Sources page biographical material

6.S.1. LOCULUS OF ARCHIMEDES
See S&B 22. I recall there is some dispute as to whether the basic diagram should be a square or a double square.

E. J. Dijksterhuis. Archimedes. Munksgaard, Copenhagen, 1956; reprinted by Princeton Univ. Press, 1987. Pp. 408 412 is the best discussion of this topic and supplies most of the classical references.

Archimedes. Letter to Eratosthenes, c-250?. Greek palimpsest, c975, on MS no. 355, from the Cloister of Saint Sabba (= Mar Saba), Jerusalem, then at Metochion of the Holy Sepulchre, Constantinopole. [This MS disappeared in the confusion in Asia Minor in the 1920s but reappeared in 1998 when it was auctioned by Christie's in New York for c2M$. Hopefully, modern technology will allow a facsimile and an improved transcription in the near future.] Described by J. L. Heiberg (& H. G. Zeuthen); Eine neue Schrift des Archimedes; Bibliotheca Math. (3) 7 (1906 1907) 321 322. Heiberg describes the MS, but only mentions the loculus. The text is in Heiberg's edition of Archimedes; Opera; 2nd ed., Teubner, Leipzig, 1913, vol. II, pp. 415 424, where it has been restored using the Suter MSS below. Heath only mentions the problem in passing. Heiberg quotes Marius Victorinus, Atilius Fortunatianus and cites Ausonius and Ennodius.

H. Suter. Der Loculus Archimedius oder das Syntemachion des Archimedes. Zeitschr. für Math. u. Phys. 44 (1899) Supplement = AGM 9 (1899) 491 499. This is a collation from two 17C Arabic MSS which describe the construction of the loculus. They are different than the above MS. The German is included in Archimedes Opera II, 2nd ed., 1913, pp. 420 424.

Dijksterhuis discusses both of the above and says that they are insufficient to determine what was intended. The Greek seems to indicate that Archimedes was studying the mathematics of a known puzzle. The Arabic shows the construction by cutting a square, but the rest of the text doesn't say much.
Lucretius. De Rerum Natura. c 70. ii, 778 783. Quoted and discussed in H. J. Rose; Lucretius ii. 778 83; Classical Review (NS) 6 (1956) 6 7. Brief reference to assembling pieces into a square or rectangle.

Decimus Magnus Ausonius. c370. Works. Edited & translated by H. G. Evelyn White. Loeb Classical Library, ??date. Vol. I, Book XVII: Cento Nuptialis (A Nuptial Cento), pp. 370-393 (particularly the Preface, pp. 374-375) and Appendix, pp. 395-397. Refers to 14 little pieces of bone which form a monstrous elephant, a brutal boar, etc. The Appendix gives the construction from the Arabic version, via Heiberg, and forms the monstrous elephant.

Marius Victorinus. 4C. VI, p. 100 in the edition of Keil, ??NYS. Given in Archimedes Opera II, 2nd ed., 1913, p. 417. Calls it 'loculus Archimedes' and says it had 14 pieces which make a ship, sword, etc.

Ennodius. Carmina: De ostomachio eburneo. c500. In: Magni Felicis Ennodii Opera; ed. by F. Vogel, p. 340. In: Monumenta Germaniae Historica, VII (1885) 249. ??NYS. Refers to ivory pieces to be assembled.

Atilius Fortunatianus. 6C. ??NYS Given in Archimedes Opera II, p. 417. Same comment as for Marius Victorinus.

E. Fourrey. Curiositiés Géométriques. (1st ed., Vuibert & Nony, Paris, 1907); 4th ed., Vuibert, Paris, 1938. Pp. 106 109. Cites Suter, Ausonius, Marius Victorinus, Atilius Fortunatianus.

Collins. Book of Puzzles. 1927. The loculus of Archimedes, pp. 7-11. Pieces made from a double square.