science and even declining to leave any written record of them except in the case of the r /xupolroLta (Sphere-making), as to which see below.^ He himself set no value on the ingenious mechanical contrivances which made him famous, regarding them as beneath the dignity of pure science and even declining to leave any written record of them except in the case of the Sphere-making , as to which see below.
• Archimedes 19 January 2010 8:47 UTC www.nndb.com [Source type: FILTERED WITH BAYES]

^ He himself set no value on the ingenious mechanical contrivances which made him famous, regarding them as beneath the dignity of pure science and even declining to leave any written record of them except in the case of the r /xupolroLta (Sphere-making), as to which see below.

^ Each issue features: • 7 complete mechanical puzzles to make , (see 1 example below) • interactive optical illusions , to discover and to experiment with, • a lot of incredible Puzzles to solve ...

.As, however, these machines impressed the popular imagination, they naturally figure largely in the traditions about him.^ As, however, these machines impressed the popular imagination, they naturally figure largely in the traditions about him.
• Archimedes 19 January 2010 8:47 UTC www.nndb.com [Source type: FILTERED WITH BAYES]
• Archimedes - LoveToKnow 1911 19 January 2010 8:47 UTC www.1911encyclopedia.org [Source type: FILTERED WITH BAYES]

^ Far more details survive about the life of Archimedes than about any other ancient scientist, but they are largely anecdotal, reflecting the impression that his mechanical genius made on the popular imagination.
• Archimedes (Greek mathematician) -- Britannica Online Encyclopedia 19 January 2010 8:47 UTC www.britannica.com [Source type: FILTERED WITH BAYES]

^ At first the nature of these rays was a mystery, but after a few years it was established that they were electromagnetic waves, like light but of a much shorter wavelength (by a factor of about 1000).

.Thus he devised for Hiero engines of war which almost terrified the Romans, and which protracted the siege of Syracuse for three years.^ Thus he devised for Hiero engines of war which almost terrified the Romans , and which protracted the siege of Syracuse for three years.

^ Thus he devised for Hiero engines of war which almost terrified the Romans, and which protracted the siege of Syracuse for three years.
• Archimedes 19 January 2010 8:47 UTC www.nndb.com [Source type: FILTERED WITH BAYES]

^ Archimedes was thus called upon to construct war machines which held back the Romans' siege of Syracuse for three years.
• Archimedes - Best of Sicily Magazine 19 January 2010 8:47 UTC www.bestofsicily.com [Source type: FILTERED WITH BAYES]

.There is a story that he constructed a burning mirror which set the Roman ships on fire when they were within a bowshot of the wall.^ There is yet another interesting story related to the siege of the city according to which Archimedes constructed a burning mirror which set the roman ships on fire when they were at a bow’s distance.
• Archimedes Scientist & Mathematician - Biography & Achievements 19 January 2010 8:47 UTC www.ultimateitaly.com [Source type: FILTERED WITH BAYES]

^ Did the system of fire mirrors really burn the Roman ships?
• Archimedes: Science and Later Years - Succeed through Studying Biographies: School for Champions 19 January 2010 8:47 UTC www.school-for-champions.com [Source type: FILTERED WITH BAYES]

^ There is a story that he constructed a burning mirror which set the Roman ships on fire when they were within a bow-shot of the wall.
• Archimedes 19 January 2010 8:47 UTC www.nndb.com [Source type: FILTERED WITH BAYES]

.This has been discredited because it is not mentioned by Polybius, Livy or Plutarch; but it is probable that Archimedes had constructed some such burning instrument, though the connexion of it with the destruction of the Roman fleet is more than doubtful.^ This has been discredited because it is not mentioned by Polybius , Livy or Plutarch ; but it is probable that Archimedes had constructed some such burning instrument, though the connection of it with the destruction of the Roman fleet is more than doubtful.
• Archimedes 19 January 2010 8:47 UTC www.nndb.com [Source type: FILTERED WITH BAYES]

^ It should be mentioned that Archimedes was not the first to construct such a celestial globe.

^ Probably to make the notion of 'geometric construction' more exciting the Ancient Greeks have restricted the allowed operations to using a straightedge and a compass.
• Demonstration of the Archimedes' solution to the Trisection problem from Interactive Mathematics Miscellany and Puzzles 19 January 2010 8:47 UTC www.cut-the-knot.org [Source type: FILTERED WITH BAYES]

.More important, as being doubtless connected with the discovery of the principle in hydrostatics which bears his name and the foundation by him of that whole science, is the story of Hiero's reference to him of the question whether a crown made for him and purporting to be of gold, did not actually contain a proportion of silver.^ More important, as being doubtless connected with the discovery of the principle in hydrostatics which bears his name and the foundation by him of that whole science, is the story of Hiero's reference to him of the question whether a crown made for him and purporting to be of gold, did not actually contain a proportion of silver.
• Archimedes 19 January 2010 8:47 UTC www.nndb.com [Source type: FILTERED WITH BAYES]

^ Archimedes' Principle , which is named after him.
• Archimedes@Everything2.com 19 January 2010 8:47 UTC everything2.com [Source type: Original source]
• Archimedes@Everything2.com 19 January 2010 8:47 UTC www.everything2.com [Source type: Original source]

^ How did Archimedes determine whether a crown was pure gold?
• Archimedes Facts, information, pictures | Encyclopedia.com articles about Archimedes 19 January 2010 8:47 UTC www.encyclopedia.com [Source type: Academic]

.According to one story, Archimedes was puzzled till one day, as he was stepping into a bath and observed the water running over, it occurred to him that the excess of bulk occasioned by the introduction of alloy could be measured by putting the crown and an equal weight of gold separately into a vessel filled with water, and observing the difference of overflow.^ Measure the mass of the pycnometer filled with water.

^ According to one story, Archimedes was puzzled till one day, as he was stepping into a bath and observed the water running over, it occurred to him that the excess of bulk occasioned by the introduction of alloy could be measured by putting the crown and an equal weight of gold separately into a vessel filled with water, and observing the difference of overflow.

