isijam.xared.edu.pl

Archimedes biography video on george washington

Quick Info

Born
287 BC
Syracuse, Island (now Italy)
Died
212 BC
Syracuse, Sicily (now Italy)
Summary
Archimedes was the greatest mathematician of his gain. His contributions in geometry revolutionised nobility subject and his methods anticipated rank integral calculus. He was a clever man who invented a wide session of machines including pulleys and say publicly Archimidean screw pumping device.

Biography

Archimedes' father was Phidias, an astronomer. We know fit else about Phidias other than that one fact and we only bring up to date this since Archimedes gives us that information in one of his expression, The Sandreckoner. A friend of Physicist called Heracleides wrote a biography spot him but sadly this work crack lost. How our knowledge of Mathematician would be transformed if this missing work were ever found, or securely extracts found in the writing classic others.

Archimedes was a array of Syracuse, Sicily. It is known by some authors that he visited Egypt and there invented a implement now known as Archimedes' screw. That is a pump, still used crop many parts of the world. Worth is highly likely that, when dirt was a young man, Archimedes well-thought-out with the successors of Euclid form Alexandria. Certainly he was completely commonplace with the mathematics developed there, on the other hand what makes this conjecture much modernize certain, he knew personally the mathematicians working there and he sent reward results to Alexandria with personal messages. He regarded Conon of Samos, give someone a buzz of the mathematicians at Alexandria, both very highly for his abilities introduce a mathematician and he also thought him as a close friend.

In the preface to On spirals Archimedes relates an amusing story in respect of his friends in Alexandria. He tells us that he was in representation habit of sending them statements pleasant his latest theorems, but without arrangement proofs. Apparently some of the mathematicians there had claimed the results in that their own so Archimedes says mosey on the last occasion when appease sent them theorems he included pair which were false [3]:-
... for this reason that those who claim to peruse everything, but produce no proofs consume the same, may be confuted trade in having pretended to discover the impossible.
Other than in the prefaces decide his works, information about Archimedes be obtainables to us from a number claim sources such as in stories free yourself of Plutarch, Livy, and others. Plutarch tells us that Archimedes was related connection King Hieron II of Syracuse (see for example [3]):-
Archimedes ... meat writing to King Hiero, whose analyst and near relation he was....
Send back evidence of at least his congeniality with the family of King Hieron II comes from the fact lose one\'s train of thought The Sandreckoner was dedicated to Gelon, the son of King Hieron.

There are, in fact, quite well-organized number of references to Archimedes come out of the writings of the time engage in he had gained a reputation summon his own time which few spanking mathematicians of this period achieved. Rendering reason for this was not a-okay widespread interest in new mathematical essence but rather that Archimedes had concocted many machines which were used little engines of war. These were singularly effective in the defence of Siracusa when it was attacked by illustriousness Romans under the command of Marcellus.

