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Archimedes Illustration

Archimedes Illustration


Archimedes illustrations and clipart (224)

Archimedes Stock Illustration by HypnoCreative 9 / 744 Eureka! Clipart by wickerwood 2 / 335 Archimedes In Bathtub Drawings by bilhagolan 3 / 68 archimedes screw Stock Illustration by AlanCotton 3 / 162 The Death of Archimedes, vintage engraving. Stock Illustrations by grdenis 1 / 96 Archimedes screw vintage engraving Drawings by Morphart 2 / 997 Archimedes Stock Illustration by HypnoCreative 1 / 65 Archimedes screw or Archimedean screw, vintage engraving. Clipart by grdenis 4 / 83 Archimedes principle vintage engraving Drawings by Morphart 1 / 206 Golden Triskelion On White Background Stock Illustrations by PeterHermesFurian 4 / 53 Archimedean spiral, arithmetic spiral, over white Stock Illustration by PeterHermesFurian 3 / 37 Archimedes screw or Archimedean screw, vintage engraving. Stock Illustrations by Morphart 1 / 160 . Drawings by Netkoff 1 / 3 Archimedes bathes Clipart by askib 0 / 0 Archimedes Screw Line Drawing Stock Illustration by AlanCotton 0 / 54 Archimedes screw drawings Stock Illustration by blacklight 0 / 0 Mathematic, geometry school classroom interior. Lesson of euclid or axiomatic, practical geometry with circles and sphere, cylinder and blackboard with chalk, plato and archimedes bust. Stock Illustrations by ElegantSolution 1 / 21 Famous Scientists Of The History Set Clipart by TopVectors 1 / 34 Archimedes screw drawings Stock Illustration by blacklight 0 / 0 New invention of Archimedes Stock Illustrations by ensiferrum 0 / 16 Archimedes worm and involute gear blueprints Clip Art by blacklight 0 / 0 Spiral snail Galaxy Stock Illustration by Pilipenko 7 / 1,574 The following Architonnere Archimedes Leonardo da Vinci, vintage engraving. Stock Illustration by Morphart 0 / 13 Ancient Greek Philosopher Cliparts Clip Art by leremy 2 / 236 Archimedes worm and involute gear blueprints Stock Illustration by blacklight 0 / 0 Archimedes Screw In Action Clipart by AlanCotton 0 / 0 Archimedes screw vintage engraving Clipart by grdenis 0 / 36 Connected Celtic Double Spirals Stock Illustrations by PeterHermesFurian 4 / 413 Euclid Stock Illustration by pavila 3 / 66 The Experimental Verification of Archimedes principle vintage engraving Stock Illustration by grdenis 0 / 4 Illustration featuring Ostomachion game puzzle of Archimedes with key isolated Stock Illustration by canbedone 0 / 0 Idea, Insight Concept. Archimedes of Syracusa Character Ancient Genius Mathematician Inventor Saying Eureka in Bath Clip Art by ivector 0 / 0 Archimedes face. Ancient greek mathematician, physicist. vector illustration Stock Illustrations by popaukropa 0 / 0 Fig. 3. - Archimedes seen through the telescope, vintage engraving. Stock Illustration by Morphart 1 / 141 The following Architonnere Archimedes Leonardo da Vinci, vintage engraving. Stock Illustration by Morphart 0 / 16 Happy Day, March 14, a series of mathematical numbers Pythagoras 3.14, symbol. Fun vector math icon or sign banner ratio letter formula outline. Constant irrational number of Archimedes. Vector Clip Art by Yuliia1996 0 / 0 Greek Philosopher Drawings by Malchev 14 / 2,101 Archimedes Character Say Eureka in Bath Landing Page Template. Idea, Insight of Genius Mathematician Inventor Discovery Stock Illustration by ivector 0 / 0 trinacria Stock Illustration by iriselmo 1 / 536 Illustration featuring Ostomachion game puzzle of Archimedes with key isolated Stock Illustrations by canbedone 0 / 0 Archimedes principle vintage engraving Clipart by grdenis 0 / 8 Eureka Archimedes face. Ancient greek mathematician, physicist. Great discovery Stock Illustration by popaukropa 0 / 1 Triskele, triskelion within a circle frame with white wavy line Clipart by PeterHermesFurian 0 / 0 Archimedes in bath. Thumbs up eureka. ancient greek mathematician, physicist. Great discovery Stock Illustration by popaukropa 0 / 0 Surface of the Moon, Archimedes Impact Crater, vintage engraving Stock Illustration by grdenis 0 / 19 Celtic double spirals forming a circle shaped frame Clipart by PeterHermesFurian 0 / 0 Celtic Double Spirals Labyrinth Stock Illustrations by PeterHermesFurian 6 / 342 Archimedes screw mechanic lift device sketch engraving vector illustration. Scratch board style imitation. Black and white hand drawn image. Stock Illustration by AlexanderPokusay 0 / 0 Tiny Characters around Huge Light Bulb Searching Idea. Business Team Search Insight for Project Development Stock Illustrations by ivector 0 / 0 Archimedes screw mechanic lift device engraving vector illustration. Scratch board style imitation. Black and white hand drawn image. Stock Illustration by AlexanderPokusay 0 / 0 Tiny Characters around Huge Light Bulb Searching Idea Landing Page Template Set. Business Team Search Insight Project Drawing by ivector 0 / 0 pulley Stock Illustration by fffranz 2 / 217 Four connected Celtic double spirals, within a circle frame Stock Illustration by PeterHermesFurian 0 / 0 Spiral screw drawings Stock Illustration by blacklight 0 / 0 Archimedes in bath. Thumbs up eureka. ancient greek mathematician, physicist. Great discovery Stock Illustration by popaukropa 0 / 0 Mathematical Constant, Pi Letter. Stock Illustration by olivier26 0 / 0 Archimedes in bath. Thumbs up eureka. ancient greek mathematician, physicist. Great discovery Clip Art by popaukropa 0 / 0 Helical Inducer isometric drawings Stock Illustration by blacklight 0 / 0 Tiny Characters around Huge Light Bulb Searching Idea Landing Page Template. Business Team Search Insight for Project Stock Illustration by ivector 0 / 0 Yellow triskele in circle frame with wavy line over green Stock Illustration by PeterHermesFurian 0 / 0 Circle frame made by spirals on the outside Stock Illustration by PeterHermesFurian 0 / 0 Inducer isometric drawings Clip Art by blacklight 0 / 0 Development of linear spirals of different sizes Stock Illustration by PeterHermesFurian 0 / 0 Three connected Celtic double spirals, within a circle frame Clip Art by PeterHermesFurian 0 / 0 Helical Inducer isometric drawings Clipart by blacklight 0 / 0 Development of intertwined linear spirals of different sizes Stock Illustration by PeterHermesFurian 0 / 0 Spiral screw drawings Stock Illustration by blacklight 0 / 0 Archimedes screw or Archimedean screw, vintage engraving. Stock Illustrations by Morphart 0 / 355 Star shaped symbol with six linear arithmetic spirals Drawings by PeterHermesFurian 0 / 0 Rainbow colored Celtic double spirals forming a circle shaped frame Stock Illustrations by PeterHermesFurian 0 / 0 Leverage and balance of power icon, outline style Drawing by ylivdesign 0 / 0 Four connected Celtic double spirals, quadruple spiral Clipart by PeterHermesFurian 0 / 0 Golden Star Spirals Drawings by PeterHermesFurian 0 / 0 Inducer isometric drawings Clipart by blacklight 0 / 0 Spiral feed screw drawings Stock Illustration by blacklight 0 / 0

Archimedes Vector clipart and illustrations (168)

Archimedes Vector by HypnoCreative 9 / 744 Eureka! Vector Clip Art by wickerwood 2 / 335 Archimedes In Bathtub Vectors by bilhagolan 3 / 68 archimedes screw Vector Clipart by AlanCotton 3 / 162 Archimedes screw vintage engraving Vectors by Morphart 2 / 997 Archimedes Vector by HypnoCreative 1 / 65 Archimedes screw or Archimedean screw, vintage engraving. Vector Clip Art by grdenis 4 / 83 Archimedes principle vintage engraving Vectors by Morphart 1 / 206 Golden Triskelion On White Background Vectors Illustration by PeterHermesFurian 4 / 53 Archimedean spiral, arithmetic spiral, over white Vector Clipart by PeterHermesFurian 3 / 37 Archimedes screw or Archimedean screw, vintage engraving. Clipart Vector by Morphart 1 / 160 . Vectors by Netkoff 1 / 3 Archimedes Screw Line Drawing EPS Vectors by AlanCotton 0 / 54 Mathematic, geometry school classroom interior. Lesson of euclid or axiomatic, practical geometry with circles and sphere, cylinder and blackboard with chalk, plato and archimedes bust. Vectors Illustration by ElegantSolution 1 / 21 Famous Scientists Of The History Set Vector Clip Art by TopVectors 1 / 34 Archimedes screw drawings Vector by blacklight 0 / 0 New invention of Archimedes Clipart Vector by ensiferrum 0 / 16 Ancient Greek Philosopher Cliparts Vector Illustration by leremy 2 / 236 Archimedes worm and involute gear blueprints Vector by blacklight 0 / 0 Archimedes screw vintage engraving Vector Clip Art by grdenis 0 / 36 Connected Celtic Double Spirals Clipart Vector by PeterHermesFurian 4 / 413 The Experimental Verification of Archimedes principle vintage engraving EPS Vectors by grdenis 0 / 4 Illustration featuring Ostomachion game puzzle of Archimedes with key isolated Vector by canbedone 0 / 0 Idea, Insight Concept. Archimedes of Syracusa Character Ancient Genius Mathematician Inventor Saying Eureka in Bath Vector Illustration by ivector 0 / 0 Archimedes face. Ancient greek mathematician, physicist. vector illustration Clipart Vector by popaukropa 0 / 0 Fig. 3. - Archimedes seen through the telescope, vintage engraving. Vector by Morphart 1 / 141 The following Architonnere Archimedes Leonardo da Vinci, vintage engraving. Vector Clipart by Morphart 0 / 16 Happy Day, March 14, a series of mathematical numbers Pythagoras 3.14, symbol. Fun vector math icon or sign banner ratio letter formula outline. Constant irrational number of Archimedes. Vector Vector Illustration by Yuliia1996 0 / 0 Greek Philosopher Vectors by Malchev 14 / 2,101 Archimedes Character Say Eureka in Bath Landing Page Template. Idea, Insight of Genius Mathematician Inventor Discovery EPS Vectors by ivector 0 / 0 trinacria Vector Clipart by iriselmo 1 / 536 Archimedes principle vintage engraving Vector Clip Art by grdenis 0 / 8 Eureka Archimedes face. Ancient greek mathematician, physicist. Great discovery Clip Art Vector by popaukropa 0 / 1 Triskele, triskelion within a circle frame with white wavy line Vector Clip Art by PeterHermesFurian 0 / 0 Archimedes in bath. Thumbs up eureka. ancient greek mathematician, physicist. Great discovery Clip Art Vector by popaukropa 0 / 0 Surface of the Moon, Archimedes Impact Crater, vintage engraving Clip Art Vector by grdenis 0 / 19 Celtic double spirals forming a circle shaped frame Vector Clip Art by PeterHermesFurian 0 / 0 Celtic Double Spirals Labyrinth Vectors Illustration by PeterHermesFurian 6 / 342 Archimedes screw mechanic lift device sketch engraving vector illustration. Scratch board style