DOCSLIB.ORG

Archimedes Aarish Shahab Archimedes’ Life

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Archimedes Aarish Shahab Archimedes’ Life Archimedes Aarish Shahab Archimedes' life Much of what we know about Archimedes is minuscule when compared to the amount we do not know. Living in the times of the Ancient Greeks, Archimedes was born in Syracuse, Sicily in 287 B.C. His father, Phidias was a man of great wealth during this era and self-proclaimed astronomer. He devoted his wealth and experience to ensure that his son received the most superior education of the time. Archimedes indeed grew up watching his father use calculations in order to explain the phenomena of the world, and used it as inspiration to become a mathematician and philosopher; however, much is unknown regarding the details of Phidias and the rest of Archimedes' relatives. In fact, the concrete information we do know are only revealed in one of Archimedes' works: The Sandreckoner. Archimedes' friend, Her- acleides, once wrote a biography of him, however, it has truly been lost in history. Much of Archimedes' inventions are told by the perspective of men like Plutarch and Livy, as they reveal the context in which he created each of these inventions, such as during times of warfare. That being said, we glean clues of Archimedes' life from the context of his environment. For instance, some proponents argue that Archimedes' wealth was due to his relations with the King of Syracuse at the time, King Hiero II. This explains why Archimedes was granted the resources and luxury to explore mathematics to its very core, and reveal inventions that are still regarded as truly spectacular. Syracuse, Sicily was a bustling city full of commerce, art, and science while Archimedes was growing up; however, its bustling economy was one of the primary reasons why other nations attacked it, wishing to claim its riches. King Hiero II spearheaded the revolt against the Mamertines, send- ing Archimedes away to Alexandria, Egypt to further his studies. At the time, Alexandria had already earned a reputation for great learning and scholarship, a beautiful complement to Archimedes' evident natural curios- ity and creative problem solving. Archimedes was extremely keen to travel to Alexandria due to his fascination with one of the most renowned mathematicians of the time, Euclid. This well-known scholar was credited for compiling a book that catalogued all existing Greek geometrical treatises - a framework that forever changed the study of geometry and influenced Archimedes' later works. Archimedes thus happily traveled to Alexandria to study under the very teachers who tutored Euclid, hoping to leave an impact just as great, if not greater than Euclid himself. In Alexandria, Archimedes corresponded with other scholars such as Conon of Samos and Eratosthenes of Cyrene. It is with these principal mathemati- cians of the time that he published many of his works. Archimedes, equipped with newfound knowledge and intuition regarding how the world worked, travelled back to Syracuse, Sicily even though his hometown was being ravaged by warfare. It is there where he aided in the war effort, defending Syracuse against the Roman Siege of 213 BC, and invented ingenious solutions to the King's various problems. Indeed, Archimedes proved himself to be not only Sicily's, but also human- ity's greatest asset in the growth of mathematics. 2 Archimedes' mathematical works Archimedes' brilliance cannot be contained to just his era, as his inventions are still being used thousands of years later. For instance, one of Archimedes' most famous moments was where he coined the comical phrase 'Eureka!' In this account, King Henry II had told his goldsmith that he required a new royal crown made of solid gold. The pure amount of gold in one setting tempted the goldsmith to cunningly steal some of it. He only used a small portion of the gold while making the crown and mixed it with enough silver in order to make it seem like the weight was the same as if it was all 100 percent gold. However, King Hiero II suspected that something was wrong with his crown and ordered Archimedes to intuitively discover a method to test his theory without damaging the crown in any way. Archimedes remained stumped on this issue, until one day he decided to take a bubble bath. As he settled himself in the bath, he noticed that some of the water fell off the sides of the tub. Suddenly, he realized that he could measure the crown's volume by measuring the amount of water that was displaced. With the volume in mind, all he had to do was find the weight of the crown and divide it by its volume in order to determine the crown's unique density. If the density (a measure of the purity of the crown) was found to be different than pure gold, then the goldsmith would be held accountable. In this moment of celebrated discovery, Archimedes shouted 'Eureka!' and journeyed across the streets of Syracuse to inform the king. Today, this method is called 'Water Displacement' and is a useful tool for mathematicians and chemists who need to measure using indirect methods. For practical purposes, water is incompressible, so Archimedes' assumption was that the crown submerged would displace the same amount of water as its volume. However, this story is not present in Archimedes' works. In fact, the measurements regarding this Water Displacement method would have to be done very precisely in that even a small error would lead to an incorrect density and therefore a blame on an innocent goldsmith. It is thus proposed that Archimedes may have used a different analysis to prove that the goldsmith was cunning: The Archimedes Principle. This theory involved the use of hydrostatics and is further explained in his work 'On Floating Bodies.' This principle states that a body immersed in fluid 3 is subject to a buoyant force that is equal to the weight of the fluid that is displaced. This law could then be tested via the use of an apparatus that consisted of balancing the crown on a scale with the gold reference sample and placing this apparatus in water. If the crown was truly made of pure gold, then the scale would remain suspended equally, meaning that the wreath and gold would have the same volume and thus the same density. However, if the scale instead tips in favor of the side with gold, than the crown has a greater volume, a lower density, and is not pure. This Buoyancy Law, though needing much more materials than regular Wa- ter Displacement, is indeed more accurate and therefore is more likely to have been used by Archimedes. F is the buoyant force p is the density of displaced fluid V is the volume of displaced fluid g is the acceleration due to gravity g = 9:8 in meters per second squared F = p × g Note: The density and volume in this equation is referencing the displaced fluid and not the object that is submerged. For instance, if an object was submerged in water and displaces 1L of water, where 1 kg/l is the density, then the equation can be used to determine the buoyant force on the object since both the volume and density of the displaced fluid are known. Plugging this in: F = 1 × 1 × 9:8 Thus, if the weight of the object is more than 9.8N, then the object will 4 sink. If it is less than 9.8N, then the object will float. But if the weight is exactly 9.8N, then the object will neither sink nor float. Another story regarding King Hiero II and Alexander detailed a problem with one of Hiero II's ship designs. Although the ship design of the Greeks was superior, rainfall posed a clear and burdensome obstacle, as the rain- water would fill the hull of the ship. In order to emerge victorious in naval battle, Hiero called upon Archimedes to remedy the situation with another act of genius. Archimedes went on to create a machine consisting of a hollow tube with a spiral that could easily be turned at one end. When it was set into the hull, the turning motion carried water up the tube out of the hull, and forever revolutionized the economy. Today, this ingenious invention is called 'The Archimedes Screw' and is a widely used irrigation technique in developing countries. Another invention by Archimedes created in order to defend Syracuse was 'The Claw of Archimedes.'The weapon consisted of a grappling hook at the end of a long crane that would rip into nearby ships. The upward 'swing' motion would lift the ship upwards and damage it, if not sink it. The realism of this device has been called into question, and only in 2005 was it declared that it truly functioned. Another one of Archimedes' widely debated inventions was his 'Archimedes Heat Ray.' It is said that Archimedes used heat reflected from mirrors to burn ships attacking Syracuse. This device used the principle of a parabolic reflector, similar to the dynamics of a solar furnace. However, in 2005 stu- dents from MIT replicated this finding and determined that if certain con- ditions are met, the ship's wood could indeed reach its melting point of 300 degrees Celsius, thus technically setting the ship on fire. Archimedes other works were more varied. While he was theorizing about levers, he exclaimed 'give me a place to stand on, and I will move the Earth.'He used combinations of levers, block-and-tackle pulleys, catapults, and odometers to aid Syracuse during the First Punic War. By all defini- tions, Archimedes was indeed a soldier of Syracuse and an essential asset to its military.