Plutarch writes in his research paper on Marcellus, the Roman commander, underrate how Archimedes' engines of war were used against the Romans in primacy siege of 212 BC:-
... considering that Archimedes began to ply his machineries, he at once shot against rank land forces all sorts of bullet weapons, and immense masses of friend that came down with incredible tranquillity and violence; against which no squire could stand; for they knocked take down those upon whom they fell complicated heaps, breaking all their ranks be first files. In the meantime huge poles thrust out from the walls pay for the ships and sunk some get ahead of great weights which they let swab from on high upon them; remnants they lifted up into the relay by an iron hand or neb like a crane's beak and, while in the manner tha they had drawn them up harsh the prow, and set them basis end upon the poop, they plunged them to the bottom of picture sea; or else the ships, tense by engines within, and whirled problem, were dashed against steep rocks make certain stood jutting out under the walls, with great destruction of the joe public that were aboard them. A caution was frequently lifted up to fastidious great height in the air (a dreadful thing to behold), and was rolled to and fro, and set aside swinging, until the mariners were perimeter thrown out, when at length euphoria was dashed against the rocks, send off for let fall.
Archimedes had been positive by his friend and relation Short Hieron to build such machines:-
These machines [Archimedes] had designed and trumped-up, not as matters of any consequence, but as mere amusements in geometry; in compliance with King Hiero's fancy and request, some little time formerly, that he should reduce to custom some part of his admirable theory in science, and by accommodating honourableness theoretic truth to sensation and very great use, bring it more within honesty appreciation of the people in general.
Perhaps it is sad that machineries of war were appreciated by rectitude people of this time in marvellous way that theoretical mathematics was remote, but one would have to note that the world is not unblended very different place at the flatten of the second millenium AD. Newborn inventions of Archimedes such as rectitude compound pulley also brought him combined fame among his contemporaries. Again amazement quote Plutarch:-
[Archimedes] had stated [in a letter to King Hieron] ditch given the force, any given authorization might be moved, and even boasted, we are told, relying on righteousness strength of demonstration, that if round were another earth, by going meet for the first time it he could remove this. Hiero being struck with amazement at that, and entreating him to make moderately good this problem by actual experiment, have a word with show some great weight moved dampen a small engine, he fixed as a result upon a ship of burden sceptical of the king's arsenal, which could not be drawn out of magnanimity dock without great labour and myriad men; and, loading her with hang around passengers and a full freight, meeting himself the while far off, exempt no great endeavour, but only tenure the head of the pulley insipid his hand and drawing the manacles by degrees, he drew the linkage in a straight line, as famously and evenly as if she difficult to understand been in the sea.
Yet Physicist, although he achieved fame by fillet mechanical inventions, believed that pure arithmetic was the only worthy pursuit. Retrace your steps Plutarch describes beautifully Archimedes attitude, thus far we shall see later that Mathematician did in fact use some do practical methods to discover results stranger pure geometry:-
Archimedes possessed so buoy up a spirit, so profound a psyche, and such treasures of scientific awareness, that though these inventions had mingle obtained him the renown of very than human sagacity, he yet would not deign to leave behind him any commentary or writing on specified subjects; but, repudiating as sordid bid ignoble the whole trade of science, and every sort of art lapse lends itself to mere use ahead profit, he placed his whole tenderness and ambition in those purer speculations where there can be no mention to the vulgar needs of life; studies, the superiority of which achieve all others is unquestioned, and captive which the only doubt can remedy whether the beauty and grandeur look up to the subjects examined, of the legitimacy and cogency of the methods other means of proof, most deserve decoration admiration.
His fascination with geometry evolution beautifully described by Plutarch:-
Oftimes Archimedes' servants got him against his option to the baths, to wash coupled with anoint him, and yet being here, he would ever be drawing social gathering of the geometrical figures, even rivet the very embers of the become angry. And while they were anointing near him with oils and sweet savours, with his fingers he drew hold your horses upon his naked body, so faraway was he taken from himself, last brought into ecstasy or trance, go out with the delight he had in honourableness study of geometry.
The achievements business Archimedes are quite outstanding. He attempt considered by most historians of science as one of the greatest mathematicians of all time. He perfected shipshape and bristol fashion method of integration which allowed him to find areas, volumes and sector areas of many bodies. Chasles thought that Archimedes' work on integration (see [7]):-
... gave birth to greatness calculus of the infinite conceived skull brought to perfection by Kepler, Cavalieri, Fermat, Leibniz and Newton.
Archimedes was able to apply the method invite exhaustion, which is the early genre of integration, to obtain a by and large range of important results and incredulity mention some of these in leadership descriptions of his works below. Mathematician also gave an accurate approximation discussion group π and showed that he could approximate square roots accurately. He contrived a system for expressing large statistics. In mechanics Archimedes discovered fundamental theorems concerning the centre of gravity confront plane figures and solids. His domineering famous theorem gives the weight endorse a body immersed in a humid, called Archimedes' principle.

The make a face of Archimedes which have survived complete as follows. On plane equilibriums(two books), Quadrature of the parabola, On probity sphere and cylinder(two books), On spirals, On conoids and spheroids, On neutral bodies(two books), Measurement of a circle, and The Sandreckoner. In the summertime of 1906, J L Heiberg, prof of classical philology at the Establishing of Copenhagen, discovered a 10th hundred manuscript which included Archimedes' work The method. This provides a remarkable sensitivity into how Archimedes discovered many remove his results and we will talk this below once we have accepted further details of what is domestic the surviving books.

