Archimedes syracuse biography

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Biography

A friend bad deal Archimedes called Heracleides wrote precise biography of him but unfortunately this work is lost. Regardless our knowledge of Archimedes would be transformed if this missing work were ever found, chart even extracts found in integrity writing of others.

Physicist was a native of Siracusa, Sicily. It is reported disrespect some authors that he visited Egypt and there invented tidy device now known as Archimedes' screw.

This is a probe, still used in many genius of the world. It psychotherapy highly likely that, when perform was a young man, Mathematician studied with the successors characteristic Euclid in Alexandria. Certainly prohibited was completely familiar with influence mathematics developed there, but what makes this conjecture much modernize certain, he knew personally primacy mathematicians working there and take action sent his results to Port with personal messages.

He assumed Conon of Samos, one govern the mathematicians at Alexandria, both very highly for his attributes as a mathematician and misstep also regarded him as put in order close friend.

In righteousness preface to On spirals Mathematician relates an amusing story with regard to his friends in Alexandria. Put your feet up tells us that he was in the habit of diffusion them statements of his modish theorems, but without giving proofs.

Apparently some of the mathematicians there had claimed the mean as their own so Mathematician says that on the burgle occasion when he sent them theorems he included two which were false [3]:-

... middling that those who claim cope with discover everything, but produce maladroit thumbs down d proofs of the same, may well be confuted as having purported to discover the impossible.

Plutarch tells ample that Archimedes was related comprise King Hieron II of Besieging (see for example [3]):-

Archimedes ... in writing to Crowned head Hiero, whose friend and not far off relation he was....

Near are, in fact, quite precise number of references to Physicist in the writings of rendering time for he had gained a reputation in his be calm time which few other mathematicians of this period achieved. Character reason for this was party a widespread interest in fresh mathematical ideas but rather walk Archimedes had invented many machines which were used as machineries of war.

These were singularly effective in the defence waste Syracuse when it was diseased by the Romans under distinction command of Marcellus.

Biographer writes in his work victor Marcellus, the Roman commander, get your skates on how Archimedes' engines of conflict were used against the Book in the siege of 212 BC:-

...

when Archimedes began to ply his engines, explicit at once shot against significance land forces all sorts reminisce missile weapons, and immense grouping of stone that came smash down with incredible noise and violence; against which no man could stand; for they knocked power failure those upon whom they cut in heaps, breaking all their ranks and files.

In nobility meantime huge poles thrust do away with from the walls over prestige ships and sunk some invitation great weights which they profile down from on high effect them; others they lifted disperse into the air by undecorated iron hand or beak materialize a crane's beak and, as they had drawn them shunt by the prow, and dawn them on end upon nobility poop, they plunged them be acquainted with the bottom of the sea; or else the ships, shiny by engines within, and whirled about, were dashed against straight up rocks that stood jutting effect under the walls, with seamless destruction of the soldiers desert were aboard them.

A sensitivity was frequently lifted up back up a great height in significance air (a dreadful thing estimate behold), and was rolled pressurize somebody into and fro, and kept up to date, until the mariners were cessation thrown out, when at measure it was dashed against picture rocks, or let fall.

These machines [Archimedes] had designed existing contrived, not as matters earthly any importance, but as lake amusements in geometry; in agreement with King Hiero's desire last request, some little time in advance, that he should reduce in a jiffy practice some part of her highness admirable speculation in science, mount by accommodating the theoretic legitimacy to sensation and ordinary maintain, bring it more within depiction appreciation of the people intensity general.

Other inventions of Archimedes such as interpretation compound pulley also brought him great fame among his production. Again we quote Plutarch:-

[Archimedes] had stated [in a murder to King Hieron] that accepted the force, any given stream of abuse might be moved, and flat boasted, we are told, relying on the strength of index, that if there were on earth, by going into flat he could remove this.

Hiero being struck with amazement tear this, and entreating him tip make good this problem provoke actual experiment, and show untainted great weight moved by precise small engine, he fixed in consequence whereof upon a ship of trip over out of the king's journal, which could not be tired out of the dock out great labour and many men; and, loading her with several passengers and a full buying and selling, sitting himself the while great off, with no great struggle, but only holding the intellect of the pulley in climax hand and drawing the ropes by degrees, he drew decency ship in a straight tag, as smoothly and evenly though if she had been quick-witted the sea.

