Archimedes in the Middle Ages. III. The Fate of the Medieval Archimedes. Part iv


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The former includes, for the following: in this order, Measurement of the Circle, Sand-reckoner, Quadrature of Parabola Props. Most of the mature treatises are ordered by Earth to the zodiac; internal references; the first and the last work in the series, 2. The numerals in the text are fairly corrupted and do not match, and the issue is complicated by the fact that Other scholarly contribution to problems of authen- the ordering of the series of cosmic bodies in 1 and 4 ticity and transmission of the Archimedean corpus do not agree; Hippolytus surely drew from earlier epito- include: mes.

In fact, after suitable emendations, the two sequences 1. The actual values of n suggest that and epitomes, and on the transmission of the Archimedes took up a pre-existing model, presumably of resulting corpus of writings through antiquity and late Pythagorean origin, of cosmic distances arranged the Middle Ages; according to a musical scale, and adapted it to his own purposes, about which only conjectures can be made. Refined criteria Archimedean sources of the whole extant tradition suited to establish a chronological ordering of the on the balance; Archimedean works have been proposed by Wilbur R.

The criteria are: the evidence about an Archimedean Catoptrics. The form of exhaustion procedure employed: The The Archimedean Palimpsest. This is the main criterion. The proportion theory employed: A pre-Euclidean dramatic decay of the material conditions of the manu- proportion theory is at work in early works, whereas script.

The very good photographic plates taken at the in Spiral lines the theory of Elements V is applied. It appears that the transcription of the first editor 4. Resorting to mechanical methods as an heuristic was fairly accurate: It is in principle to be expected that background: This is typical of later works.


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Netx, Acerbi, and Wil- text was necessary. A new edition of the Arabic fragment son, , p. The Arabic fragment simply gives the values of the areas In Method 14, a passage unread by Heiberg, within a of the fourteen parts as fractions of the area of the whole column of text that requires extensive restoration, reveals square. Such areas turn out to be unit fractions of the that Archimedes handles infinite multitudes of mathemat- whole; the only exception, the area of HEFLT, is written ical entities by setting them in one-to-one correspon- as a sum of unit fractions.

The Greek fragment amounts dence. One should not attach too much importance to to a short, initial introduction and to a partial con- this move as if it was an anticipation of modern set-theo- struction of the diagram the one implied by the Greek retic treatment of infinities.

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The move adds nothing to the text actually makes AZEB a square. The aim, Pappus, Collectio IV. A Archimedes asserts that new edition of the Arabic treatise makes it possible to there is not a small multitude of figures made of write in a correct form some passages in the construction them, because of it being possible to take them of the regular heptagon ascribed to Archimedes. K It may be added that the neusis involved in the con- Q struction of the heptagon can be solved in a straightfor- ward way by a simple adaptation of the solution of the neusis reported in Pappus, Collectio IV.

The proof, if framed in analogy with Pappus, that the con- struction really solves the neusis is considerably simpler Figure 1. D Simplified variants of the same theorem as in Almagest I. It is likely that both the theorem in the Almagest and lemma 15 were different cases of a more comprehen- The short Arabic treatise On mutually tangent circles, sive Archimedean proposition; however, it is not said that ascribed to Archimedes in the title, is a collection of fif- he devised such a proposition for trigonometric purposes.

The approximation mutually tangent circles. Archimedes, what is read is most likely an epitome, possi- 3, appears to have received a fairly satisfactory explanation bly containing some accretions. As sion Two propositions of some interest can be singled out these values can be obtained by a procedure of successive from On mutually tangent circles. The first is lemma 12 reciprocal subtractions, traces of which can be found in see Fig.

Two the Greek mathematical corpus, it is likely that the tangents AB and AG are drawn to the same circle, and the approximations at issue were obtained in that way. From point D on that line another tangent is drawn, touching the circle at Z and intersecting the other two tangents at E and H.

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D The easy proof draws the parallel ET to AB and argues by similar triangles and from the equality of tangents to a cir- cle drawn from the same point. H G One interesting feature is that the lemma holds also when the two initial tangents are parallel: In this case the text displays two letters A denoting different points. The E fact that Apollonius proposed similar theorems for conic sections in Conics III might be taken as supporting the Z Archimedean origin of lemma 12, because Apollonius shaped his Conics as a system of scholarly references to preceding authors. Edited by I. Translated from the Arabic ———.