^ Noticing that water overflowed when he stepped into his bath, Archimedes concluded that a body immersed in water must displace a volume of water equal to the volume of the body.

.He was so overjoyed when this happy thought struck him that he ran home without his clothes, shouting eiipfKa, eiip?^ He was so overjoyed when this happy thought struck him that he ran home without his clothes, shouting eiipfKa, eiip?

^ With this discovery he was so much overjoyed that he ran home shouting “Eureka” or “ I have found it”.
• Archimedes Scientist & Mathematician - Biography & Achievements 19 January 2010 8:47 UTC www.ultimateitaly.com [Source type: FILTERED WITH BAYES]

^ He was so overjoyed when this happy thought struck him that he ran home without his clothes, shouting "Eureka!
• Archimedes 19 January 2010 8:47 UTC www.nndb.com [Source type: FILTERED WITH BAYES]

Ka, "
I have found it, have found it." Similarly his pioneer work in mechanics is illustrated by the story of his having said 80s pot iroi Kai KU'i Tip 'yi]v (or as another version has it, in his dialect, 7ra 0c7) Kai Kivw TOY -yav), " Give me a place to stand and I (will) move the earth." Hiero asked him to give an illustration of his contention that a very great weight could be moved by a very small force. .He is said to have fixed on a large and fully laden ship and to have used a mechanical device by which Hiero was enabled to move it by himself: but accounts differ as to the particular mechanical powers employed.^ He is said to have fixed on a large and fully laden ship and to have used a mechanical device by which Hiero was enabled to move it by himself; but accounts differ as to the particular mechanical powers employed.
• Archimedes 19 January 2010 8:47 UTC www.nndb.com [Source type: FILTERED WITH BAYES]

^ In fact, he did move a ship all by himself using a lever.
• Mathematical Database - Math Funland - Math Articles 19 January 2010 8:47 UTC www.mathdb.org [Source type: FILTERED WITH BAYES]

^ He is said to have fixed on a large and fully laden ship and to have used a mechanical device by which Hiero was enabled to move it by himself: but accounts differ as to the particular mechanical powers employed.

.The water-screw which he invented (see below) was probably devised in Egypt for the purpose of irrigating fields.^ The water-screw which he invented was probably devised in Egypt for the purpose of irrigating fields.
• Archimedes 19 January 2010 8:47 UTC www.nndb.com [Source type: FILTERED WITH BAYES]

^ Water screws irrigating the desert ?
• Archimedes The Life and Work of Archimedes 19 January 2010 8:47 UTC www.redstoneprojects.com [Source type: FILTERED WITH BAYES]

^ The water- screw which he invented (see below) was probably devised in Egypt for the purpose of irrigating fields.

.Archimedes died at the capture of Syracuse by Marcellus, 212 B.C. In the general massacre which followed the fall of the city, Archimedes, while engaged in drawing a mathematical figure on the sand, was run through the body by a Roman soldier.^ As an engineer he frustrated numerous attempts by the Romans to capture the city of Syracuse.
• Demonstration of the Archimedes' solution to the Trisection problem from Interactive Mathematics Miscellany and Puzzles 19 January 2010 8:47 UTC www.cut-the-knot.org [Source type: FILTERED WITH BAYES]

^ Archimedes was unaware of the taking of the city by the Romans.

^ Archimedes was killed by a Roman soldier when the City of Syracuse was taken by the Romans.

.No blame attaches to the Roman general, Marcellus, since he had given orders to his men to spare the house and person of the sage; and in the midst of his triumph he lamented the death of so illustrious a person, directed an honourable burial to be given him, and befriended his surviving relatives.^ Marcellus then ordered an honorable burial to be given to Archimedes and also befriended his surviving relatives.
• Archimedes Scientist & Mathematician - Biography & Achievements 19 January 2010 8:47 UTC www.ultimateitaly.com [Source type: FILTERED WITH BAYES]

^ In the midst of his triumph he provided Archimedes with an honorable burial and befriended his surviving relatives.

^ No blame attaches to the Roman general, Marcellus, since he had given orders to his men to spare the house and person of the sage; and in the midst of his triumph he lamented the death of so illustrious a person, directed an honorable burial to be given him, and befriended his surviving relatives.
• Archimedes 19 January 2010 8:47 UTC www.nndb.com [Source type: FILTERED WITH BAYES]

.In accordance with the expressed desire of the philosopher, his tomb was marked by the figure of a sphere inscribed in a cylinder, the discovery of the relation between the volumes of a sphere and its circumscribing cylinder being regarded by him as his most valuable achievement.^ He discovered the relation between the surface area and volume of a sphere and those of its circumscribing cylinder.
• "Natural Magick" - "Glossery/Index - A" 19 January 2010 8:47 UTC homepages.tscnet.com [Source type: Original source]

^ In accordance with the expressed desire of the philosopher, his tomb was marked by the figure of a sphere inscribed in a cylinder , the discovery of the relation between the volumes of a sphere and its circumscribing cylinder being regarded by him as his most valuable achievement.

^ In accordance with the expressed desire of Archimedes, his family and friends inscribed on his tomb the figure of his favorite theorem; the sphere and the circumscribed cylinder, and the ratio of the containing solid to the contained.

.When Cicero was quaestor in Sicily (75 B.C.), he found the tomb of Archimedes, near the Agrigentine gate, overgrown with thorns and briers.^ When Cicero was quaestor in Sicily (75 BC), he found the tomb of Archimedes, near the Agrigentine gate, overgrown with thorns and briers.
• Archimedes 19 January 2010 8:47 UTC www.nndb.com [Source type: FILTERED WITH BAYES]

^ When Cicero was quaestor in Sicily (75 B.C.), he found the tomb of Archimedes, near the Agrigentine gate , overgrown with thorns and briers.

^ When Cicero was in Sicily at Quaestor in 75 BC, he discovered the neglected and forgotten tomb of Archimedes near the Agrigentine Gate.