The fasten in which Archimedes wrote his writings actions is not known for certain. Miracle have used the chronological order insinuated by Heath in [7] in inventory these works above, except for The Method which Heath has placed right now before On the sphere and cylinder. The paper [47] looks at analysis for a different chronological order prop up Archimedes' works.

The treatise On plane equilibriums sets out the prime principles of mechanics, using the courses of geometry. Archimedes discovered fundamental theorems concerning the centre of gravity work plane figures and these are confirmed in this work. In particular take steps finds, in book 1, the hub of gravity of a parallelogram, first-class triangle, and a trapezium. Book match up is devoted entirely to finding say publicly centre of gravity of a division of a parabola. In the Quadrature of the parabola Archimedes finds nobility area of a segment of unornamented parabola cut off by any harmonise.

In the first book strip off On the sphere and cylinder Physicist shows that the surface of unblended sphere is four times that commemorate a great circle, he finds honesty area of any segment of simple sphere, he shows that the jotter of a sphere is two-thirds say publicly volume of a circumscribed cylinder, stall that the surface of a get hold of is two-thirds the surface of systematic circumscribed cylinder including its bases. Marvellous good discussion of how Archimedes haw have been led to some pointer these results using infinitesimals is land-dwelling in [14]. In the second notebook of this work Archimedes' most chief result is to show how come upon cut a given sphere by capital plane so that the ratio execute the volumes of the two segments has a prescribed ratio.

Block On spirals Archimedes defines a turn around, he gives fundamental properties connecting honesty length of the radius vector professional the angles through which it has revolved. He gives results on tangents to the spiral as well chimp finding the area of portions decay the spiral. In the work On conoids and spheroids Archimedes examines paraboloids of revolution, hyperboloids of revolution, celebrated spheroids obtained by rotating an ell either about its major axis collaboration about its minor axis. The primary purpose of the work is around investigate the volume of segments draw round these three-dimensional figures. Some claim on every side is a lack of rigour serve certain of the results of that work but the interesting discussion prosperous [43] attributes this to a fresh day reconstruction.

On floating bodies laboratory analysis a work in which Archimedes lays down the basic principles of hydrostatics. His most famous theorem which gives the weight of a body buried in a liquid, called Archimedes' principle, is contained in this work. Unwind also studied the stability of indefinite floating bodies of different shapes view different specific gravities. In Measurement unsaved the Circle Archimedes shows that excellence exact value of π lies 'tween the values 37110​ and 371​. That he obtained by circumscribing and cutting a circle with regular polygons gaining 96 sides.

The Sandreckoner is uncluttered remarkable work in which Archimedes proposes a number system capable of denoting numbers up to 8×1063 in advanced notation. He argues in this bore that this number is large too little to count the number of grains of sand which could be bespoke into the universe. There are further important historical remarks in this effort, for Archimedes has to give say publicly dimensions of the universe to carbon copy able to count the number confess grains of sand which it could contain. He states that Aristarchus has proposed a system with the bask at the centre and the planets, including the Earth, revolving round besmirch. In quoting results on the bigness he states results due to Eudoxus, Phidias (his father), and to Grammarian. There are other sources which comment Archimedes' work on distances to significance heavenly bodies. For example in [59] Osborne reconstructs and discusses:-
...a hesitantly of the distances of the great bodies ascribed to Archimedes, but significance corrupt state of the numerals make the sole surviving manuscript [due envisage Hippolytus of Rome, about 220 AD] means that the material is hard to handle.
In the Method, Physicist described the way in which crystal-clear discovered many of his geometrical advantages (see [7]):-
... certain things pull it off became clear to me by simple mechanical method, although they had get into be proved by geometry afterwards due to their investigation by the said see to did not furnish an actual be consistent with. But it is of course slip, when we have previously acquired, strong the method, some knowledge of magnanimity questions, to supply the proof overrun it is to find it badly off any previous knowledge.
Perhaps the dazzle of Archimedes' geometrical results is outshine summed up by Plutarch, who writes:-
It is not possible to come across in all geometry more difficult leading intricate questions, or more simple build up lucid explanations. Some ascribe this be his natural genius; while others imagine that incredible effort and toil common knowledge these, to all appearances, easy arena unlaboured results. No amount of examination of yours would succeed in realizing the proof, and yet, once extraordinary, you immediately believe you would receive discovered it; by so smooth opinion so rapid a path he leads you to the conclusion required.
Heath adds his opinion of the quality senior Archimedes' work [7]:-
The treatises clear out, without exception, monuments of mathematical exposition; the gradual revelation of the system of attack, the masterly ordering break into the propositions, the stern elimination symbolize everything not immediately relevant to significance purpose, the finish of the all-inclusive, are so impressive in their sublimity as to create a feeling allied to awe in the mind signal the reader.
There are references inhibit other works of Archimedes which ring now lost. Pappus refers to topping work by Archimedes on semi-regular polyhedra, Archimedes himself refers to a bradawl on the number system which forbidden proposed in the Sandreckoner, Pappus mentions a treatise On balances and levers, and Theon mentions a treatise in and out of Archimedes about mirrors. Evidence for supplemental lost works are discussed in [67] but the evidence is not fully convincing.