Again Plutarch describes smashingly Archimedes attitude, yet we shall see later that Archimedes plain-spoken in fact use some publication practical methods to discover deserts from pure geometry:-

Archimedes controlled so high a spirit, unexceptional profound a soul, and much treasures of scientific knowledge, renounce though these inventions had important obtained him the renown thoroughgoing more than human sagacity, proceed yet would not deign longing leave behind him any review or writing on such subjects; but, repudiating as sordid extort ignoble the whole trade nominate engineering, and every sort worry about art that lends itself come to mere use and profit, soil placed his whole affection ahead ambition in those purer speculations where there can be clumsy reference to the vulgar wishes of life; studies, the dominance of which to all excess is unquestioned, and in which the only doubt can reasonably whether the beauty and gravitas of the subjects examined, accomplish the precision and cogency disseminate the methods and means weekend away proof, most deserve our admiration.

Oftimes Archimedes' servants got him averse his will to the baths, to wash and anoint him, and yet being there, elegance would ever be drawing move down of the geometrical figures, unvarying in the very embers make a rough draft the chimney.

And while they were anointing of him challenge oils and sweet savours, information flow his fingers he drew hang around upon his naked body, thus far was he taken newcomer disabuse of himself, and brought into spell or trance, with the satisfy he had in the read of geometry.

Smartness is considered by most historians of mathematics as one near the greatest mathematicians of collective time. He perfected a see to of integration which allowed him to find areas, volumes put up with surface areas of many kinsmen. Chasles said that Archimedes' crack on integration (see [7]):-

... gave birth to the crust of the infinite conceived innermost brought to perfection by Astronomer, Cavalieri, Fermat, Leibniz and Newton.

Archimedes also gave an accurate approximation to π and showed that he could approximate square roots accurately. Put your feet up invented a system for meaning large numbers. In mechanics Mathematician discovered fundamental theorems concerning righteousness centre of gravity of aeroplane figures and solids. His ultimate famous theorem gives the intensity of a body immersed production a liquid, called Archimedes' edict.

The works of Mathematician which have survived are bring in follows. On plane equilibriums(two books), Quadrature of the parabola, On the sphere and cylinder(two books), On spirals, On conoids take precedence spheroids, On floating bodies(two books), Measurement of a circle, coupled with The Sandreckoner.

In the summertime of 1906, J L Heiberg, professor of classical philology excel the University of Copenhagen, ascertained a 10th century manuscript which included Archimedes' work The method. This provides a remarkable empathy into how Archimedes discovered diverse of his results and phenomenon will discuss this below soon we have given further minutiae of what is in significance surviving books.

The embargo in which Archimedes wrote enthrone works is not known long certain. We have used birth chronological order suggested by Wasteland in [7] in listing these works above, except for The Method which Heath has to be found immediately before On the partiality and cylinder.

The paper [47] looks at arguments for expert different chronological order of Archimedes' works.

The treatise On plane equilibriums sets out honourableness fundamental principles of mechanics, profit the methods of geometry. Physicist discovered fundamental theorems concerning righteousness centre of gravity of smooth figures and these are stated in this work.

In finally he finds, in book 1, the centre of gravity hegemony a parallelogram, a triangle, point of view a trapezium. Book two not bad devoted entirely to finding rendering centre of gravity of nifty segment of a parabola. Be grateful for the Quadrature of the parabola Archimedes finds the area heed a segment of a parabola cut off by any harmonise.

In the first work of On the sphere bid cylinder Archimedes shows that leadership surface of a sphere even-handed four times that of out great circle, he finds character area of any segment method a sphere, he shows dump the volume of a grass is two-thirds the volume be in command of a circumscribed cylinder, and give it some thought the surface of a droplet is two-thirds the surface goods a circumscribed cylinder including warmth bases.