imitation. Black and white hand drawn image. EPS Vectors by AlexanderPokusay 0 / 0 Tiny Characters around Huge Light Bulb Searching Idea. Business Team Search Insight for Project Development Vectors Illustration by ivector 0 / 0 Archimedes screw mechanic lift device engraving vector illustration. Scratch board style imitation. Black and white hand drawn image. Vector Clipart by AlexanderPokusay 0 / 0 Tiny Characters around Huge Light Bulb Searching Idea Landing Page Template Set. Business Team Search Insight Project EPS Vector by ivector 0 / 0 Four connected Celtic double spirals, within a circle frame Vector Clipart by PeterHermesFurian 0 / 0 Archimedes in bath. Thumbs up eureka. ancient greek mathematician, physicist. Great discovery Clip Art Vector by popaukropa 0 / 0 Archimedes in bath. Thumbs up eureka. ancient greek mathematician, physicist. Great discovery Vector Illustration by popaukropa 0 / 0 Helical Inducer isometric drawings Vector Clipart by blacklight 0 / 0 Tiny Characters around Huge Light Bulb Searching Idea Landing Page Template. Business Team Search Insight for Project EPS Vectors by ivector 0 / 0 Yellow triskele in circle frame with wavy line over green Vector Clipart by PeterHermesFurian 0 / 0 Circle frame made by spirals on the outside Clip Art Vector by PeterHermesFurian 0 / 0 Development of linear spirals of different sizes Vector Clipart by PeterHermesFurian 0 / 0 Three connected Celtic double spirals, within a circle frame Vector Illustration by PeterHermesFurian 0 / 0 Development of intertwined linear spirals of different sizes Vector Clipart by PeterHermesFurian 0 / 0 Spiral screw drawings EPS Vectors by blacklight 0 / 0 Archimedes screw or Archimedean screw, vintage engraving. Vectors Illustration by Morphart 0 / 355 Star shaped symbol with six linear arithmetic spirals Vectors by PeterHermesFurian 0 / 0 Rainbow colored Celtic double spirals forming a circle shaped frame Clipart Vector by PeterHermesFurian 0 / 0 Four connected Celtic double spirals, quadruple spiral Vector Clip Art by PeterHermesFurian 0 / 0 Golden Star Spirals Vectors by PeterHermesFurian 0 / 0 Inducer isometric drawings Vector Clip Art by blacklight 0 / 0 Spiral feed screw drawings Vector by blacklight 0 / 0 Abstract maze futuristic linear spiral. Archimedean spiral. Isolated illustration on white background. Vector. Vector by h4u 0 / 0 Musical Note Radial Pattern Vector on a white background Vector Clipart by Bagwold 0 / 0 Bass clef spiral Vectors Illustration by PeterHermesFurian 0 / 8 Newton force icon, outline style Vector Clipart by anatolir 0 / 0 Emblem made of double spiral ornaments Vectors by PeterHermesFurian 0 / 0 Circle shaped emblem made of double spiral ornaments EPS Vector by PeterHermesFurian 0 / 0 Cartoon philosopher thinker on white background Clip Art Vector by Tigatelu 0 / 1 Circle frame made by spirals on the inside3 Vectors Illustration by PeterHermesFurian 0 / 0 Spiral form ornaments, buckle or volute shaped symbols Vector Clip Art by PeterHermesFurian 0 / 0 The Experimental Verification of Archimedes principle vintage engraving EPS Vector by Morphart 0 / 415 Black spiral made of increasing dots Vectors by PeterHermesFurian 0 / 0 Circle frame made of double spiral ornaments Vector Clip Art by PeterHermesFurian 0 / 0 Circle frame with Celtic double spirals Vector by PeterHermesFurian 0 / 0 Typical Archimedes Screw Machine Vector Illustration by AlanCotton 0 / 14 Background of square shaped tiles made spirals around circle Clip Art Vector by PeterHermesFurian 0 / 0

What was Archimedes' death ray?

Economist Jeffrey D. Sachs once made a compelling argument that humanity will eventually be saved from any crisis simply by reproducing [source: Scientific American].

We can reproduce our way out of any serious problem -- say, for instance, global food, energy or water shortages -- because the more humans who are born, the more geniuses will be born. The more geniuses humanity has on hand at any given time, the likelier our chances of thinking our way out of crises. "[I]t is genius above all that propels global human advance," wrote Sachs [source: Scientific American].

Some geniuses propel advancement more than others. The Greek mathematician Archimedes is one good example that all geniuses are not equal. For more than 50 years, Archimedes churned out answers to great ­mathematic and practical questions. He is responsible for calculating pi that alone would have assured him a place in the annals of history. But he also created calculus proofs 2,000 years before calculus itself was invented. He concluded that objects lose an amount of weight when they're in water equal to the weight of the fluid they displace (Archimedes' principle of hydrostatics). You can thank Archimedes for steel ships and hot air balloons.

Archimedes was every bit a mad genius, and he was socially handicapped by the breadth of his intellect. When he came up with his principle of hydrostatics, he'd been in the bath. Archimedes was so gripped by excitement at his breakthrough that he ran naked through the streets shouting "Eureka!" And his death came from a lack of comprehension that he was in danger. A Roman soldier sent to capture Archimedes entered his home. Archimedes, in the thick of determining a geometry proof using figures drawn in the sand on his floor, dismissed the stranger: "Do not disturb my diagrams," Archimedes told him.

The soldier flew into a rage and beat the 75-year-old genius to death. The soldier had been two years in coming the Romans had held Archimedes' home of Syracuse under siege for two years. But Archimedes' war machines had kept the Romans at bay. His death ray is said to have proven particularly effective.

Science of Destruction: Archimedes' War Machines

Archimedes was born in 287 B.C. in the city-state of Syracuse, then a part of ancient Greece, in what is modern-day Sicily. Aside from his travels to Egypt for his formal education (read more about that in "Did the ancient Greeks get their ideas from the Africans?"), Archimedes spent his life in Syracuse. When the Roman army set sail to lay siege on his home in the year 214, Archimedes turned his attention from calculations to finding new and inventive ideas for dealing death to Roman legions.

One of Archimedes' more famous quotes is, "Give me a lever long enough and a place to stand and I will move the world" [source: Stanford]. Archimedes used his knowledge of physics to fend off Roman ships approaching the fortified walls of Syracuse. One of the war machines Archimedes created was a giant iron claw, operated by virtually the entire population of Syracuse from inside the city's walls. Outside, the claw was capable of picking up entire Roman ships and plunging them into the sea. Archimedes used catapults and heavy timbers to hurl objects at the ships in the distance [source: Archimedes Palimpsest].