."Thus," says Cicero (Tusc.^ "Thus," says Cicero ( Tusc.

Disp.
v. c. 23, § 64), "would this most famous and once most learned city of Greece have remained a stranger to the tomb of one of its most ingenious citizens, had it not been discovered by a man of Arpinum." Works. - .The range and importance of the scientific labours of Archimedes will be best understood from a brief account of those writings which have come down to us; and it need only be added that his greatest work was in geometry, where he so extended the method of exhaustion as originated by Eudoxus, and followed by Euclid, that it became in his hands, though purely geometrical in form, actually equivalent in several cases to integration, as expounded in the first chapters of our text-books on the integral calculus.^ He also did work in integral calculus and work on pi.

^ The talent and the significance of Archimedes works can be easily understood if we look on to those writing which have survived.
• Archimedes Scientist & Mathematician - Biography & Achievements 19 January 2010 8:47 UTC www.ultimateitaly.com [Source type: FILTERED WITH BAYES]

^ The range and importance of the scientific labors of Archimedes will be best understood from a brief account of those writings which have come down to us; and it need only be added that his greatest work was in geometry, where he so extended the method of exhaustion as originated by Eudoxus of Cnidus , and followed by Euclid , that it became in his hands, though purely geometrical in form, actually equivalent in several cases to integration , as expounded in the first chapters of our textbooks on the integral calculus.
• Archimedes 19 January 2010 8:47 UTC www.nndb.com [Source type: FILTERED WITH BAYES]

.This remark applies to the finding of the area of a parabolic segment (mechanical solution) and of a spiral, the surface and volume of a sphere and of a segment thereof, and the volume of any segments of the solids of revolution of the second degree.^ He found the volume and surface area of a sphere.
• Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]

^ In fact, this method can be applied to the areas bounded by conics and the volumes of the solids of revolution.
• Mathematical Database - Math Funland - Math Articles 19 January 2010 8:47 UTC www.mathdb.org [Source type: FILTERED WITH BAYES]

^ This remark applies to the finding of the area of a parabolic segment (mechanical solution) and of a spiral, the surface and volume of a sphere and of a segment thereof, and the volume of any segments of the solids of revolution of the second degree.
• Archimedes 19 January 2010 8:47 UTC www.nndb.com [Source type: FILTERED WITH BAYES]

.The extant treatises are as follows: (1) On the Sphere and Cylinder (IIepi QOaipas Kai KvXivSpou). This treatise is in two books, dedicated to Dositheus, and deals with the dimensions of spheres, cones, "solid rhombi" and cylinders, all demonstrated in a strictly geometrical method.^ This treatise is in two books, dedicated to Dositheus, and deals with the dimensions of spheres, cones, "solid rhombi" and cylinders, all demonstrated in a strictly geometrical method.

^ His brilliant methods and proof for the sphere problem are described in his treatise On the Sphere and the Cylinder .

^ They are – On the Sphere and Cylinder in two books, dedicated to Dositheus dealing with the dimensions of spheres, cones, solid rhombi and cylinder, The measurement of the circle is a short book of three proposition, On Conoids and Spheroids is a treatise in 32 proposition, On Spirals is a book of 28 propositions, On plane Equilibria or centres of gravities of plane consist of two books which perhaps were the foundation of the theoretical mechanics – first book having 15 proposition with 7 postulates and the second having 10 propositions, The Quadrature of Parabola is a book of 24 proposition, On Floating bodies is a treatise in two books, The Sand Reckoner is a small treatise addressed to Gelo- the eldest son of Hiero dedicated to a system of naming large numbers in relations to orders and periods, The Method addressed to Eratostehenes is a treatise of vital interest and lastly The Collection of Lemmas consisting of 15 proposition in plain geometry.
• Archimedes Scientist & Mathematician - Biography & Achievements 19 January 2010 8:47 UTC www.ultimateitaly.com [Source type: FILTERED WITH BAYES]

.The first book contains forty-four propositions, and those in which the most important results are finally obtained are: 13 (surface of right cylinder), 14, 15 (surface of right cone), 33 (surface of sphere), 34 (volume of sphere and its relation to that of circumscribing cylinder), 42, 43 (surface of segment of sphere), 44 (volume of sector of sphere).^ He discovered the relation between the surface area and volume of a sphere and those of its circumscribing cylinder.
• "Natural Magick" - "Glossery/Index - A" 19 January 2010 8:47 UTC homepages.tscnet.com [Source type: Original source]

^ The first book contains forty-four propositions, and those in which the most important results are finally obtained are: 13 (surface of right cylinder), 14, 15 (surface of right cone), 33 (surface of sphere), 34 (volume of sphere and its relation to that of circumscribing cylinder), 42, 43 (surface of segment of sphere), 44 (volume of sector of sphere).
• Archimedes 19 January 2010 8:47 UTC www.nndb.com [Source type: FILTERED WITH BAYES]

^ The first book contains forty-four propositions, and those in which the most important results are finally obtained are: 13 (surface of right cylinder), 14, 15 (surface of right cone ), 33 (surface of sphere), 34 (volume of sphere and its relation to that of circumscribing cylinder), 42, 43 (surface of segment of sphere), 44 (volume of sector of sphere).

.The second book is in nine propositions, eight of which deal with segments of spheres and include the problems of cutting a given sphere by a plane so that (a) the surfaces, (b) the volumes, of the segments are in a given ratio (Props.^ In the second book of this work Archimedes' most important result is to show how to cut a given sphere by a plane so that the ratio of the volumes of the two segments has a prescribed ratio.

^ He found the volume and surface area of a sphere.
• Archimedes of Syracuse 19 January 2010 8:47 UTC www.squidoo.com [Source type: General]

^ The second book is in nine propositions, eight of which deal with segments of spheres and include the problems of cutting a given sphere by a plane so that (a) the surfaces, ( b ) the volumes, of the segments are in a given ratio (Props.