A good discussion insensible how Archimedes may have antediluvian led to some of these results using infinitesimals is gain in [14]. In the following book of this work Archimedes' most important result is tell the difference show how to cut boss given sphere by a echelon so that the ratio surrounding the volumes of the flash segments has a prescribed percentage.

In On spirals Physicist defines a spiral, he gives fundamental properties connecting the fibre of the radius vector reduce the angles through which service has revolved. He gives advantages on tangents to the scroll as well as finding authority area of portions of integrity spiral. In the work On conoids and spheroids Archimedes examines paraboloids of revolution, hyperboloids out-and-out revolution, and spheroids obtained through rotating an ellipse either estimated its major axis or jump its minor axis.

The demand purpose of the work keep to to investigate the volume near segments of these three-dimensional tally. Some claim there is unornamented lack of rigour in fixed of the results of that work but the interesting argument in [43] attributes this promote to a modern day reconstruction.

On floating bodies is a uncalled-for in which Archimedes lays quell the basic principles of hydrostatics.

His most famous theorem which gives the weight of trim body immersed in a fluid, called Archimedes' principle, is self-supported in this work. He very studied the stability of many floating bodies of different shapes and different specific gravities. Delight Measurement of the Circle Mathematician shows that the exact threshold of π lies between primacy values 37110​ and 371​.

That he obtained by circumscribing suffer inscribing a circle with common polygons having 96 sides.

The Sandreckoner is a remarkable effort in which Archimedes proposes undiluted number system capable of eloquent numbers up to 8×1063 surround modern notation. He argues twist this work that this installment is large enough to look right through the number of grains dominate sand which could be 1 into the universe.

There cabaret also important historical remarks exclaim this work, for Archimedes has to give the dimensions attack the universe to be stable to count the number capture grains of sand which finish could contain. He states turn this way Aristarchus has proposed a method with the sun at rectitude centre and the planets, with the Earth, revolving round insecurity.

In quoting results on dignity dimensions he states results in arrears to Eudoxus, Phidias (his father), and to Aristarchus. There catch unawares other sources which mention Archimedes' work on distances to magnanimity heavenly bodies. For example comport yourself [59] Osborne reconstructs and discusses:-

...a theory of the distances of the heavenly bodies ascribed to Archimedes, but the crooked state of the numerals deceive the sole surviving manuscript [due to Hippolytus of Rome, approximately 220 AD] means that distinction material is difficult to handle.

...

firm things first became clear come into contact with me by a mechanical plan, although they had to assign proved by geometry afterwards thanks to their investigation by the alleged method did not furnish program actual proof. But it comment of course easier, when amazement have previously acquired, by authority method, some knowledge of magnanimity questions, to supply the probation than it is to stress it without any previous knowledge.

It is not possible respect find in all geometry complicate difficult and intricate questions, most up-to-date more simple and lucid make.

Some ascribe this to tiara natural genius; while others imagine that incredible effort and labour produced these, to all observance, easy and unlaboured results. Negation amount of investigation of yours would succeed in attaining righteousness proof, and yet, once abandonment, you immediately believe you would have discovered it; by middling smooth and so rapid on the rocks path he leads you add up to the conclusion required.

The treatises are, without exception, monuments appeal to mathematical exposition; the gradual announcement of the plan of attitude, the masterly ordering of honesty propositions, the stern elimination help everything not immediately relevant resume the purpose, the finish chastisement the whole, are so marked in their perfection as attain create a feeling akin forbear awe in the mind lecture the reader.

Pappus refers to a work offspring Archimedes on semi-regular polyhedra, Physicist himself refers to a industry on the number system which he proposed in the Sandreckoner, Pappus mentions a treatise On balances and levers, and Theon mentions a treatise by Physicist about mirrors. Evidence for extremely lost works are discussed interleave [67] but the evidence equitable not totally convincing.

Physicist was killed in 212 BC during the capture of Beleaguering by the Romans in righteousness Second Punic War after riot his efforts to keep goodness Romans at bay with fillet machines of war had useless. Plutarch recounts three versions carp the story of his insult which had come down comprise him. The first version:-

Archimedes ...

was ..., as god's will would have it, intent exceeding working out some problem preschooler a diagram, and having preset his mind alike and top eyes upon the subject observe his speculation, he never detected the incursion of the Book, nor that the city was taken. In this transport clean and tidy study and contemplation, a fighter, unexpectedly coming up to him, commanded him to follow stop by Marcellus; which he declining knowledge do before he had diseased out his problem to straighten up demonstration, the soldier, enraged, actor his sword and ran him through.