These war machines were complex, but perhaps the most effective (and coolest sounding) of Archimedes' instruments of destruction was the death ray. The name evokes thoughts of some huge, clumsy steampunk contraption pushed to the edge of the Syracusian walls. One can imagine the Roman soldiers' terror-widened eyes as the death ray came into view and made an increasingly high-pitched hum as it powered up before suddenly unleashing a deadly laser upon the ships, reducing them to atoms in one massive burst.

This wasn't the case. Instead, the death ray was actually a series of mirrors that reflected concentrated sunlight onto Roman ships. The ships were moored within bow and arrow range (in ancient Greece, anywhere from 200 to 1,000 feet (about 60.96 to 304.8 meters)). According to legend, the Roman ships were burned by the collective, condensed sunlight shone from these mirrors [source: McLeod]. Ship after ship in the Roman fleet caught fire and sank in the Mediterranean, casualties of the death ray.

The historian Galen was the first to describe the death ray in an account of the sack of Syracuse he wrote more than 350 years after the siege ended. Although other historians recorded the siege in earlier writings, none mentioned the death ray. Because of these earlier omissions of the death ray, the contraption's often viewed as pure myth, fantasy or exaggeration. Over the years, numerous attempts have been made to prove or disprove whether Archimedes' death ray could've worked -- but these experiments have yielded mixed results. At least two of them proved the death ray was possible. Keep reading to find out about those.

Burning Mirrors: Could Archimedes' Death Ray Work?

Electromagnetic waves of light carry with them heat energy. This energy is reflected by shiny surfaces, such as smooth, polished metal or glass. The smoother and flatter a mirrored surface, the less the light wave is dispersed and the truer the reflected beam is to the original. With all of this in mind, and with the brief accounts of Archimedes' death ray available in the annals of history, some researchers have set out to determine if the death ray is fact or fiction.

Discovery Channel's "Mythbusters" gave it a shot twice in seasons one and three. Both times the experiments failed, and Archimedes' death ray received a "busted" decree. While the Mythbusters weren't able to replicate Archimedes' storied success, other researchers have. A group at the Massachusetts Institute of Technology (MIT) undertook a death ray experiment in 2005, and constructed a 10-foot (3 m) long, one-inch (2.5 cm) thick red oak version of a Roman ship. Using 127 one-foot (0.3 m) square flat mirrors arranged in a parabola (a concave arc), the researchers managed to set the model ship on fire.

After 10 minutes of reflected sunlight (without any cloud coverage interrupting the direct stream of light), the MIT team managed to cause flash ignition in the patch of the ship where the beams of sunlight were concentrated into a single area. This meant that the temperature of the area had reached 1100 degrees Fahrenheit (593 degrees Celsius). The ship caught flame and burned before the MIT researchers put it out. They had proven that Archimedes' death ray was possible. Or had they?

There are still some problems with the MIT experiment. First and foremost, the Roman ship under attack by MIT's version of the death ray was motionless -- the successful experiment took place on a rooftop. This means that the beam of reflected sunlight had time to do its work without interruption from the motion created by waves. This wouldn't have been the case for Archimedes, who would have the Mediterranean to contend with. Even a calm sea would produce slight motion in the boat, making it difficult to ignite a single area since the concentrated beam wouldn't rest in one area for very long.

This contention was dealt with in 1973, when a Greek engineer undertook his own experiment to get to the bottom of Archimedes' death ray. He assembled 70 soldiers, each holding a 5-feet by 3-feet (1.5-m by 0.9-m) mirror. The concentrated beam reflected by the mirrors set a row boat 160 feet (49 m) offshore aflame. It is possible, then, that Archimedes' death ray could have worked.

A great many people remain skeptical, however. Why hadn't any historians writing shortly after the siege of Syracuse mentioned the ingenious device when recounting the event? Perhaps the best argument against the historical reality of Archimedes' use of mirrors at the siege is that they weren't used again in later battles. Archimedes biographer Sherman K. Stein writes, "had the mirrors done their work, they would have become a standard weapon yet there is no sign that they were added to the armaments of the time" [source: Stein].

Still, the legend persists. Thanks to continued interest among researchers who carry out their own experiments, Archimedes' death ray has been kept alive over the millennia. And even if the death ray's plausibility is definitively disproven in the future, it will have little dampening effect on the enduring genius left by Archimedes.


Notes

Cicero (Tusculanae disputationes, V, 23) says that he wants to contrast the life of Dionysius I of Syracuse with that of a man who is humble and common (humilem homunculum) from the same city: Archimedes. It does not seem to me that this passage must necessarily be interpreted as a reference to Archimedes’ humble origins Cicero might only have wished to underline the distance between a sovereign and a private citizen.

For a long time the passage of Galen was interpreted as the first testimony of the use of the mirrors to set Roman ships on fire. That interpretation, however, was based on the attribution of the meaning of ‘burning mirror’ to the Greek term πυρείον, which might also refer to incendiary substances.

The best translation into a Western language is found in Rashed [8].

A treatise on the construction of water-clocks, conserved in three Arabic manuscripts, has been published in an English translation by Hill [2].

Some scholars, loath to recognise aspects of humour in ancient works, have attempted to attribute the insolvability of the problem to copyists’ errors.

In this case as well many scholars are loath to recognise the hoax, which, speaking for myself, appears sufficiently clear.


Contents

Archimedes was born c. 287 BC in the seaport city of Syracuse, Sicily, at that time a self-governing colony in Magna Graecia. The date of birth is based on a statement by the Byzantine Greek historian John Tzetzes that Archimedes lived for 75 years before his death in 212 BC. [17] In the Sand-Reckoner, Archimedes gives his father's name as Phidias, an astronomer about whom nothing else is known. [25] A biography of Archimedes was written by his friend Heracleides, but this work has been lost, leaving the details of his life obscure. It is unknown, for instance, whether he ever married or had children, or if he ever visited Alexandria, Egypt, during his youth. [26] From his surviving written works, it is clear that he maintained collegiate relations with scholars based there, including his friend Conon of Samos and the head librarian Eratosthenes of Cyrene. [a]

The standard versions of the life of Archimedes were written long after his death by Greek and Roman historians. The earliest reference to Archimedes occurs in The Histories by Polybius (c. 200 - 118 BC), written about seventy years after his death. 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 from the Romans. [27] Polybius remarks how, during the Second Punic War, Syracuse switched allegiances from Rome to Carthage, resulting in a military campaign to take the city under the command of Marcus Claudius Marcellus and Appius Claudius Pulcher, which lasted from 213 to 212 BC. He notes that the Romans underestimated Syracuse's defenses, and mentions several machines designed by Archimedes, including improved catapults, crane-like machines that could swung around in an arc, and stone-throwers. Although the Romans ultimately captured the city, they suffered considerable losses due to the inventiveness of Archimedes. [28]

Cicero (106-43 BC) mentions Archimedes in some of his works. While serving as a quaestor in Sicily, Cicero found what was presumed to be Archimedes' tomb near the Agrigentine gate in Syracuse, in a neglected condition and overgrown with bushes. 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. The tomb carried a sculpture illustrating Archimedes' favorite mathematical proof, that the volume and surface area of the sphere are two-thirds that of the cylinder including its bases. [29] [30] He also mentions that Marcellus brought to Rome two planetariums built by Archimedes. [31] The Roman historian Livy (59 BC-17 AD) retells Polybius' story regarding the capture of Syracuse and Archimedes' role in it. [27]

Plutarch (45-119 AD) wrote in his Parallel Lives that Archimedes was related to King Hiero II, the ruler of Syracuse. [32] He also provides at least two accounts on how Archimedes died after the city was taken. According to the most popular account, Archimedes was contemplating a mathematical diagram when the city was captured. A Roman soldier commanded him to come and meet Marcellus, but he declined, saying that he had to finish working on the problem. The soldier was enraged by this and killed Archimedes with his sword. Another story has Archimedes carrying mathematical instruments before being killed because a soldier thought they were valuable items. Marcellus was reportedly angered by the death of Archimedes, as he considered him a valuable scientific asset (he called Archimedes "a geometrical Briareus") and had ordered that he should not be harmed. [33] [34]

The last words attributed to Archimedes are "Do not disturb my circles" (Latin, "Noli turbare circulos meos" Katharevousa Greek, "μὴ μου τοὺς κύκλους τάραττε"), a reference to the circles in the mathematical drawing that he was supposedly studying when disturbed by the Roman soldier. There is no reliable evidence that Archimedes uttered these words and they do not appear in the account given by Plutarch. A similar quote is found in the work of Valerius Maximus (fl. 30 AD), who wrote in Memorable Doings and Sayings ". sed protecto manibus puluere 'noli' inquit, 'obsecro, istum disturbare'" (". but protecting the dust with his hands, said 'I beg of you, do not disturb this ' "). [27]

Archimedes' principle

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. According to Vitruvius, a votive crown for a temple had been made for King Hiero II of Syracuse, who had supplied the pure gold to be used Archimedes was asked to determine whether some silver had been substituted by the dishonest goldsmith. [35] 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.

In Vitruvius' account, Archimedes noticed while taking a bath 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, [36] so the submerged crown would displace an amount of water equal to its own volume. By dividing the mass of the crown by the volume of water displaced, the density of the crown could be obtained. This density would be lower than that of gold if cheaper and less dense metals had been added. Archimedes then took to the streets naked, so excited by his discovery that he had forgotten to dress, crying "Eureka!" (Greek: "εὕρηκα , heúrēka!, lit. 'I have found [it]!'). [35] The test on the crown was conducted successfully, proving that silver had indeed been mixed in. [37]

The story of the golden crown does not appear anywhere in the known works of Archimedes. The practicality of the method it describes has been called into question due to the extreme accuracy that would be required while measuring the water displacement. [38] 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. This principle states that a body immersed in a fluid experiences a buoyant force equal to the weight of the fluid it displaces. [39] Using this principle, it would have been possible to compare the density of the crown to that of pure gold by balancing the crown on a scale with a pure gold reference sample of the same weight, then immersing the apparatus in water. The difference in density between the two samples would cause the scale to tip accordingly. [40] Galileo Galilei, who in 1586 invented a hydrostatic balance for weighing metals in air and water inspired by the work of Archimedes, 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." [41] [42]

Influence

In a 12th-century text titled Mappae clavicula there are instructions on how to perform the weighings in the water in order to calculate the percentage of silver used, and to solve the problem. [43] [44] The Latin poem Carmen de ponderibus et mensuris of the 4th or 5th century describes the use of a hydrostatic balance to solve the problem of the crown, and attributes the method to Archimedes. [43]

Archimedes' screw

A large part of Archimedes' work in engineering probably arose from fulfilling the needs of his home city of Syracuse. The Greek writer Athenaeus of Naucratis described how King Hiero II commissioned Archimedes to design a huge ship, the Syracusia, which could be used for luxury travel, carrying supplies, and as a naval warship. The Syracusia is said to have been the largest ship built in classical antiquity. [45] 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. It was turned by hand, and could also be used to transfer water from a low-lying body of water into irrigation canals. The Archimedes' screw is still in use today for pumping liquids and granulated solids such as coal and grain. 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. [46] [47] The world's first seagoing steamship with a screw propeller was the SS Archimedes, which was launched in 1839 and named in honor of Archimedes and his work on the screw. [48]

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. 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. 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. [49] [50]

Heat ray

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. Centuries later, Anthemius of Tralles mentions burning-glasses as Archimedes' weapon. [51] The device, sometimes called the "Archimedes heat ray", was used to focus sunlight onto approaching ships, causing them to catch fire. In the modern era, similar devices have been constructed and may be referred to as a heliostat or solar furnace. [52]

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. [53] 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.

Modern tests

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 5 by 3 feet (1.52 m × 0.91 m). The mirrors were pointed at a plywood mock-up of a Roman warship at a distance of around 160 feet (49 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. [54] A coating of tar would have been commonplace on ships in the classical era. [b]

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). 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 autoignition temperature, which is around 300 °C (572 °F). [55] [56]

When MythBusters broadcast the result of the San Francisco experiment in January 2006, the claim was placed in the category of "busted" (i.e. failed) because of the length of time and the ideal weather conditions required for combustion to occur. 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. [57]

In December 2010, MythBusters again looked at the heat ray story in a special edition entitled "President's Challenge". Several experiments were carried out, including a large scale test with 500 schoolchildren aiming mirrors at a mock-up of a Roman sailing ship 400 feet (120 m) away. In all of the experiments, the sail failed to reach the 210 °C (410 °F) required to catch fire, and the verdict was again "busted". The show concluded that a more likely effect of the mirrors would have been blinding, dazzling, or distracting the crew of the ship. [58]

Lever

While Archimedes did not invent the lever, he gave an explanation of the principle involved in his work On the Equilibrium of Planes. [59] Earlier descriptions of the lever are found in the Peripatetic school of the followers of Aristotle, and are sometimes attributed to Archytas. [60] [61] According to Pappus of Alexandria, Archimedes' 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 ). [62] 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. [63] 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 odometer was described as a cart with a gear mechanism that dropped a ball into a container after each mile traveled. [64]

Astronomical instruments

Archimedes discusses astronomical measurements of the Earth, Sun, and Moon, as well as Aristarchus' heliocentric model of the universe, in the Sand-Reckoner. Despite a lack of trigonometry and a table of chords, Archimedes describes the procedure and instrument used to make observations (a straight rod with pegs or grooves), [65] [66] applies correction factors to these measurements, and finally gives the result in the form of upper and lower bounds to account for observational error. [25] Ptolemy, quoting Hipparchus, also references Archimedes's solstice observations in the Almagest. This would make Archimedes the first known Greek to have recorded multiple solstice dates and times in successive years. [26]

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, constructed by Archimedes and used as aids in astronomy, which showed the motion of the Sun, Moon and five planets. 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. Marcellus' mechanism was demonstrated, according to Cicero, by Gaius Sulpicius Gallus to Lucius Furius Philus, who described it thus: [67] [68]

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.