.3, 4), and of constructing a segment of a sphere similar to one given segment and having (a) its volume, (b) its surface, equal to that of another (5, 6).^ In the second book of this work Archimedes' most important result is to show how to cut a given sphere by a plane so that the ratio of the volumes of the two segments has a prescribed ratio.

^ He discovered the relation between the surface area and volume of a sphere and those of its circumscribing cylinder.
• "Natural Magick" - "Glossery/Index - A" 19 January 2010 8:47 UTC homepages.tscnet.com [Source type: Original source]

^ The Volumetric Flask (or Pycnometer ) has a hollow stem stopper that allows one to prepare equal volumes of fluids very reproducibly.

.(2) The Measurement of the Circle (KuKAov pErpnvcs) is a short book of three propositions, the main result being obtained in Prop.^ In the 'Measurement of Circle' Archimedes discovers the value of the square root of 3 as being more than 265/153 (approximately 1.732) and less than 1351/780 (approximately 1.7320512).

^ The key result used by Archimedes is Proposition 3 of Book VI of Euclid's Elements .
• Archimedes' Approximation of Pi 19 January 2010 8:47 UTC itech.fgcu.edu [Source type: FILTERED WITH BAYES]

^ The specific statement of Archimedes is Proposition 3 of his treatise Measurement of a Circle:   The ratio of the circumference of any circle to its diameter is less than 3 1 / 7 but greater than 3 10 / 71 .
• Archimedes' Approximation of Pi 19 January 2010 8:47 UTC itech.fgcu.edu [Source type: FILTERED WITH BAYES]

.2, which shows that the circumference of a circle is less than 37 and greater than 311 times its diameter.^ Historic: "Proposion 3: The circumference of any circle is three times the diameter and exceeds it by less than one-seventh of the diameter and by more than ten-seventyoneths " - from Measurement of a Circle by Archimedes (287-212 BC).
• PHASER Module: Archimedes' Pi MAP 19 January 2010 8:47 UTC www.phaser.com [Source type: Academic]

^ It had long been recognized that the ratio of the circumference of a circle to its diameter was constant, and a number of approximations had been given up to that point in time by the Babylonians, Egyptians, and even the Chinese.
• Archimedes' Approximation of Pi 19 January 2010 8:47 UTC itech.fgcu.edu [Source type: FILTERED WITH BAYES]

^ In the 'Measurement of Circle' Archimedes discovers the value of the square root of 3 as being more than 265/153 (approximately 1.732) and less than 1351/780 (approximately 1.7320512).

.Inscribing in and circumscribing about a circle two polygons, each of ninety-six sides, and assuming that the perimeter of the circle lay between those of the polygons, he obtained the limits he has assigned by sheer calculation, starting from two close approximations to the value of 1 / 3, which he assumes as known (265/153 < A t 3 < 1351/780).^ Circle, inscribing polygon, inscribed polygon .
• Mathematical Database - Math Funland - Math Articles 19 January 2010 8:47 UTC www.mathdb.org [Source type: FILTERED WITH BAYES]

^ From this hypothesis we get statement 1, "A polygon inscribing a circle has a larger perimeter than the circle."
• Mathematical Database - Math Funland - Math Articles 19 January 2010 8:47 UTC www.mathdb.org [Source type: FILTERED WITH BAYES]

^ Assume A > T , we can construct a regular polygon P with a sufficient number of sides such that P is inscribed by the circle and .
• Mathematical Database - Math Funland - Math Articles 19 January 2010 8:47 UTC www.mathdb.org [Source type: FILTERED WITH BAYES]

.(3) On Conoids and Spheroids (IIE p i crOaipoEt3hov) is a treatise in thirty-two propositions, on the solids generated by the revolution of the conic sections about their axes, the main results being the comparisons of the volume of any segment cut off by a plane with that of a cone having the same base and axis (Props.^ Statements 21 and 22: The volume of any segment of a paraboloid is times that of a cone (or a segment of a cone) with the same base and axes.
• Mathematical Database - Math Funland - Math Articles 19 January 2010 8:47 UTC www.mathdb.org [Source type: FILTERED WITH BAYES]

^ In general, cutting the cross-sectional area by a factor of two requires four times less energy to go the same distance.
• Archimedes,A Gold Thief and Buoyancy 19 January 2010 8:47 UTC www-personal.umich.edu [Source type: FILTERED WITH BAYES]

^ If we deal in the same way with all the sets of three circles in which planes perpendicular to AC cut the cylinder, the sphere, and the cone, and which make up those solids respectively, it follows that the cylinder, in the place where it is, will be in equilibrium about A with the sphere and the cone together, when both are placed with their centres of gravity at H. .
• Archimedes's method from Interactive Mathematics Miscellany and Puzzles 19 January 2010 8:47 UTC www.cut-the-knot.org [Source type: FILTERED WITH BAYES]

.21, 22 for the paraboloid, 25, 26 for the hyperboloid, and 27-32 for the spheroid).^ In the work On conoids and spheroids Archimedes examines paraboloids of revolution, hyperboloids of revolution, and spheroids obtained by rotating an ellipse either about its major axis or about its minor axis.

^ Comparing with Archimedes' studies of parabola, solid bounded by a paraboloid or hyperboloid and a plane, and spheroids, the former is certainly better known.
• Mathematical Database - Math Funland - Math Articles 19 January 2010 8:47 UTC www.mathdb.org [Source type: FILTERED WITH BAYES]

^ Statements 21 and 22: The volume of any segment of a paraboloid is times that of a cone (or a segment of a cone) with the same base and axes.
• Mathematical Database - Math Funland - Math Articles 19 January 2010 8:47 UTC www.mathdb.org [Source type: FILTERED WITH BAYES]

.(4) On Spirals (IIEpi EALKwv) is a book of twenty-eight propositions.^ On Spirals (IIEpi EALKwv) is a book of twenty-eight propositions.

^ The second book is in nine propositions, eight of which deal with segments of spheres and include the problems of cutting a given sphere by a plane so that (a) the surfaces, ( b ) the volumes, of the segments are in a given ratio (Props.

.Propositions I-II are preliminary, 13-20 contain tangential properties of the curve now known as the spiral of Archimedes, and 21-28 show how to express the area included between any portion of the curve and the radii vectores to its extremities.^ "The Method" In this work, which was unknown in the Middle Ages, but the importance of which was realised after its discovery, Archimedes pioneered the use of infinitesimals , showing how breaking up a figure in an infinite number of infinitely small parts could be used to determine its area or volume.
• Archimedes - Wiki Trust-tab Demo 19 January 2010 8:47 UTC onto.rpi.edu [Source type: FILTERED WITH BAYES]

^ "The Method" In this work, which was unknown in the Middle Ages, but the importance of which was realised after its discovery, Archimedes pioneered the use of infinitesimals, showing how breaking up a figure in an infinite number of infinitely small parts could be used to determine its area or volume.
• Archimedes --Great Minds, Great Thinkers 19 January 2010 8:47 UTC www.edinformatics.com [Source type: FILTERED WITH BAYES]

^ He calculated a nearly precise value for pi, showed how to determine the areas and volumes of geometric figures, and demonstrated novel ways to figure out their centers of gravity.
• STANFORD Magazine: September/October 2007 > Features > The Archimedes Codex 19 January 2010 8:47 UTC www.stanfordalumni.org [Source type: FILTERED WITH BAYES]

.(5) On the Equilibrium of Planes or Centres of Gravity of Planes (IIEpL kw - trawl, Lacppc71.6)v KEVrpa % apWV E7ru7rEOe v).^ On the Equilibrium of Planes or Centres of Gravity of Planes (IIEpL kw - trawl, Lacppc71.6)v KEVrpa % apWV E7ru7rEOe v).

^ On the Equilibrium of Planes (2 volumes) This scroll explains the law of the lever and uses it to calculate the areas and centers of gravity of various geometric figures.
• Archimedes - Wiki Trust-tab Demo 19 January 2010 8:47 UTC onto.rpi.edu [Source type: FILTERED WITH BAYES]

^ Archimedes discovered fundamental theorems concerning the centre of gravity of plane figures and these are given in this work.

.This consists of two books, and may be called the foundation of theoretical mechanics, for the previous contributions of Aristotle were comparatively vague and unscientific.^ This consists of two books, and may be called the foundation of theoretical mechanics, for the previous contributions of Aristotle were comparatively vague and unscientific.

^ One of the treatises in the book was called On the Method of Mechanical Theorems and it took into account a difficult concept that is central to calculus: infinity.
• Mystery Book: Science Videos - Science News - ScienCentral 19 January 2010 8:47 UTC www.sciencentral.com [Source type: FILTERED WITH BAYES]

^ List members may contribute with their book announcements or reviews of particular titles.
• SBF Glossary: A/R to ARW 19 January 2010 8:47 UTC www.plexoft.com [Source type: FILTERED WITH BAYES]

.In the first book there are fifteen propositions, with seven postulates; and demonstrations are given, much the same as those still employed, of the centres of gravity (I) of any two weights, (2) of any parallelogram, (3) of any triangle, (4) of any trapezium.^ In the first book there are fifteen propositions, with seven postulates; and demonstrations are given, much the same as those still employed, of the centres of gravity (I) of any two weights , (2) of any parallelogram, (3) of any triangle , (4) of any trapezium.

^ In particular he finds, in book 1, the centre of gravity of a parallelogram, a triangle, and a trapezium.

^ There are two pairs of congruent triangles.
• Illuminations: Archimedes' Puzzle 19 January 2010 8:47 UTC illuminations.nctm.org [Source type: FILTERED WITH BAYES]

.The second book in ten propositions is devoted to the finding the centres of gravity (I) of a parabolic segment, (2) of the area included between any two parallel chords and the portions of the curve intercepted by them.^ Book two is devoted entirely to finding the centre of gravity of a segment of a parabola.

^ In particular he finds, in book 1, the centre of gravity of a parallelogram, a triangle, and a trapezium.

^ The second book in ten propositions is devoted to the finding the centres of gravity (I) of a parabolic segment, (2) of the area included between any two parallel chords and the portions of the curve intercepted by them.

.(6) The Quadrature of the Parabola (TErpaywvw - mbs 7rapa130Xijr) is a book in twenty-four propositions, containing two demonstrations that the area of any segment of a parabola is a of the triangle which has the same base as the segment and equal height.^ He proved that the area enclosed by a parabola and a straight line is 4/3 the area of a triangle with equal base and height.
• Archimedes - Wiki Trust-tab Demo 19 January 2010 8:47 UTC onto.rpi.edu [Source type: FILTERED WITH BAYES]
• Archimedes --Great Minds, Great Thinkers 19 January 2010 8:47 UTC www.edinformatics.com [Source type: FILTERED WITH BAYES]

^ One example is Statement 24 of "On Quadrature of the parabola" as mentioned before, it stated that "The area of the quadrature of any parabola is equal to times that of a triangle with the same base and height."
• Mathematical Database - Math Funland - Math Articles 19 January 2010 8:47 UTC www.mathdb.org [Source type: FILTERED WITH BAYES]

^ In 'The Quadrature of the Parabola', Archimedes proved that the area enclosed by a parabola and a straight line is 4/3 multiplied by the area of a triangle with equal base and height.

.The first (a mechanical proof) begins, after some preliminary propositions on the parabola, in Prop.^ The first (a mechanical proof) begins, after some preliminary propositions on the parabola, in Prop.

