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Hall of Inventors & Engineers
Archimedes
Mathematician and engineer of Syracuse; the screw, levers, buoyancy
- c. 287 – 212 BCE
- Inventors & Engineers · 2 of 12
Hall of Inventors & Engineers
Mathematician and engineer of Syracuse; the screw, levers, buoyancy
Fetching the article from Wikipedia…
Archimedes of Syracuse ( AR-kih-MEE-deez; c. 287 – c. 212 BC) was an Ancient Greek mathematician, physicist, engineer, astronomer, and inventor from the city of Syracuse in Sicily. Although few details of his life are known, based on his surviving work, he is considered one of the leading scientists in classical antiquity, and one of the greatest mathematicians of all time. Archimedes anticipated modern calculus and analysis by applying the concept of the infinitesimals and the method of exhaustion to derive and rigorously prove many geometrical theorems, including the area of a circle, the surface area and volume of a sphere, the area of an ellipse, the area under a parabola, the volume of a segment of a paraboloid of revolution, the volume of a segment of a hyperboloid of revolution, and the area of a spiral.
Archimedes' other mathematical achievements include deriving an approximation of pi (π), defining and investigating the Archimedean spiral, and devising a system using exponentiation for expressing very large numbers. He was also one of the first to apply mathematics to physical phenomena, working on statics and hydrostatics. Archimedes' achievements in this area include a proof of the law of the lever, the widespread use of the concept of center of gravity, and the enunciation of the law of buoyancy known as Archimedes' principle. In astronomy, he made measurements of the apparent diameter of the Sun and the size of the universe. He is also said to have built a planetarium device that demonstrated the movements of the known celestial bodies, and may have been a precursor to the Antikythera mechanism. He is also credited with designing innovative machines, such as his screw pump, compound pulleys, and defensive war machines to protect his native Syracuse from invasion.
Archimedes died during the siege of Syracuse, when he was killed by a Roman soldier despite orders that he should not be harmed. Cicero describes visiting Archimedes' tomb, which was surmounted by a sphere and a cylinder that Archimedes requested be placed there to represent his most valued mathematical discovery.
Unlike his inventions, Archimedes' mathematical writings were little known in antiquity. Alexandrian mathematicians read and quoted him, but the first comprehensive compilation was not made until c. 530 AD by Isidore of Miletus in Byzantine Constantinople, while Eutocius' commentaries on Archimedes' works in the same century opened them to wider readership for the first time. In the Middle Ages, Archimedes' work was translated into Arabic in the 9th century and then into Latin in the 12th century, and were an influential source of ideas for scientists during the Renaissance and in the Scientific Revolution. The discovery in 1906 of works by Archimedes in the Archimedes Palimpsest has provided new insights into how he obtained mathematical results.
The details of Archimedes's life are obscure; a biography of Archimedes mentioned by Eutocius was allegedly written by his friend Heraclides Lembus, but this work has been lost, and modern scholarship is doubtful that it was written by Heraclides to begin with.
Based on a statement by the Byzantine Greek scholar John Tzetzes that Archimedes lived for 75 years before his death in 212 BC, Archimedes is estimated to have been born c. 287 BC in the seaport city of Syracuse, Sicily, at that time a self-governing colony in Magna Graecia. In the Sand-Reckoner, Archimedes gives his father's name as Phidias, an astronomer about whom nothing else is known; Plutarch wrote in his Parallel Lives that Archimedes was related to King Hiero II, the ruler of Syracuse, although Cicero and Silius Italicus suggest he was of humble origin. It is also unknown whether he ever married or had children, or if he ever visited Alexandria, Egypt, during his youth; though his surviving written works, addressed to Dositheus of Pelusium, a student of the Alexandrian astronomer Conon of Samos, and to the head librarian Eratosthenes of Cyrene, suggested that he maintained collegial relations with scholars based there. In the preface to On Spirals addressed to Dositheus, Archimedes says that "many years have elapsed since Conon's death." Conon of Samos lived c. 280 – c. 220 BC, suggesting that Archimedes may have been an older man when writing some of his works.
Another story of a problem that Archimedes is credited solving with in service of Hiero II is the "wreath problem." According to Vitruvius, writing about two centuries after Archimedes' death, King Hiero II of Syracuse had commissioned a golden wreath for a temple to the immortal gods, and had supplied pure gold to be used by the goldsmith. However, the king had begun to suspect that the goldsmith had substituted some cheaper silver and kept some of the pure gold for himself, and, unable to make the smith confess, asked Archimedes to investigate. Later, while stepping into a bath, Archimedes allegedly noticed that the level of the water in the tub rose more the lower he sank in the tub and, realizing that this effect could be used to determine the golden crown's volume, was so excited that he took to the streets naked, having forgotten to dress, crying "Eureka!", meaning "I have found [it]!" According to Vitruvius, Archimedes then took a lump of gold and a lump of silver that were each equal in weight to the wreath, and, placing each in the bathtub, showed that the wreath displaced more water than the gold and less than the silver, demonstrating that the wreath was gold mixed with silver.
A different account is given in the Carmen de Ponderibus, an anonymous 5th-century Latin didactic poem on weights and measures once attributed to the grammarian Priscian. In this poem, the lumps of gold and silver were placed on the scales of a balance, and then the entire apparatus was immersed in water; the difference in density between the gold and the silver, or between the gold and the crown, causes the scale to tip accordingly. Unlike the more famous bathtub account given by Vitruvius, this poetic account uses the hydrostatics principle now known as Archimedes' principle that is found in his treatise On Floating Bodies, where a body immersed in a fluid experiences a buoyant force equal to the weight of the fluid it displaces. Galileo Galilei, who invented a hydrostatic balance in 1586 inspired by Archimedes' work, 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."
