previous next
[528b] The right way is next in order after the second dimension1 to take the third. This, I suppose, is the dimension of cubes and of everything that has depth.” “Why, yes, it is,” he said; “but this subject, Socrates, does not appear to have been investigated yet.2” “There are two causes of that,” said I: “first, inasmuch as no city holds them in honor, these inquiries are languidly pursued owing to their difficulty. And secondly, the investigators need a director,3 who is indispensable for success and who, to begin with, is not easy to find, and then, if he could be found, as things are now, seekers in this field would be too arrogant4

1 Lit. “increase” Cf. Pearson, The Grammar of Science, p. 411: “He proceeds from curves of frequency to surfaces of frequency, and then requiring to go beyond these he finds his problem lands him in space of many dimensions.”

2 This is not to be pressed. Plato means only that the progress of solid geometry is unsatisfactory. Cf. 528 D. There may or may not be a reference here to the “Delian problem” of the duplication of the cube (cf. Wilamowitz, Platon, i. p. 503 for the story) and other specific problems which the historians of mathematics discuss in connection with this passage. Cf. Adam ad loc. To understand Plato we need only remember that the extension of geometry to solids was being worked out in his day, perhaps partly at his suggestion, e.g. by Theaetetus for whom a Platonic dialogue is named, and that Plato makes use of the discovery of the five regular solids in his theory of the elements in the Timaeus. Cf. also Laws 819 E ff. for those who wish to know more of the ancient traditions and modern conjectures I add references: Eva Sachs, De Theaeteto Ath. