The Legacy of Archimedes (287-212 B.C.)

Any cylinder having for its base the greatest of the circles in the sphere, and having its height equal to the diameter of the sphere, is one and a half times the sphere


  1. (5) On the Sphere and Cylinder, I, II.
  2. (9) Measurement of the Circle.
  3. (7) On Conoids and Spheroids.
  4. (6) On Spirals.
  5. (1) On the Equilibrium of Planes.
  6. (3) On the Equilibrium of Planes II.
  7. (10) The Sand Reckoner, in ancient Greek.
  8. (2) Quadrature of the Parabola.
  9. (8) On Floating Bodies, I, II.
  10. (4) The Method.
  11. Stomachion.
  12. The Book of Lemmas.
  13. The Cattle Problem.

The order is the one given in J.L. Heiberg's definitive edition, [Archimedes, ``Opera Omnia,'' with commentary by Eutocius, edited by I.L.~Heiberg and additional corrections by E.S.~Stamatis, B.G.~Teubner, Stuttgart, 1972]. The bracketed numbers represent the conjectured historical order in which the papers were written. Recent opinion is that ``Measurement of the Circle'' was an early work.

An excellent translation of this edition is [Archim`ede, ``Oeuvres, 4 vol.,'' texte 'etabli et traduit par C. Mugler, Les Belles Lettres, Paris, 1970--71].

Why study the works of Archimedes?

Every mathematician knows that the only people who do history of math are the ones who can't do math, either because they're too old, or were just never good enough. So why spend time looking at the works of Archimedes when you should really be spending your time writing papers so you can finally get that job you always wanted? Here are my answers:

Cultural legacy.

Much has been written about the life of Archimedes but few details are actually known. Even the one information about his family is conjectural. In ``The Sand Reckoner,'' there appears in the manuscripts the passage: ``Feid'ia d`e to~u >Ak'o'upatros,'' which make no sense. F.~Blass made the conjecture [Ast. Nach. #104 (1883), p. 255] that this is actually: ``Feid'ia d`e to~u >amo~u patr`os,'' which means ``our father Phidias.'' The reference is to the estimate given by Pheidias that the sun is 12 times larger than the moon, so this would imply that Archimedes' father was an astronomer.

Reviel Netz has proposed the theory that his name might be derived from the Greek ``m~hdos'', which means cunning, so that combined with the usual meaning of ``archi'', his name means ``master of cunning.'' This is confirmed in the Greek to French dictionary [A.~Bailly, ``Abr'eg'e du dictionaire Grec Francais, Hachette, Paris, 1901] which gives approximately the same meaning based on the Greek words ``'arqw'' and ``m'hdomai''. This clearly implies that the name Archimedes is a pseudonym, thus much less is known about him than can be believed. Moreover, this is consistent with the hypothesis that he wanted to be remembered for his intellectual contribution.

Nevertheless, the cultural impact of Archimedes is impressive.

Transmission of works.


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