A large part of Archimedes' work in engineering probably arose from fulfilling the needs of his home city of Syracuse. Athenaeus of Naucratis in his Deipnosophistae quotes a certain Moschion for a description on how King Hiero II commissioned the design of a huge ship, the Syracusia, which is said to have been the largest ship built in classical antiquity and, according to Moschion's account, it was launched by Archimedes. Plutarch tells a slightly different account, relating that Archimedes boasted to Hiero that he was able to move any large weight, at which point Hiero challenged him to move a ship. These accounts contain many fantastic details that are historically implausible, and the authors of these stories provide conflicting ideas about how this task was accomplished: Plutarch states that Archimedes constructed a block-and-tackle pulley system, while Hero of Alexandria attributed the same boast to Archimedes' invention of the baroulkos, a kind of windlass. Pappus of Alexandria attributed this feat, instead, to Archimedes' use of mechanical advantage, the principle of leverage to lift objects that would otherwise have been too heavy to move, attributing to him the oft-quoted remark: "Give me a place to stand on, and I will move the Earth."
Athenaeus, likely garbling the details of Hero's account of the baroulkos, also mentions that Archimedes used a "screw" in order to remove any potential water leaking through the hull of the Syracusia. Although this device is sometimes referred to as Archimedes' screw, it likely predates him by a significant amount, and none of his closest contemporaries who describe its use (Philo of Byzantium, Strabo, and Vitruvius) credit him with its use.
The greatest reputation Archimedes earned during antiquity was for the defense of his city from the Romans during the Siege of Syracuse. According to Plutarch, Archimedes had constructed war machines for Hiero II, but had never been given an opportunity to use them during Hiero's lifetime. In 214 BC, however, during the Second Punic War, when Syracuse switched allegiances from Rome to Carthage, the Roman army under Marcus Claudius Marcellus attempted to take the city, Archimedes allegedly personally oversaw the use of these war machines in the defense of the city, greatly delaying the Romans, who were only able to capture the city after a long siege. Three different historians, Plutarch, Livy, and Polybius provide testimony about these war machines, describing improved catapults, cranes that dropped heavy pieces of lead on the Roman ships or which used an iron claw to lift them out of the water, dropping them back in so that they sank.
A much more improbable account, not found in any of the three earliest accounts (Plutarch, Polybius, or Livy) describes how Archimedes used "burning mirrors" to focus the sun's rays onto the attacking Roman ships, setting them on fire. The earliest account to mention ships being set on fire, by the 2nd century CE satirist Lucian of Samosata, does not mention mirrors, and only says the ships were set on fire by artificial means, which may imply that burning projectiles were used. The first author to mention mirrors is Galen, writing later in the same century. Nearly four hundred years after Lucian and Galen, Anthemius, despite skepticism, tried to reconstruct Archimedes' hypothetical reflector geometry. The purported device, sometimes called "Archimedes' heat ray", has been the subject of an 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, with mixed results.
There are several divergent accounts of Archimedes' death during the sack of Syracuse after it fell to the Romans: The oldest account, from Livy, says that, while drawing figures in the dust, Archimedes was killed by a Roman soldier who did not know he was Archimedes. According to Plutarch, the soldier demanded that Archimedes come with him, but Archimedes declined, saying that he had to finish working on the problem, and the soldier killed Archimedes with his sword. Another story from Plutarch has Archimedes carrying mathematical instruments before being killed because a soldier thought they were valuable items. Another Roman writer, Valerius Maximus (fl. 30 AD), wrote in Memorable Doings and Sayings that Archimedes' last words as the soldier killed him were "... but protecting the dust with his hands, said 'I beg of you, do not disturb this.'" which is similar to the last words now commonly attributed to him, "Do not disturb my circles," which do not appear in any ancient sources.
Marcellus was reportedly angered by Archimedes' death, as he considered him a valuable scientific asset (he called Archimedes "a geometrical Briareus") and had ordered that he should not be harmed. Cicero (106–43 BC) mentions that Marcellus brought to Rome two planetariums Archimedes built, which were constructed by Archimedes and which showed the motion of the Sun, Moon and five planets, one of which he donated to the Temple of Virtue in Rome, and the other he allegedly kept as his only personal loot from Syracuse." Pappus of Alexandria reports on a now lost treatise by Archimedes On Sphere-Making, which may have dealt with the construction of these mechanisms. Constructing mechanisms of this kind would have required a sophisticated knowledge of differential gearing, which was once thought to have been beyond the range of the technology available in ancient times, but the discovery in 1902 of the Antikythera mechanism, another device built c. 100 BC designed with a similar purpose, has confirmed that devices of this kind were known to the ancient Greeks, with some scholars regarding Archimedes' device as a precursor.
While serving as a quaestor in Sicily, Cicero himself 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 an enclosing cylinder including its bases.
While he is often regarded as a designer of mechanical devices, Archimedes also made contributions to the field of mathematics, both in applying the techniques of his predecessors to obtain new results, and developing new methods of his own.
In Quadrature of the Parabola, Archimedes states that a certain proposition in Euclid's Elements demonstrating that the area of a circle is proportional to its diameter was proven using a lemma now known as the Archimedean property, that “the excess by which the greater of two unequal regions exceed the lesser, if added to itself, can exceed any given bounded region.” Prior to Archimedes, Eudoxus of Cnidus and other earlier mathematicians applied this lemma, a technique now referred to as the "method of exhaustion," to find the volume of a tetrahedron, cylinder, cone, and sphere, for which proofs are given in book XII of Euclid's Elements.
Text from the Wikipedia article “Archimedes”, available under CC BY-SA 4.0.