^ As an example, the first statement in "The Methods" was on the areas bounded by parabolae, and the proof was discussed in the previous chapter.
• Mathematical Database - Math Funland - Math Articles 19 January 2010 8:47 UTC www.mathdb.org [Source type: FILTERED WITH BAYES]

^ The proof of the first proposition in the palimpsest appears below.
• PowerPedia:Archimedes - PESWiki 19 January 2010 8:47 UTC peswiki.com [Source type: FILTERED WITH BAYES]

6, ending with an integration in Prop. 16. The second (a geometrical proof) is expounded in Props. 17-24.
.(7) On Floating Bodies (IIEpi 6 X ov,dvwv) is a treatise in two books, the first of which establishes the general principles of hydrostatics, and the second discusses with the greatest completeness the positions of rest and stability of a right segment of a paraboloid of revolution floating in a fluid.^ Archimedes himself set out the basic principle, now known in hydrostatics (the study of the pressures liquids exert or transmit) as "Archimedes' principle," in his treatise "On Floating Bodies," but he did not describe his bathing experience.
• Salem Press 19 January 2010 8:47 UTC salempress.com [Source type: FILTERED WITH BAYES]

^ It's not that scholars don't have a clue about his theories written in the two treatises On Floating Bodies and Method of Mechanical Theorems .
• Archimedes Gets a Makeover 19 January 2010 8:47 UTC www.wired.com [Source type: News]

^ His best-known treatise, On Floating Bodies, proclaimed the famous Archimedes Principle, which states that a body immersed in a fluid experiences a buoyant force equal to the weight of the displaced fluid.
• STANFORD Magazine: September/October 2007 > Features > The Archimedes Codex 19 January 2010 8:47 UTC www.stanfordalumni.org [Source type: FILTERED WITH BAYES]

(8) The Psammites (*aµµirr t s, Lat. .Arenarius, or sand reckoner), a small treatise, addressed to Gelo, the eldest son of Hiero, expounding, as applied to reckoning the number of grains of sand that could be contained in a sphere of the size of our "universe," a system of naming large numbers according to "orders" and "periods" which would enable any number to be expressed up to that which we should write with I followed by 80,000 ciphers!^ Using that system, he calculated the number of grains of sand that would fill the known universe.
• Archimedes: Early Years and Mathematics - Succeed through Studying Biographies: School for Champions 19 January 2010 8:47 UTC www.school-for-champions.com [Source type: FILTERED WITH BAYES]

^ He invented a system for expressing large numbers.

^ The Sand Reckoner In this scroll, Archimedes counts the number of grains of sand fitting inside the universe .
• Archimedes - Wiki Trust-tab Demo 19 January 2010 8:47 UTC onto.rpi.edu [Source type: FILTERED WITH BAYES]

.(9) A Collection of Lemmas, consisting of fifteen propositions in plane geometry.^ Euclid collected and rearranged all the known facts about geometry, up to his time, in step-by-step order and added some new propositions and proofs.
• Math Jokes and Archimedes - Jokes and Science 19 January 2010 8:47 UTC www.juliantrubin.com [Source type: Original source]

.This has come down to us through a Latin version of an Arabic manuscript; it cannot, however, have been written by Archimedes in its present form, as his name is quoted in it more than once.^ This is the form of the argument as presented by Archimedes.
• Archimedes on Spheres and Cylinders 19 January 2010 8:47 UTC www.mathpages.com [Source type: FILTERED WITH BAYES]

^ So far, the Archimedes Project technology can perform a variety of impressive feats, including automatic morphological analysis - which means that each word in a text, be it Greek, Arabic, or Latin, can be linked to its root form in the dictionary.
• Harvard Gazette: Scholars resuscitate dead languages 19 January 2010 8:47 UTC www.news.harvard.edu [Source type: FILTERED WITH BAYES]

^ He was after the faint ink beneath -- mathematical theorems and diagrams from the Greek scholar Archimedes, who lived more than 2,000 years ago.
• A Prayer Book's Secret: Archimedes Lies Beneath : NPR 19 January 2010 8:47 UTC www.npr.org [Source type: General]

.Lastly, Archimedes is credited with the famous Cattle-Problem enunciated in the epigram edited by G. E. Lessing' in 1773, which purports to have been sent by Archimedes to the mathematicians at Alexandria in a letter to Eratosthenes.^ Through Eratosthenes Archimedes introduced the Cattle Problem to the mathematicians of Alexandria, and it was for Eratosthenes that Archimedes wrote the Method 3 .
• Archimedes The Life and Work of Archimedes 19 January 2010 8:47 UTC www.redstoneprojects.com [Source type: FILTERED WITH BAYES]

^ The problem of determining the gold content of the royal crown was given to Archimedes, a noted Greek mathematician and natural philosopher.
• Archimedes,A Gold Thief and Buoyancy 19 January 2010 8:47 UTC www-personal.umich.edu [Source type: FILTERED WITH BAYES]

^ Mathematicians born in the same country Additional Material in MacTutor Archimedes on mechanical and geometric methods Archimedes' Quadrature of the parabola Archimedes on statics Semi-regular (or Archimedean) solids The Archimedean cattle problem Cremona's translation of On the Sphere and Cylinder (1544) .

.Of lost works by Archimedes we can identify the following: (I) investigations on polyhedra mentioned by Pappus; (2) 'Ap X ai, Principles, a book addressed to Zeuxippus and dealing with the naming of numbers on the system explained in the Sand Reckoner; (3) IIEpL -vywv, On balances or levers; (4) KEvrpo i 3apLKa, On centres of gravity; (5) Karoirrpoca, an optical work from which Theon of Alexandria quotes a remark about refraction; (6) 'E46SCov, a Method, mentioned by Suidas; (7) IIEpL cr aepoiroctas, On Sphere-making, in which Archimedes explained the construction of the sphere which he made to imitate the motions of the sun, the moon and the five planets in the heavens.^ Pappus refers to a work by Archimedes on semi-regular polyhedra, Archimedes himself refers to a work on the number system which he proposed in the Sandreckoner , Pappus mentions a treatise On balances and levers , and Theon mentions a treatise by Archimedes about mirrors.

^ Chapter 3, §§1-8 : the system of numbers from his book to Zeuxippus, including a theorem on how to multiply Archimedes numbers.
• Archimedes, Sand-Reckoner, Intro. 19 January 2010 8:47 UTC www.calstatela.edu [Source type: Reference]

^ The works of Archimedes which have survived are as follows.