Load more

Recommended publications
  • Ancient Roman Admirals"
    RRROM@NROM@N N@VY Caius Duilius Columna rostrata (Szczebrzeszynski, Wikipedia, Creative Commons). NAVIGARE NECESSE EST Non solo per gli appassionati di storia navale, ma per tutti gli amanti del mare e della classicità, ed in particolare per coloro che, come me, non sanno sottrarsi al fascino della civiltà romana. di DOMENICO CARRO Introduzione (in Italiano): genesi e nome di questo sito Web. Parte I VETRINA « CLASSICA» sulla storia navale e marittima dell'antica Roma (in Italiano): elementi relativi alla ricerca che da diversi anni sto conducendo al fine di pervenire ad una migliore messa a fuoco degli aspetti navali e marittimi del mondo romano. Dati sulle pubblicazioni maggiori (situazione e progetti) e bibliografia delle fonti antiche. Parte II ROMA MARITTIMA - Roma Eterna sul mare (in Italiano, con un po' di Francese e un po' di Inglese): altri miei contributi alla ricostruzione della storia navale e marittima dell'antica Roma e alla conoscenza dei Romani che si sono illustrati sul mare. Contiene alcuni saggi, qualche altro scritto minore e una bibliografia di fonti moderne. Parte III TESTI ANTICHI (in Italiano e Latino): alcuni scritti poco conosciuti, che trattano questioni navali o marittime secondo gli usi degli antichi Romani. Parte IV CONTRIBUTI ESTERNI (in Italiano): spazio predisposto per ospitare scritti di altri autori, quali ulteriori contributi alla conoscenza della storia navale e marittima dell'antica Roma. Parte V GALLERIA NAVALE (in Italiano): selezione di immagini navali romane (affreschi, mosaici, bassorilievi, sculture, monete e altri reperti) pubblicate su «Classica» o sulla Rete. Accreditamenti (titoli in Italiano e Inglese; commenti in Italiano): Guida alle risorse Internet d'interesse per la ricerca di altri elementi relativi alla storia navale e marittima dell'antica Roma.
    [Show full text]
  • Greeks Doing Algebra
    Greeks Doing Algebra There is a long-standing consensus in the history of mathematics that geometry came from ancient Greece, algebra came from medieval Persia, and the two sciences did not meet until seventeenth-century France (e.g. Bell 1945). Scholars agree that the Greek mathematicians had no methods comparable to algebra before Diophantus (3rd c. CE) or, many hold, even after him (e.g. Szabó 1969, Unguru and Rowe 1981, Grattan-Guinness 1996, Vitrac 2005. For a survey of arguments see Blåsjö 2016). The problems that we would solve with algebra, the Greeks, especially the authors of the canonical and most often studied works (such as Euclid and Apollonius of Perga), approached with spatial geometry or not at all. This paper argues, however, that the methods which uniquely characterize algebra, such as information compression, quantitative abstraction, and the use of unknowns, do in fact feature in Greek mathematical works prior to Diophantus. We simply have to look beyond the looming figures of Hellenistic geometry. In this paper, we shall examine three instructive cases of algebraic problem-solving methods in Greek mathematical works before Diophantus: The Sand-reckoner of Archimedes, the Metrica of Hero of Alexandria, and the Almagest of Ptolemy. In the Sand-reckoner, Archimedes develops a system for expressing extremely large numbers, in which the base unit is a myriad myriad. His process is indefinitely repeatable, and theoretically scalable to express a number of any size. Simple though it sounds to us, this bit of information compression, by which a cumbersome quantity is set to one in order to simplify notation and computation, is a common feature of modern mathematics but was almost alien to the Greeks.