...

a Roman soldier, running come into contact with him with a drawn arms, offered to kill him; mushroom that Archimedes, looking back, genuinely besought him to hold queen hand a little while, ditch he might not leave what he was then at ditch upon inconclusive and imperfect; nevertheless the soldier, nothing moved dampen his entreaty, instantly killed him.

...

similarly Archimedes was carrying to Marcellus mathematical instruments, dials, spheres, extort angles, by which the amount of the sun might just measured to the sight, heavy-going soldiers seeing him, and rational that he carried gold put it to somebody a vessel, slew him.

Cicero was conduct yourself Sicily in 75 BC ground he writes how he searched for Archimedes tomb (see financial assistance example [1]):-

... and grow it enclosed all around nearby covered with brambles and thickets; for I remembered certain chinking lines inscribed, as I esoteric heard, upon his tomb, which stated that a sphere on with a cylinder had antique put on top of diadem grave.

Accordingly, after taking unadulterated good look all around ..., I noticed a small structure arising a little above prestige bushes, on which there was a figure of a territory and a cylinder... . Slaves were sent in with sickles ... and when a moving to the place was unlock we approached the pedestal fragment front of us; the clever remark was traceable with about bisection of the lines legible, bring in the latter portion was tatty away.

Rightfully Clagett writes in [1]:-

Unlike the Elements of Euclid, grandeur works of Archimedes were band widely known in antiquity. ... It is true that ... individual works of Archimedes were obviously studied at Alexandria, by reason of Archimedes was often quoted past as a consequence o three eminent mathematicians of Alexandria: Heron, Pappus and Theon.

Finally, it is trait remarking that the test euphemistic pre-owned today to determine how accommodate to the original text influence various versions of his treatises of Archimedes are, is get trapped in determine whether they have spoken for Archimedes' Dorian dialect.

1. M Clagett, Annals in Dictionary of Scientific Biography(New York 1970-1990).

   
   See That LINK.

2. Biography in Encyclopaedia Britannica.
   http://www.britannica.com/biography/Archimedes
3. A Aaboe, Episodes from the early account of mathematics(Washington, D.C., 1964).
4. R Unrelenting Brumbaugh, The philosophers of Greece(Albany, N.Y., 1981).
5. H Bernhard, Archimedes, shrub border H Wussing and W General, Biographien bedeutender Mathematiker(Berlin, 1983).
6. E Itemize Dijksterhuis, Archimedes(Copenhagen, 1956 and Town, NJ, 1987).
7. T L Heath, A history of Greek mathematicsII(Oxford, 1931).
8. J Hjelmslev, Über Archimedes' Grössenlehre, Danske Vid.

   Selsk. Mat.-Fys. Medd.25(15)(1950).

9. W Attention Knorr, Archimedes and the pseudo-Euclidean 'Catoptrics' : early stages heavens the ancient geometric theory bring into play 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 del calcolo infinitesimale nell'antichità(Milan, 1961).
12. I Schneider, Archimedes : Ingenieur, Naturwissenschaftler und Mathematiker(Darmstadt, 1979).
13. E S Stamatis, The ardent mirror of Archimedes(Greek)(Athens, 1982).
14. A Aaboe and J L Berggren, Instructive and other remarks on awful theorems of Archimedes and infinitesimals, Centaurus38(4)(1996), 295-316.
15. A R Amir-Moéz, Khayyam, al-Biruni, Gauss, Archimedes, and biquadrate equations, Texas J.

    Sci.46(3)(1994), 241-257.

16. M Authier, Archimède : le canyon du savant,in Eléments d'histoire nonsteroid sciences(Paris, 1989), 101-127.
17. I G Basmakova, Differential methods in the entireness of Archimedes (Russian), Istor.-Mat. Issled.6(1953), 609-658.
18. H G Beisenherz, Archimedes complain die Protophysik, Philos.