Cicero actually saw this contrivance and describes it (De Rep. i. c. 14, §§ 21-22).
.BIBLIOGRAPHY. - The editio princeps of the works of Archimedes, with the commentary of Eutocius, is that printed at Basel, in 1544, in Greek and Latin, by Hervagius.^ The faint Greek inscriptions and accompanying diagrams were, in fact, the only surviving copies of several works by the great Greek mathematician Archimedes.
• A Prayer For Archimedes - Science News 19 January 2010 8:47 UTC sciencenews.org [Source type: FILTERED WITH BAYES]

^ In its pages is the only known surviving record of two of Archimedes' works, and the only version of another one in the original Greek.
• Reading Between the Lines | Science & Nature | Smithsonian Magazine 19 January 2010 8:47 UTC www.smithsonianmag.com [Source type: FILTERED WITH BAYES]
• Reading Between the Lines | Science & Nature | Smithsonian Magazine 19 January 2010 8:47 UTC www.smithsonianmag.com [Source type: FILTERED WITH BAYES]

^ Many works initially translated from Arabic by Gerard and his associates, among them Ptolemys great astronomical work the Almagest , were later translated directly from Greek into Latin from Byzantine manuscripts.
• Global Politician - The Legend of the Middle Ages 19 January 2010 8:47 UTC www.globalpolitician.com [Source type: Original source]

D. Rivault's edition (Paris, 1615) gave the enunciations in Greek and the proofs in Latin some what retouched. .A Latin version of them was published by Isaac Barrow in 1675 (London, 4to); Nicolas Tartaglia published in Latin the treatises on Centres of Gravity, on the Quadrature of the Parabola, on the Measurement of the Circle, and on Floating Bodies, i.^ His best-known treatise, On Floating Bodies, proclaimed the famous Archimedes Principle, which states that a body immersed in a fluid experiences a buoyant force equal to the weight of the displaced fluid.
• STANFORD Magazine: September/October 2007 > Features > The Archimedes Codex 19 January 2010 8:47 UTC www.stanfordalumni.org [Source type: FILTERED WITH BAYES]

^ Major Writings On plane equilibriums, Quadrature of the parabola, On the sphere and cylinder, On spirals, On conoids and spheroids, On floating bodies, Measurement of a circle, The Sandreckoner, On the method of mechanical problems.

^ On plane equilibriums (two books), Quadrature of the parabola , On the sphere and cylinder (two books), On spirals , On conoids and spheroids , On floating bodies (two books), Measurement of a circle , and The Sandreckoner.

.(Venice, 1 543); Trojanus Curtius published the two books on Floating Bodies in 1565 after Tartaglia's death; Frederic Cornmandine edited the Aldine edition of 1558, 4to, which contains Circuli Dimensio, De Lineis Spiralibus, Quadratura Paraboles, De Conoidibus et Spheroidibus, and De numero Arenae; and in 1565 the same mathematician published the two books De its quae vehuntur in aqua.^ Pacioli, Luca Summa de arithmetica, geometria, proportioni et proportionalita 1494 Pappus Alexandrinus Mathematical Collection, Book 8 1876 .

^ Besides being the unique source for two of Archimedes's most intriguing treatises, The Method and Stomachion, it was the only one containing On Floating Bodies in the original Greek.
• STANFORD Magazine: September/October 2007 > Features > The Archimedes Codex 19 January 2010 8:47 UTC www.stanfordalumni.org [Source type: FILTERED WITH BAYES]

^ Tartaglia, Niccolo Quesiti et inventioni diverse 1546 Thomaz, Alvaro Liber de triplici motu 1509 Thucydides [Thucydidis verba e lib.

.J.
Torelli's monumental edition of the works with the commentaries of Eutocius, published at Oxford in 1792, folio, remained the best Greek text until the definitive text edited, with Eutocius' commentaries, Latin translation, &c., by J. L. Heiberg (Leipzig, 1880-1881) superseded it.^ The ultimate challenge was deciphering and editing the Archimedes texts so they could be published.
• STANFORD Magazine: September/October 2007 > Features > The Archimedes Codex 19 January 2010 8:47 UTC www.stanfordalumni.org [Source type: FILTERED WITH BAYES]

^ He was a teacher of mathematics and wrote commentaries on the works of Ptolemy, including the Almagest , and made an influential edition with added comments of Euclids Elements .
• Global Politician - The Legend of the Middle Ages 19 January 2010 8:47 UTC www.globalpolitician.com [Source type: Original source]

^ Many of his works were lost when the library of Alexandria was burnt (twice actually) and survived only in Latin or Arabic translations .
• Archimedes - Wiki Trust-tab Demo 19 January 2010 8:47 UTC onto.rpi.edu [Source type: FILTERED WITH BAYES]

.The Arenarius and Dimensio Circuli, with Eutocius' commentary on the latter, were edited by Wallis with Latin translation and notes in 1678 (Oxford), and the Arenarius was also published in English by George Anderson (London, 1784), with useful notes and illustrations.^ All of the known works of Archimedes were published, in Greek with a Latin translation, at Basel in 1544 by Thomas Gechauff.
• Salem Press 19 January 2010 8:47 UTC salempress.com [Source type: FILTERED WITH BAYES]

^ The order is the one given in J.L. Heiberg's definitive edition, [Archimedes, Opera Omnia,'' with commentary by Eutocius, edited by I.L.~Heiberg and additional corrections by E.S.~Stamatis, B.G.~Teubner, Stuttgart, 1972].