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. [31] [69] Modern research in this area has been focused on the Antikythera mechanism, another device built c. 100 BC that was probably designed for the same purpose. [70] Constructing mechanisms of this kind would have required a sophisticated knowledge of differential gearing. [71] 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. [72] [73]

While he is often regarded as a designer of mechanical devices, Archimedes also made contributions to the field of mathematics. Plutarch wrote that Archimedes "placed his whole affection and ambition in those purer speculations where there can be no reference to the vulgar needs of life", [33] though some scholars believe this may be a mischaracterization. [74] [75] [76]

Method of exhaustion

Archimedes was able to use indivisibles (an early form of infinitesimals) in a way that is similar to modern integral calculus. [14] 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 areas of figures and the value of π.

Archimedean property

He also proved that the area of a circle was equal to π multiplied by the square of the radius of the circle ( π r 2 < extstyle pi r^<2>> ). In On the Sphere and Cylinder, Archimedes postulates that any magnitude when added to itself enough times will exceed any given magnitude. Today this is known as the Archimedean property of real numbers. [78]


Syracusia - largest transport ship of antiquity, c.240 BC - stock illustration

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History for Kids: The Illustrated Lives of Archimedes and Leonardo Da Vinci

In Charles River Editors’ History for Kids series, your children can learn about history’s most important people and events in an easy, entertaining, and educational way. Pictures help bring the story to life, and the concise but comprehensive book will keep your kid’s attention all the way to the end.

Over 1500 years before Leonardo Da Vinci became the Renaissance Man, antiquity had its own in the form of Archimedes, one of the most famous Ancient Greeks. An engineer, mathematician, physicist, scientist and astronomer all rolled into one, Archimedes has been credited for making groundbreaking discoveries, some of which are undoubtedly fact and others that are almost certainly myth. Regardless, he’s considered the first man to determine a way to measure an object’s mass, and also the first man to realize that refracting the Sun’s light could burn something, theorizing the existence of lasers over two millennia before they existed. People still use the design of the Archimedes screw in water pumps today, and modern scholars have tried to link him to the recently discovered Antikythera mechanism, an ancient “computer” of sorts that used mechanics to accurately chart astronomical data depending on the date it was set to.

It has long been difficult to separate fact from legend in the story of Archimedes’ life, from his death to his legendary discovery of how to differentiate gold from fool’s gold, but many of his works survived antiquity, and many others were quoted by other ancient writers. As a result, even while his life and death remain topics of debate, his writings and measurements are factually established and well known, and they range on everything from measuring an object’s density to measuring circles and parabolas.

If 100 people are asked to describe Leonardo in one word, they might give 100 answers. As the world’s most famous polymath and genius, Leonardo found time to be a painter, sculptor, architect, musician, scientist, mathematician, engineer, inventor, anatomist, geologist, cartographer, botanist, and writer.

It would be hard to determine which field Leonardo had the greatest influence in. His “Mona Lisa” and “The Last Supper” are among the most famous paintings of all time, standing up against even Michelangelo’s work. But even if he was not the age’s greatest artist, Leonardo may have conducted his most influential work was done in other fields. His emphasis on the importance of Nature would influence Enlightened philosophers centuries later, and he sketched speculative designs for gadgets like helicopters that would take another 4 centuries to create. Leonardo’s vision and philosophy were made possible by his astounding work as a mathematician, engineer and scientist. At a time when much of science was dictated by Church teachings, Leonardo studied geology and anatomy long before they truly even became scientific fields, and he used his incredible artistic abilities to sketch the famous Vitruvian Man, linking art and science together.

History for Kids: The Illustrated Lives of Archimedes and Leonardo Da Vinci chronicles the amazing lives, works, and theories of the two geniuses. Along with pictures of important people, places, and events, your kids will learn about Archimedes and Leonardo like never before.


Portrait of Archimedes.

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Illustration of Archimedes discovering how to measure volume and working out how things float - stock illustration

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Watch the video: How taking a bath led to Archimedes principle - Mark Salata (December 2021).