    [Show full text]
  • Great Inventors of the Ancient World Preliminary Syllabus & Course Outline
    CLA 46 Dr. Patrick Hunt Spring Quarter 2014 Stanford Continuing Studies http://www.patrickhunt.net Great Inventors Of the Ancient World Preliminary Syllabus & Course Outline A Note from the Instructor: Homo faber is a Latin description of humans as makers. Human technology has been a long process of adapting to circumstances with ingenuity, and while there has been gradual progress, sometimes technology takes a downturn when literacy and numeracy are lost over time or when humans forget how to maintain or make things work due to cataclysmic change. Reconstructing ancient technology is at times a reminder that progress is not always guaranteed, as when Classical civilization crumbled in the West, but the history of technology is a fascinating one. Global revolutions in technology occur in cycles, often when necessity pushes great minds to innovate or adapt existing tools, as happened when humans first started using stone tools and gradually improved them, often incrementally, over tens of thousands of years. In this third course examining the greats of the ancient world, we take a close look at inventions and their inventors (some of whom might be more legendary than actually known), such as vizier Imhotep of early dynastic Egypt, who is said to have built the first pyramid, and King Gudea of Lagash, who is credited with developing the Mesopotamian irrigation canals. Other somewhat better-known figures are Glaucus of Chios, a metallurgist sculptor who possibly invented welding; pioneering astronomer Aristarchus of Samos; engineering genius Archimedes of Siracusa; Hipparchus of Rhodes, who made celestial globes depicting the stars; Ctesibius of Alexandria, who invented hydraulic water organs; and Hero of Alexandria, who made steam engines.
    [Show full text]
  • Squaring the Circle a Case Study in the History of Mathematics the Problem
    Squaring the Circle A Case Study in the History of Mathematics The Problem Using only a compass and straightedge, construct for any given circle, a square with the same area as the circle. The general problem of constructing a square with the same area as a given figure is known as the Quadrature of that figure. So, we seek a quadrature of the circle. The Answer It has been known since 1822 that the quadrature of a circle with straightedge and compass is impossible. Notes: First of all we are not saying that a square of equal area does not exist. If the circle has area A, then a square with side √A clearly has the same area. Secondly, we are not saying that a quadrature of a circle is impossible, since it is possible, but not under the restriction of using only a straightedge and compass. Precursors It has been written, in many places, that the quadrature problem appears in one of the earliest extant mathematical sources, the Rhind Papyrus (~ 1650 B.C.). This is not really an accurate statement. If one means by the “quadrature of the circle” simply a quadrature by any means, then one is just asking for the determination of the area of a circle. This problem does appear in the Rhind Papyrus, but I consider it as just a precursor to the construction problem we are examining. The Rhind Papyrus The papyrus was found in Thebes (Luxor) in the ruins of a small building near the Ramesseum.1 It was purchased in 1858 in Egypt by the Scottish Egyptologist A.
    [Show full text]
  • Mathematicians
    MATHEMATICIANS [MATHEMATICIANS] Authors: Oliver Knill: 2000 Literature: Started from a list of names with birthdates grabbed from mactutor in 2000. Abbe [Abbe] Abbe Ernst (1840-1909) Abel [Abel] Abel Niels Henrik (1802-1829) Norwegian mathematician. Significant contributions to algebra and anal- ysis, in particular the study of groups and series. Famous for proving the insolubility of the quintic equation at the age of 19. AbrahamMax [AbrahamMax] Abraham Max (1875-1922) Ackermann [Ackermann] Ackermann Wilhelm (1896-1962) AdamsFrank [AdamsFrank] Adams J Frank (1930-1989) Adams [Adams] Adams John Couch (1819-1892) Adelard [Adelard] Adelard of Bath (1075-1160) Adler [Adler] Adler August (1863-1923) Adrain [Adrain] Adrain Robert (1775-1843) Aepinus [Aepinus] Aepinus Franz (1724-1802) Agnesi [Agnesi] Agnesi Maria (1718-1799) Ahlfors [Ahlfors] Ahlfors Lars (1907-1996) Finnish mathematician