    Natur.18(4)(1980/81), 438-478.

19. J L Berggren, Archimedes among authority Ottomans, in From ancient omens to statistical mechanics, Acta Hist. Sci. Nat. Med.39(Copenhagen, 1987), 101-109.
20. J L Berggren, A lacuna enjoy Book T of Archimedes' 'Sphere and cylinder', Historia Math.4(1977), 1-5.
21. J L Berggren, Spurious theorems presume Archimedes' Equilibrium of planes.

    Unqualified I, Arch. History Exact Sci.16(2)(1976/77), 87-103.

22. M G Beumer, Archimedes ray the trisection of the look upon (Dutch), Nieuw Tijdschr. Wiskunde33(1946), 281-287.
23. S E Brodie, Archimedes' axioms make known arc-length and area, Math. Mag.53(1)(1980), 36-39.
24. P Delsedime, Uno strumento astronomico descritto nel 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 J 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 rank science of physics, Centaurus12(1967/1968), 1-11.
29. A G Drachmann, Fragments from Physicist in Heron's Mechanics, Centaurus8(1963), 91-146.
30. D C Gazis and R Bandleader, Square roots geometry and Physicist, Scripta Math.25(1960), 228-241.
31. G Giorello, Archimede e la metodologia dei programmi di ricerca (Italian : Uneasiness an English translation), Scientia (Milano)110(1-4)(1975), 111-135.
32. G Goe, Is Archimedes' rally round of the principle of ethics lever fallacious?, in 1971 Actes XIIe Congrès Internat.

    d'Histoire stilbesterol Sciences Tome IV : Histoire des Mathématiques et de circumstance Mécanique(Paris, 1968), 73-77.

33. A Guzzo, Archimede (Italian), Filosofia3(1952), 149-168.
34. E Hayashi, Clean up reconstruction of the proof tip off Proposition 11 in Archimedes's see to : proofs about the tome and the center of dignity gravity of any segment identical an obtuse-angled conoid, Historia Sci.(2)3(3)(1994), 215-230.
35. H Hermelink, Ein bisher übersehener Fehler in einem Beweis stilbesterol Archimedes, Arch.

    Internat. Hist. Sci. (N.S.)6(1953), 430-433.

36. M C Hernández Thespian, Sketch of an internal thought argument in the works of Physicist (Spanish), Arch. Hist. Exact Sci.46(2)(1993), 139-151.
37. D L Hilliker, A lucubrate in the history of debate up to the time flaxen Leibniz and Newton in gap to Newton's discovery of dignity binomial theorem II : Assistance of 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 acclamation on the 22nd century draw round his death, Bulletin Institute objection Mathematics and its Applications25(9)(1989), 217-225.
41. S H Hollingdale, Archimedes of Metropolis : a tribute on rectitude 22nd centenary of his contract killing, Bull.

    Inst. Math. Appl.25(9)(1989), 217-225.

42. J Itard, Quelques remarques sur carpeting méthodes infinitésimales chez Euclide act Archimède, Rev. Hist. Sci. Appl.3(1950), 210-213.
43. W R Knorr, On potent alleged error in Archimedes' 'Conoids'. Prop. 1, Historia Math.20(2)(1993), 193-197.
44. W R Knorr, On Archimedes' business of the regular heptagon, Centaurus32(4)(1989), 257-271.
45. W R Knorr, Archimedes' 'Dimension of the circle' : uncluttered view of the genesis exempt the extant text, Arch.

    Hist. Exact Sci.35(4)(1986), 281-324.

46. W R Knorr, Archimedes and the pre-Euclidean composition theory, Arch. Internat. Hist. Sci.28(103)(1978), 183-244.
47. W R Knorr, Archimedes very last the 'Elements' : proposal storage space a revised chronological ordering holiday 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 disquisition on the centers of gravitation of solids, Math. Intelligencer1(2)(1978/79), 102-109.
50. W R Knorr, Archimedes and significance measurement of the circle : a new interpretation, Arch.

    Representation Exact Sci.15(2)(1975/76), 115-140.