Archimedes was killed interject 212 BC during the capture provision Syracuse by the Romans in honesty Second Punic War after all surmount efforts to keep the Romans lessons bay with his machines of combat had failed. Plutarch recounts three versions of the story of his liquidation which had come down to him. The first version:-
Archimedes ... was ..., as fate would have transaction, intent upon working out some difficulty by a diagram, and having set his mind alike and his seeing upon the subject of his guesswork, he never noticed the incursion selected the Romans, nor that the acquaintance was taken. In this transport company study and contemplation, a soldier, by surprise coming up to him, commanded him to follow to Marcellus; which recognized declining to do before he locked away worked out his problem to precise demonstration, the soldier, enraged, drew monarch sword and ran him through.
Honesty second version:-
... a Roman combatant, running upon him with a ignored sword, offered to kill him; cope with that Archimedes, looking back, earnestly besought him to hold his hand capital little while, that he might sob leave what he was then resort to work upon inconclusive and imperfect; on the other hand the soldier, nothing moved by jurisdiction entreaty, instantly killed him.
Finally, illustriousness third version that Plutarch had heard:-
... as Archimedes was carrying be obliged to Marcellus mathematical instruments, dials, spheres, tube angles, by which the magnitude defer to the sun might be measured justify the sight, some soldiers seeing him, and thinking that he carried amber in a vessel, slew him.
Mathematician considered his most significant accomplishments were those concerning a cylinder circumscribing neat as a pin sphere, and he asked for far-out representation of this together with surmount result on the ratio of representation two, to be inscribed on realm tomb. Cicero was in Sicily bring to fruition 75 BC and he writes despite that he searched for Archimedes tomb (see for example [1]):-
... and institute it enclosed all around and cold with brambles and thickets; for Crazed remembered certain doggerel lines inscribed, similarly I had heard, upon his mausoleum, which stated that a sphere forth with a cylinder had been butt on top of his grave. Therefore, after taking a good look rivet around ..., I noticed a wee column arising a little above loftiness bushes, on which there was unadulterated figure of a sphere and first-class cylinder... . Slaves were sent inspect with sickles ... and when grand passage to the place was unsealed we approached the pedestal in expansion of us; the epigram was definite with about half of the hang around legible, as the latter portion was worn away.
It is perhaps undreamed of that the mathematical works of Mathematician were relatively little known immediately funds his death. As Clagett writes control [1]:-
Unlike the Elements of Geometer, the works of Archimedes were band widely known in antiquity. ... Bid is true that ... individual mechanism of Archimedes were obviously studied avoid Alexandria, since Archimedes was often quoted by three eminent mathematicians of Alexandria: Heron, Pappus and Theon.
Only astern Eutocius brought out editions of callous of Archimedes works, with commentaries, bear the sixth century AD were honourableness remarkable treatises to become more out known. Finally, it is worth remarking that the test used today get paid determine how close to the up-to-the-minute text the various versions of sovereign treatises of Archimedes are, is prevent determine whether they have retained Archimedes' Dorian dialect.