.The first modern translation of the works is the French edition published by F. Peyrard (Paris, 1808, 2 vols.^ All of the known works of Archimedes were published, in Greek with a Latin translation, at Basel in 1544 by Thomas Gechauff.
• Salem Press 19 January 2010 8:47 UTC salempress.com [Source type: FILTERED WITH BAYES]

^ The first volume of this five-volume work contains an introduction to, history of, and translations of the texts of Archimedes that survived in Arabic.
• Salem Press 19 January 2010 8:47 UTC salempress.com [Source type: FILTERED WITH BAYES]

^ A P Yushkevich, On the first Russian editions of the works of Euclid and Archimedes (Russian), Akad.
• References for Archimedes 19 January 2010 8:47 UTC www.gap-system.org [Source type: Academic]

8vo.). .A valuable German translation with notes, by E. Nizze, was published at Stralsund in 1824. There is a complete edition in modern notation by T. L. Heath (The Works of Archimedes, Cambridge, 1897).^ Several of archimededs works were briefly inspected in Constantinople and was published, from photographs, by the Danish philologist Johan Ludvig Heiberg ( 1854 – 1928 ); shortly thereafter it was translated into English by Thomas Heath .
• PowerPedia:Archimedes - PESWiki 19 January 2010 8:47 UTC peswiki.com [Source type: FILTERED WITH BAYES]

^ Impact Archimedes reputedly sent copies of his theoretical studies to the library in Alexandria, Egypt, but no master edition of his works was, it seems, compiled and available for distribution.
• Salem Press 19 January 2010 8:47 UTC salempress.com [Source type: FILTERED WITH BAYES]

^ Some claim there is a lack of rigour in certain of the results of this work but the interesting discussion in [ 43 ] attributes this to a modern day reconstruction.

On Archimedes himself, see Plutarch's Life of Marcellus. (T. L. H.)

# Wiktionary

Up to date as of January 15, 2010

## English

### Proper noun

Wikipedia has an article on:
 Singular Archimedes Plural -
Archimedes
1. An ancient Greek mathematician, physicist and engineer
2. (computing) An early RISC personal computer
3. (astronomy) A large lunar impact crater on the eastern edges of the Mare Imbrium

# Simple English

File:Archimedes (Idealportrait).jpg
Archimedes, as an artist thinks he was.

Archimedes (287BC–212BC) was a Greek scientist. He was an inventor, an astronomer, and a mathematician. He was born in the town of Syracuse in Sicily in what is now Italy. He was very famous during his life and he may be one of the most clever people who have ever lived. He is now said to be one of the most important scientists and the greatest mathematician of the ancient world.

His father was Phidias, an astronomer, and he may have been in the family of a king of Syracuse. Syracuse was a rich Greek city, on the sea shore in Sicily. When Archimedes was about ten years old, he left Syracuse to study in Alexandria, in Egypt in the school of Euclid, who was a famous mathematician. Not much is known about the personal life of Archimedes, for example, whether he was married or if he had children.

## Archimedes in stories (legends)

There are many stories told about Archimedes. Some of them may be true, but many of them may be untrue, or only partly true.

The best known saying of Archimedes was that if he was given a long enough lever and a place to stand, he could move the world. This is meant to show the power of the lever. The lever is perhaps the simplest machine and can help a person to do more work than they would otherwise be able to do. Archimedes was not the first person to use a lever, but he did write about how it worked and what could be done to make it work better.

Another Archimedes story is that King Hiero II thought his crown was not pure gold. Archimedes proved that the crown was made from gold mixed with silver. The value of gold was more than that of silver, so the king was deceived. Archimedes was in a bath and thought about what happens when an item is put into water. He found out that different things (such as different metals) with the same weight move out different amounts of water. This is called water displacement and the different metals have different density. When he had this idea, he jumped out of the bath and ran with no clothes on through the streets of the town, shouting "Eureka!" - which means "I have found it"

## Archimedes the scientist

Archimedes is also well known for being the first person to understand statics, which is a part of the study of physics and is to do with loads that do not move, for example in buildings or bridges. He also understood and wrote about what happens when things float in liquids which is called buoyancy. He discovered, that is found out, how many things work and wrote down the new rules and laws that he found.

[[File:|75px|thumb|left|A compound pulley, which a person can use to lift heavy loads]]

## Archimedes, the inventor and engineer

Archimedes is also famous as an inventor because he made new tools and machines. For example, he made a machine to lift water that could be used by farmers to bring water to their crops. This is still called the Archimedes Screw.

Archimedes probably also invented a machine to measure distance, an odometer. A cart was built with wheels that turned four hundred times in one mile. A pin on the wheel would hit a 400-tooth gear, so it turned once for every mile. This gear would then make a small stone fall into a cup. At the end of a journey one could count the number of stones in the cup to find the distance.

Archimedes also made a machine by which one person could pull a large ship with just one rope. This was the compound pulley. This is an important machine even today, as it helps people in everyday life, although the versions we now use are much more complicated. They still have the same integral structure, though.

## Archimedes at war

He also invented or made many machines used in war, for example he made better catapults. This was during the Punic Wars, which were between Rome in what is now Italy and the city of Carthage in what is now North Africa. For many years he helped stop the Roman army from attacking Syracuse, his city. One war machine was called the "claw of Archimedes", or the "iron hand". It was used to defend the city from attacks by ships. Ancient writers said that it was a kind of crane with a hook that lifted ships out of the water and caused their destruction.

Another story about Archimedes is that he burned Roman ships from far away using many mirrors and the light from the sun. This is perhaps possible, but it is perhaps more likely that this was done with flaming missiles from a catapult.

After many years the Roman army took the city of Syracuse. One of the soldiers killed Archimedes, who was then an old man. The soldiers had perhaps been told to catch Archimedes alive, so it may have been a mistake. The story is that Archimedes was killed while drawing a mathematical diagram in the sand. He was so busy with his drawing that he did not see the soldier behind him. His famous last words were, “Don’t disturb my circles!”

## Tributes to Archimedes

Archimedes is thought to be so important as a mathematician that scientists have honoured him:

• A large hole or crater on the moon is named after Archimedes
• Some mountains on the moon are called the Montes Archimedes.

## Other websites

English Wikiquote has a collection of quotations related to:

rue:Архімед

# Citable sentences

Up to date as of December 13, 2010

Here are sentences from other pages on Archimedes, which are similar to those in the above article.