working in complex analysis, was also professor at Harvard from 1946, retiring in 1977. Ahlfors won both the Fields medal in 1936 and the Wolf prize in 1981. Ahmes [Ahmes] Ahmes (1680BC-1620BC) Aida [Aida] Aida Yasuaki (1747-1817) Aiken [Aiken] Aiken Howard (1900-1973) Airy [Airy] Airy George (1801-1892) Aitken [Aitken] Aitken Alec (1895-1967) Ajima [Ajima] Ajima Naonobu (1732-1798) Akhiezer [Akhiezer] Akhiezer Naum Ilich (1901-1980) Albanese [Albanese] Albanese Giacomo (1890-1948) Albert [Albert] Albert of Saxony (1316-1390) AlbertAbraham [AlbertAbraham] Albert A Adrian (1905-1972) Alberti [Alberti] Alberti Leone (1404-1472) Albertus [Albertus] Albertus Magnus
    [Show full text]
  • Archimedes of Syracuse
    5 MARCH 2020 Engineering: Archimedes of Syracuse Professor Edith Hall Archimedes and Hiero II’s Syracuse Archimedes was and remains the most famous person from Syracuse, Sicily, in history. He belonged to the prosperous and sophisticated culture which the dominantly Greek population had built in the east of the island. The civilisation of the whole of ancient Sicily and South Italy was called by the Romans ‘Magna Graecia’ or ‘Great Greece’. The citis of Magna Graecia began to be annexed by the Roman Republic from 327 BCE, and most of Sicily was conquered by 272. But Syracuse, a large and magnificent kingdom, the size of Athens and a major player in the politics of the Mediterranean world throughout antiquity, succeeded in staying independent until 212. This was because its kings were allies of Rome in the face of the constant threat from Carthage. Archimedes was born into this free and vibrant port city in about 287 BCE, and as far as we know lived there all his life. When he was about twelve, the formidable Hiero II came to the throne, and there followed more than half a century of peace in the city, despite momentous power struggles going on as the Romans clashed with the Carthaginians and Greeks beyond Syracuse’s borders. Hiero encouraged arts and sciences, massively expanding the famous theatre. Archimedes’ background enabled him to fulfil his huge inborn intellectual talents to the full. His father was an astronomer named Pheidias. He was probably sent to study as a young man to Alexandria, home of the famous library, where he seems to have became close friend and correspondent of the great geographer and astonomer Eratosthenes, later to become Chief Librarian.
    [Show full text]
  • A Centennial Celebration of Two Great Scholars: Heiberg's
    A Centennial Celebration of Two Great Scholars: Heiberg’s Translation of the Lost Palimpsest of Archimedes—1907 Heath’s Publication on Euclid’s Elements—1908 Shirley B. Gray he 1998 auction of the “lost” palimp- tains four illuminated sest of Archimedes, followed by col- plates, presumably of laborative work centered at the Walters Matthew, Mark, Luke, Art Museum, the palimpsest’s newest and John. caretaker, remind Notices readers of Heiberg was emi- Tthe herculean contributions of two great classical nently qualified for scholars. Working one century ago, Johan Ludvig support from a foun- Heiberg and Sir Thomas Little Heath were busily dation. His stature as a engaged in virtually “running the table” of great scholar in the interna- mathematics bequeathed from antiquity. Only tional community was World War I and a depleted supply of manuscripts such that the University forced them to take a break. In 2008 we as math- of Oxford had awarded ematicians should honor their watershed efforts to him an honorary doc- make the cornerstones of our discipline available Johan Ludvig Heiberg. torate of literature in Photo courtesy of to even mathematically challenged readers. The Danish Royal Society. 1904. His background in languages and his pub- Heiberg lications were impressive. His first language was In 1906 the Carlsberg Foundation awarded 300 Danish but he frequently published in German. kroner to Johan Ludvig Heiberg (1854–1928), a He had publications in Latin as well as Arabic. But classical philologist at the University of Copenha- his true passion was classical Greek. In his first gen, to journey to Constantinople (present day Is- position as a schoolmaster and principal, Heiberg tanbul) to investigate a palimpsest that previously insisted that his students learn Greek and Greek had been in the library of the Metochion, i.e., the mathematics—in Greek.
