“Given Magnitudes [Data]; the book of Tones, known under the name of Music, not genuine; the book of Division, emended by Thābit; the book of Utilisations or Applications [Porisms], not genuine; the book of the Canon; the book of the Heavy and Light; the book of Synthesis, not genuine; and the book of Analysis, not genuine.”
It is to be observed that the Arabs already regarded the book of Tones (by which must be meant the εἰσαγωγὴ ἁρμονική) as spurious. The book of Division is evidently the book on Divisions (of figures). The next book is described by Casiri as “liber de utilitate suppositus.”
Suter gives reason for believing the Porisms to be meant1,but does not apparently offer any explanation of why the work is supposed to be spurious. The book of the Canon is clearly the κατατομὴ κανόνος. The book on “the Heavy and Light”
is apparently the tract De levi et ponderoso, included in the Basel Latin translation of 1537, and in Gregory's edition. The fragment, however, cannot safely be attributed to Euclid, for (1) we have nowhere any mention of his having written on mechanics, (2) it contains the notion of specific gravity in a form so clear that it could hardly be attributed to anyone earlier than Archimedes2.Suter thinks3that the works on Analysis and Synthesis (said to be spurious in the extract) may be further developments of the Data or Porisms, or may be the interpolated proofs of Eucl. XIII. 1-5, divided into analysis and synthesis, as to which see the notes on those propositions.
1 Suter, op. cit. pp. 49, 50. Wenrich translated the word as “utilia.” Suter says that the nearest meaning of the Arabic word as of “porism” is use, gain (Nutzen, Gewinn), while a further meaning is explanation, observation, addition: a gain arising out of what has preceded (cf. Proclus' definition of the porism in the sense of a corollary).
2 Heiberg, Euklid-Studien, pp. 9, 10.
3 Suter, op. cit. p. 50.
Euclid. Euclid's Elements. Sir Thomas Little Heath. New York. Dover. 1956.
The National Science Foundation provided support for entering this text.
Purchase a copy of this text (not necessarily the same edition) from Amazon.com
This work is licensed under a
Creative Commons Attribution-ShareAlike 3.0 United States License.
An XML version of this text is available for download, with the additional restriction that you offer Perseus any modifications you make. Perseus provides credit for all accepted changes, storing new additions in a versioning system.