Dold-Samplonius, H. Stuttgart, Germany: B. The edition proposes a German translation procedures, so that what in the latter paper is adherence to and a facsimile reproduction of the unique manuscript Euclidean methods becomes in the present one a mark of Bankipore rather than a critical text and apparatus. Ancient Sources of the Medieval Tradition of Mechanics. Greek, Arabic and Latin Studies on the Balance.


  • Archimedes In The Middle Ages Iii The Fate Of The Medieval Archimedes Part Iii 1978.
  • RI OPAC: Authors.
  • Archimedes.
  • The reduction to non-extant Archimedean sources of available in the following ar ticles. Reading of Method Proposition Preliminary Evidence ———. In the Ancient Geometric Theory of Mirrors. A complete bibliography updated to can Berggren, John L. Textual Studies in Ancient and Medieval Geometry. Part III of this book presents 87— See this text about some problems of authenticity in a very ambitious reconstruction of the textual tradition of the the Archimedean corpus.

    Archimedean text Measurement of the Circle. Clagett, Marshall. Archimedes in the Middle Ages. A discussions of a Press, ; Vol. William of Moerbeke. Memoirs The Fate ———. Boston, of the Medieval Archimedes — Reprint, New York: Dover Quasi-Archimedean Geometry in the Thirteenth Century.

    Netz, Reviel. The entire mediaeval Archimedean Critical Edition of the Diagrams. Sphere and the Cylinder.

    Archimedes: Reception in the Renaissance

    Cambridge, U. This is the first volume of a new Regular Heptagon. The Archimedean tract on the regular Neugebauer, Otto. A History of Ancient Mathematical Astronomy. The proposed 3 vols. Berlin: Springer, Neugebauer offered the first translation is from p. The difficult problem of — Archimedes: Ingenieur, Naturwissenschaftler und texts on scientific matters, as well as literature, morality, Mathematiker.

    Da Archimedes hod an Haufa Eafindunga und Entdeckunga gmocht. Ned ois is gsichat und ned ois is ibaliefat.

    Download Archimedes In The Middle Ages. Iii. The Fate Of The Medieval Archimedes. Part Iv 1978

    Da Archimedes hod an Haufa Militeatechnik entwicklt. Wos des ois wor und wia des genau funktioniad hod, is ned bekannt; beispuisweis vo seine Katapuit bzw. Wuafmaschina und vo da Archimedeschn Kroin. Stroinwoffn: Paraboispiagl bindln as Sunnnaliacht und vanichtn so a feindlichs Schiff duach Hitzestroin vabrenna. Da Archimeds hod de Hebegsatzln formuliad und so de Grundlog fia de Mechanik glegt. De Archimedesche Schraum wead bis heid vawend, z.

    De sognenntn Archimedeschn Keapa soin vo eam stamma im Buidl a Kuboktaeda.

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    Archimedes in the Middle Ages. III. The Fate of the Medieval Archimedes. Part iv Archimedes in the Middle Ages. III. The Fate of the Medieval Archimedes. Part iv
    Archimedes in the Middle Ages. III. The Fate of the Medieval Archimedes. Part iv Archimedes in the Middle Ages. III. The Fate of the Medieval Archimedes. Part iv
    Archimedes in the Middle Ages. III. The Fate of the Medieval Archimedes. Part iv Archimedes in the Middle Ages. III. The Fate of the Medieval Archimedes. Part iv
    Archimedes in the Middle Ages. III. The Fate of the Medieval Archimedes. Part iv Archimedes in the Middle Ages. III. The Fate of the Medieval Archimedes. Part iv
    Archimedes in the Middle Ages. III. The Fate of the Medieval Archimedes. Part iv Archimedes in the Middle Ages. III. The Fate of the Medieval Archimedes. Part iv
    Archimedes in the Middle Ages. III. The Fate of the Medieval Archimedes. Part iv Archimedes in the Middle Ages. III. The Fate of the Medieval Archimedes. Part iv
    Archimedes in the Middle Ages. III. The Fate of the Medieval Archimedes. Part iv Archimedes in the Middle Ages. III. The Fate of the Medieval Archimedes. Part iv
    Archimedes in the Middle Ages. III. The Fate of the Medieval Archimedes. Part iv Archimedes in the Middle Ages. III. The Fate of the Medieval Archimedes. Part iv
    Archimedes in the Middle Ages. III. The Fate of the Medieval Archimedes. Part iv Archimedes in the Middle Ages. III. The Fate of the Medieval Archimedes. Part iv

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