    [Show full text]
  • General Disclaimer One Or More of the Following Statements May Affect
    https://ntrs.nasa.gov/search.jsp?R=19710025504 2020-03-11T22:36:49+00:00Z View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by NASA Technical Reports Server General Disclaimer One or more of the Following Statements may affect this Document This document has been reproduced from the best copy furnished by the organizational source. It is being released in the interest of making available as much information as possible. This document may contain data, which exceeds the sheet parameters. It was furnished in this condition by the organizational source and is the best copy available. This document may contain tone-on-tone or color graphs, charts and/or pictures, which have been reproduced in black and white. This document is paginated as submitted by the original source. Portions of this document are not fully legible due to the historical nature of some of the material. However, it is the best reproduction available from the original submission. Produced by the NASA Center for Aerospace Information (CASI) 6 X t B ICC"m date: July 16, 1971 955 L'Enfant Plaza North, S. W Washington, D. C. 20024 to Distribution B71 07023 from. J. W. Head suhiecf Derivation of Topographic Feature Names in the Apollo 15 Landing Region - Case 340 ABSTRACT The topographic features in the region of the Apollo 15 landing site (Figure 1) are named for a number of philosophers, explorers and scientists (astronomers in particular) representing periods throughout recorded history. It is of particular interest that several of the individuals were responsible for specific discoveries, observations, or inventions which considerably advanced the study and under- standing of the moon (for instance, Hadley designed the first large reflecting telescope; Beer published classic maps and explanations of the moon's surface).
    [Show full text]
  • Unit 3, Lesson 1: How Well Can You Measure?
    GRADE 7 MATHEMATICS NAME DATE PERIOD Unit 3, Lesson 1: How Well Can You Measure? 1. Estimate the side length of a square that has a 9 cm long diagonal. 2. Select all quantities that are proportional to the diagonal length of a square. A. Area of a square B. Perimeter of a square C. Side length of a square 3. Diego made a graph of two quantities that he measured and said, “The points all lie on a line except one, which is a little bit above the line. This means that the quantities can’t be proportional.” Do you agree with Diego? Explain. 4. The graph shows that while it was being filled, the amount of water in gallons in a swimming pool was approximately proportional to the time that has passed in minutes. a. About how much water was in the pool after 25 minutes? b. Approximately when were there 500 gallons of water in the pool? c. Estimate the constant of proportionality for the number of gallons of water per minute going into the pool. Unit 3: Measuring Circles Lesson 1: How Well Can You Measure? 1 GRADE 7 MATHEMATICS NAME DATE PERIOD Unit 3: Measuring Circles Lesson 1: How Well Can You Measure? 2 GRADE 7 MATHEMATICS NAME DATE PERIOD Unit 3, Lesson 2: Exploring Circles 1. Use a geometric tool to draw a circle. Draw and measure a radius and a diameter of the circle. 2. Here is a circle with center and some line segments and curves joining points on the circle. Identify examples of the following.
    [Show full text]
  • Archimedes and Pi
    Archimedes and Pi Burton Rosenberg September 7, 2003 Introduction Proposition 3 of Archimedes’ Measurement of a Circle states that π is less than 22/7 and greater than 223/71. The approximation πa ≈ 22/7 is referred to as Archimedes Approximation and is very good. It has been reported that a 2000 B.C. Babylonian approximation is πb ≈ 25/8. We will compare these two approximations. The author, in the spirit of idiot’s advocate, will venture his own approximation of πc ≈ 19/6. The Babylonian approximation is good to one part in 189, the author’s, one part in 125, and Archimedes an astonishing one part in 2484. Archimedes’ approach is to circumscribe and inscribe regular n-gons around a unit circle. He begins with a hexagon and repeatedly subdivides the side to get 12, 24, 48 and 96-gons. The semi-circumference of these polygons converge on π from above and below. In modern terms, Archimede’s derives and uses the cotangent half-angle formula, cot x/2 = cot x + csc x. In application, the cosecant will be calculated from the cotangent according to the (modern) iden- tity, csc2 x = 1 + cot2 x Greek mathematics dealt with ratio’s more than with numbers. Among the often used ratios are the proportions among the sides of a triangle. Although Greek mathematics is said to not know trigonometric functions, we shall see how conversant it was with these ratios and the formal manipulation of ratios, resulting in a theory essentially equivalent to that of trigonometry. For the circumscribed polygon We use the notation of the Dijksterhuis translation of Archimedes.