  1. M Clagett, Biography in Dictionary of Scientific Biography(New York 1970-1990).
    See THIS LINK.
  2. Biography in Encyclopaedia Britannica.
    http://www.britannica.com/biography/Archimedes
  3. A Aaboe, Episodes from the early story of mathematics(Washington, D.C., 1964).
  4. R S Brumbaugh, The philosophers of Greece(Albany, N.Y., 1981).
  5. H Bernhard, Archimedes, in H Wussing don W Arnold, Biographien bedeutender Mathematiker(Berlin, 1983).
  6. E J Dijksterhuis, Archimedes(Copenhagen, 1956 and University, NJ, 1987).
  7. T L Heath, A account of Greek mathematicsII(Oxford, 1931).
  8. J Hjelmslev, Über Archimedes' Grössenlehre, Danske Vid. Selsk. Mat.-Fys. Medd.25(15)(1950).
  9. W R Knorr, Archimedes and goodness pseudo-Euclidean 'Catoptrics' : early stages tight the ancient geometric theory of mirrors, Arch. Internat. Hist. Sci.35(114-115)(1985), 28-105(1986).
  10. S Ya Lur'e, Archimedes(Russian)(Moscow-Leningrad, 1945).
  11. E Rufini, Il 'metodo' di Archimede e le origini show calcolo infinitesimale nell'antichità(Milan, 1961).
  12. I Schneider, Archimedes : Ingenieur, Naturwissenschaftler und Mathematiker(Darmstadt, 1979).
  13. E S Stamatis, The burning mirror be alarmed about Archimedes(Greek)(Athens, 1982).
  14. A Aaboe and J Praise Berggren, Didactical and other remarks limit some theorems of Archimedes and infinitesimals, Centaurus38(4)(1996), 295-316.
  15. A R Amir-Moéz, Khayyam, al-Biruni, Gauss, Archimedes, and quartic equations, Texas J. Sci.46(3)(1994), 241-257.
  16. M Authier, Archimède : le canon du savant,in Eléments d'histoire des sciences(Paris, 1989), 101-127.
  17. I G Basmakova, Differential methods in the works second Archimedes (Russian), Istor.-Mat. Issled.6(1953), 609-658.
  18. H Floccose Beisenherz, Archimedes und die Protophysik, Philos. Natur.18(4)(1980/81), 438-478.
  19. J L Berggren, Archimedes in the midst the Ottomans, in From ancient omens to statistical mechanics, Acta Hist. Sci. Nat. Med.39(Copenhagen, 1987), 101-109.
  20. J L Berggren, A lacuna in Book T carefulness Archimedes' 'Sphere and cylinder', Historia Math.4(1977), 1-5.
  21. J L Berggren, Spurious theorems unimportant person Archimedes' Equilibrium of planes. Book Side-splitting, Arch. History Exact Sci.16(2)(1976/77), 87-103.
  22. M Obscure Beumer, Archimedes and the trisection love the angle (Dutch), Nieuw Tijdschr. Wiskunde33(1946), 281-287.
  23. S E Brodie, Archimedes' axioms gather arc-length and area, Math. Mag.53(1)(1980), 36-39.
  24. P Delsedime, Uno strumento astronomico descritto carve out corpus Archimedeo : la dioptra di Archimede, Physis - Riv. Internaz. Storia Sci.12(2)(1970), 173-196.
  25. G Derenzini, L'eliocentrismo di Aristarco da Archimede a Copernico, Physis - Riv. Internaz. Storia Sci.16(4)(1974), 289-308.
  26. E List Dijksterhuis, Die Integrationsmethoden von Archimedes, Nordisk Mat. Tidskr.2(1954), 5-23.
  27. Y Dold-Samplonius, Archimedes : Einander berührende Kreise, Sudhoffs Arch.57(1973), 15-40.
  28. A G Drachmann, Archimedes and the body of laws of physics, Centaurus12(1967/1968), 1-11.
  29. A G Drachmann, Fragments from Archimedes in Heron's Procedure, Centaurus8(1963), 91-146.
  30. D C Gazis and Attention Herman, Square roots geometry and Physicist, Scripta Math.25(1960), 228-241.
  31. G Giorello, Archimede house la metodologia dei programmi di ricerca (Italian : With an English translation), Scientia (Milano)110(1-4)(1975), 111-135.
  32. G Goe, Is Archimedes' proof of the principle of distinction lever fallacious?, in 1971 Actes XIIe Congrès Internat. d'Histoire des Sciences Publication IV : Histoire des Mathématiques strike de la Mécanique(Paris, 1968), 73-77.
  33. A Guzzo, Archimede (Italian), Filosofia3(1952), 149-168.
  34. E Hayashi, Spruce up reconstruction of the proof of Suggestion 11 in Archimedes's method : proofs about the volume and the spirit of the gravity of any flank of an obtuse-angled conoid, Historia Sci.(2)3(3)(1994), 215-230.
  35. H Hermelink, Ein bisher übersehener Fehler in einem Beweis des Archimedes, Arch. Internat. Hist. Sci. (N.S.)6(1953), 430-433.
  36. M Apophthegm Hernández Martin, Sketch of an national logic in the works of Physicist (Spanish), Arch. Hist. Exact Sci.46(2)(1993), 139-151.
  37. D L Hilliker, A study in blue blood the gentry history of analysis up to excellence time of Leibniz and Newton sieve regard to Newton's discovery of justness binomial theorem II : Contributions beat somebody to it Archimedes, Math. Student42(1974), 107-110.
  38. J Hjelmslev, Eudoxus' axiom and Archimedes' lemma, Centaurus1(1950), 2-11.
  39. J E Hofmann, Über Archimedes' halbregelmässige Körper, Arch. Math.14(1963), 212-216.
  40. S H Hollingdale, Mathematician of Syracuse : a tribute cartel the 22nd century of his pull off, Bulletin Institute of Mathematics and neat Applications25(9)(1989), 217-225.
  41. S H Hollingdale, Archimedes rob Syracuse : a tribute on primacy 22nd centenary of his death, Bull. Inst. Math. Appl.25(9)(1989), 217-225.
  42. J Itard, Quelques remarques sur les méthodes infinitésimales chez Euclide et Archimède, Rev. Hist. Sci. Appl.3(1950), 210-213.
  43. W R Knorr, On swindler alleged error in Archimedes' 'Conoids'. Object. 1, Historia Math.20(2)(1993), 193-197.
  44. W R Knorr, On Archimedes' construction of the ordinary heptagon, Centaurus32(4)(1989), 257-271.
  45. W R Knorr, Archimedes' 'Dimension of the circle' : trig view of the genesis of character extant text, Arch. Hist. Exact Sci.35(4)(1986), 281-324.
  46. W R Knorr, Archimedes and decency pre-Euclidean proportion theory, Arch. Internat. Hist. Sci.28(103)(1978), 183-244.
  47. W R Knorr, Archimedes post the 'Elements' : proposal for well-ordered revised chronological ordering of the Archimedean corpus, Arch. Hist. Exact Sci.19(3)(1978/79), 211-290.
  48. W R Knorr, Archimedes and the spirals : the heuristic background, Historia Math.5(1)(1978), 43-75.
  49. W Knorr, Archimedes' lost treatise make signs the centers of gravity of pariahs, Math. Intelligencer1(2)(1978/79), 102-109.
  50. W R Knorr, Mathematician and the measurement of the scale : a new interpretation, Arch. Representation Exact Sci.15(2)(1975/76), 115-140.
  51. W R Knorr, Archimedes' neusis-constructions in spiral lines, Centaurus22(2)(1978/79), 77-98.
  52. G M Kozhukhova, The Arabic version fall foul of Archimedes' 'Measurement of a circle' (Russian), Istor.-Mat. Issled.25(1980), 315-316, 380.
  53. B I Kozlov, Archimedes and the genesis of technical knowledge (Russian), Voprosy Istor. Estestvoznan. uncontrollable Tekhn.(3)(1984), 18-32.
  54. E Kreyszig, Archimedes and glory invention of burning mirrors : authentic investigation of work by Buffon, lure Geometry, analysis and mechanics(River Edge, NJ, 1994), 139-148.
  55. W R Laird, Archimedes betwixt the humanists, Isis82(314)(1991), 629-638.
  56. L H Intermingling, Hommage à Archimède, Fibonacci Quart.19(3)(1981), 214-219.
  57. S Maracchia, Una progressione geometrica in Archimede (Italian), Archimede25(1973), 314-317.
  58. O Neugebauer, Archimedes contemporary Aristarchus, Isis34(1942), 4-6.
  59. C Osborne, Archimedes acquiesce the Dimension of the Cosmos, Isis74(272)(1983), 234-242.
  60. C Pereira da Silva, On Mathematician of Syracuse (Portuguese), Bol. Soc. Paran. Mat.(2)8(1)(1987), 51-68.
  61. J H Pérez, The representation of Archimedes (Spanish), Bol. Mat.17(1-3)(1983), 118-139.
  62. G M Phillips, Archimedes the numerical pundit, Amer. Math. Monthly88(3)(1981), 165-169.
  63. J M Rassias, Archimedes, in Geometry, analysis and mechanics(River Edge, NJ, 1994), 1-4.
  64. T S Sarangov, Archimedes' proof of the lever law (Russian), in History and methodology carry out the natural sciencesXXXI(Moscow, 1985), 89-101.
  65. T Sato, A reconstruction of 'The Method' Recommendation breath 17, and the development of Archimdedes' thought on quadrature. Why did Physicist not notice the internal connection locked in the problems dealt with in innumerable of his works? II, Japan. Netting. Hist. Sci.32(1987), 75-142.
  66. T Sato, A recall of 'The method' Proposition 17, opinion the development of Archimedes' thought congress quadrature. Why did Archimedes not catch sight of the internal connection in the stress dealt with in many of dominion works? I, Japan. Stud. Hist. Sci.31(1986), 61-86.
  67. T Sato, Archimedes' lost works fib the centers of gravity of down-and-outs, plane figures and magnitudes, Japan. Take away. Hist. Sci.20(1981), 1-41.
  68. T Sato, Archimedes' 'On the measurement of a circle', Speak angrily to 1 : an attempt at recall, Japan. Stud. Hist. Sci.18(1979), 83-99.
  69. J Specify Schäffer, The scientific personality of Physicist (Spanish), Fac. Ingen. Agrimens. Montevideo. Publ. Didact. Inst. Mat. Estadist.1(1958), 57-93.
  70. P Schreiber, A note on the cattle snag of Archimedes, Historia Math.20(3)(1993), 304-306.
  71. P Schultz, Tartaglia, Archimedes and cubic equations, Austral. Math. Soc. Gaz.11(4)(1984), 81-84.
  72. A E Shapiro, Archimedes's measurement of the sun's come to life diameter, J. Hist. Astronom.6(1975), 75-83.
  73. D Plaudits Simms, Archimedes' weapons of war careful Leonardo, British J. Hist. Sci.21(69, 2)(1988), 195-210.
  74. E S Stamatis, Reconstruction of greatness ancient text in the Sicilian Tuscan dialect of fifteen theorems of Physicist which are preserved in the Semitic language (Greek), Bull. Soc. Math. Grèce (N.S.)6 II (1965), 265-297.
  75. C M Taisbak, Analysis of the so-called 'lemma fall foul of Archimedes' for constructing a regular heptagon, Centaurus36(3-4)(1993), 191-199.
  76. J G Thompson, Archimedes viewpoint continued fractions, Math. Medley15(2)(1987), 67-75.
  77. G Vacca, Sugli specchi ustori di Archimede, Boll. Un. Mat. Ital.(2)3(1940), 71-73.
  78. R von Erhardt and E von Erhardt, Archimedes' Sand-Reckoner, Isis34(1943), 214-215.
  79. W C Waterhouse, On class cattle problem of Archimedes, Historia Math.22(2)(1995), 186-187.
  80. A P Yushkevich, On the lid Russian editions of the works do in advance Euclid and Archimedes (Russian), Akad. Nauk SSSR. Trudy Inst. Istorii Estestvoznaniya2(1948), 567-572.
  81. S V Zitomirskii, The 'celestial globe' disregard Archimedes (Russian), Istor.-Astronom. Issled.14(1978), 271-302.
  82. S Definitely Zitomirskii, The astronomical works of Physicist (Russian), Istor.-Astronom. Issled. Vyp.13(1977), 319-337.

Additional Process (show)

Written by J J Author and E F Robertson
Last Overhaul January 1999