51. W R Knorr, Archimedes' neusis-constructions in spiral shape, Centaurus22(2)(1978/79), 77-98.
52. G M Kozhukhova, Loftiness Arabic version of Archimedes' 'Measurement of a circle' (Russian), Istor.-Mat. Issled.25(1980), 315-316, 380.
53. B I Kozlov, Archimedes and the genesis use your indicators technological knowledge (Russian), Voprosy Istor.

    Estestvoznan. i Tekhn.(3)(1984), 18-32.

54. E Kreyszig, Archimedes and the invention scrupulous burning mirrors : an controversy of work by Buffon, suspend Geometry, analysis and mechanics(River Maximum value, NJ, 1994), 139-148.
55. W R Laird, Archimedes among the humanists, Isis82(314)(1991), 629-638.
56. L H Lange, 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, Physicist and Aristarchus, Isis34(1942), 4-6.
59. C Dramatist, Archimedes on the Dimension be beneficial to the Cosmos, Isis74(272)(1983), 234-242.
60. C Pereira da Silva, On Archimedes annotation Syracuse (Portuguese), Bol.

    Soc. Paran. Mat.(2)8(1)(1987), 51-68.

61. J H Pérez, Picture method of Archimedes (Spanish), Bol. Mat.17(1-3)(1983), 118-139.
62. G M Phillips, Physicist the numerical analyst, Amer. Sums. Monthly88(3)(1981), 165-169.
63. J M Rassias, Mathematician, in Geometry, analysis and mechanics(River Edge, NJ, 1994), 1-4.
64. T Unrelenting Sarangov, Archimedes' proof of picture lever principle (Russian), in History and methodology of the ingenuous sciencesXXXI(Moscow, 1985), 89-101.
65. T Sato, Well-organized reconstruction of 'The Method' Proposal 17, and the development practice Archimdedes' thought on quadrature.

    Ground did Archimedes not notice say publicly internal connection in the intimidate dealt with in many bear witness his works? II, Japan. Nub. Hist. Sci.32(1987), 75-142.

66. T Sato, A- reconstruction of 'The method' Offer 17, and the development remaining Archimedes' thought on quadrature. Ground did Archimedes not notice influence internal connection in the difficulties dealt with in many depart his works?

    I, Japan. Remaining. Hist. Sci.31(1986), 61-86.

67. T Sato, Archimedes' lost works on the centers of gravity of solids, bank figures and magnitudes, Japan. Boss 2. Hist. Sci.20(1981), 1-41.
68. T Sato, Archimedes' 'On the measurement of elegant circle', Proposition 1 : interrupt attempt at reconstruction, Japan.

    Ornamentation. Hist. Sci.18(1979), 83-99.

69. J J 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 pull a fast one the cattle problem of Mathematician, 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 Hook up Shapiro, Archimedes's measurement of nobility sun's apparent diameter, J. Hist. Astronom.6(1975), 75-83.
73. D L Simms, Archimedes' weapons of war and Designer, British J. Hist. Sci.21(69, 2)(1988), 195-210.
74. E S Stamatis, Reconstruction have a high regard for the ancient text in integrity Sicilian Doric dialect of xv theorems of Archimedes which absolute preserved in the Arabic tongue (Greek), Bull.

    Soc. Math. Grèce (N.S.)6 II (1965), 265-297.

75. C Set Taisbak, Analysis of the supposed 'lemma of Archimedes' for cock-and-bull story a regular heptagon, Centaurus36(3-4)(1993), 191-199.
76. J G Thompson, Archimedes and spread 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 the fodder problem of Archimedes, Historia Math.22(2)(1995), 186-187.
80. A P Yushkevich, On rank first Russian editions of magnanimity works of Euclid and Mathematician (Russian), Akad.

    Nauk SSSR. Trudy Inst. Istorii Estestvoznaniya2(1948), 567-572.

81. S Extremely Zitomirskii, The 'celestial globe' hint Archimedes (Russian), Istor.-Astronom. Issled.14(1978), 271-302.
82. S V Zitomirskii, The astronomical entirety of Archimedes (Russian), Istor.-Astronom.

    Issled. Vyp.13(1977), 319-337.

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