    [Show full text]
  • He One and the Dyad: the Foundations of Ancient Mathematics1 What Exists Instead of Ininite Space in Euclid’S Elements?
    ARCHIWUM HISTORII FILOZOFII I MYŚLI SPOŁECZNEJ • ARCHIVE OF THE HISTORY OF PHILOSOPHY AND SOCIAL THOUGHT VOL. 59/2014 • ISSN 0066–6874 Zbigniew Król he One and the Dyad: the Foundations of Ancient Mathematics1 What Exists Instead of Ininite Space in Euclid’s Elements? ABSTRACT: his paper contains a new interpretation of Euclidean geometry. It is argued that ancient Euclidean geometry was created in a quite diferent intuitive model (or frame), without ininite space, ininite lines and surfaces. his ancient intuitive model of Euclidean geometry is reconstructed in connection with Plato’s unwritten doctrine. he model cre- ates a kind of “hermeneutical horizon” determining the explicit content and mathematical methods used. In the irst section of the paper, it is argued that there are no actually ininite concepts in Euclid’s Elements. In the second section, it is argued that ancient mathematics is based on Plato’s highest principles: the One and the Dyad and the role of agrapha dogmata is unveiled. KEYWORDS: Euclidean geometry • Euclid’s Elements • ancient mathematics • Plato’s unwrit- ten doctrine • philosophical hermeneutics • history of science and mathematics • philosophy of mathematics • philosophy of science he possibility to imagine all of the theorems from Euclid’s Elements in a Tquite diferent intuitive framework is interesting from the philosophical point of view. I can give one example showing how it was possible to lose the genuine image of Euclidean geometry. In many translations into Latin (Heiberg) and English (Heath) of the theorems from Book X, the term “area” (spatium) is used. For instance, the translations of X. 26 are as follows: ,,Spatium medium non excedit medium spatio rationali” and “A medial area does not exceed a medial area by a rational area”2.
    [Show full text]
  • Archimedes Palimpsest a Brief History of the Palimpsest Tracing the Manuscript from Its Creation Until Its Reappearance Foundations...The Life of Archimedes
    Archimedes Palimpsest A Brief History of the Palimpsest Tracing the manuscript from its creation until its reappearance Foundations...The Life of Archimedes Birth: About 287 BC in Syracuse, Sicily (At the time it was still an Independent Greek city-state) Death: 212 or 211 BC in Syracuse. His age is estimated to be between 75-76 at the time of death. Cause: Archimedes may have been killed by a Roman soldier who was unaware of who Archimedes was. This theory however, has no proof. However, the dates coincide with the time Syracuse was sacked by the Roman army. The Works of Archimedes Archimedes' Writings: • Balancing Planes • Quadrature of the Parabola • Sphere and Cylinder • Spiral Lines • Conoids and Spheroids • On Floating Bodies • Measurement of a Circle • The Sandreckoner • The Method of Mechanical Problems • The Stomachion The ABCs of Archimedes' work Archimedes' work is separated into three Codeces: Codex A: Codex B: • Balancing Planes • Balancing Planes • Quadrature of the Parabola • Quadrature of the Parabola • Sphere and Cylinder • On Floating Bodies • Spiral Lines Codex C: • Conoids and Spheroids • The Method of Mechanical • Measurement of a Circle Problems • The Sand-reckoner • Spiral Lines • The Stomachion • On Floating Bodies • Measurement of a Circle • Balancing Planes • Sphere and Cylinder The Reappearance of the Palimpsest Date: On Thursday, October 29, 1998 Location: Christie's Acution House, NY Selling price: $2.2 Million Research on Palimpsest was done by Walter's Art Museum in Baltimore, MD The Main Researchers Include: William Noel Mike Toth Reviel Netz Keith Knox Uwe Bergmann Codex A, B no more Codex A and B no longer exist.
    [Show full text]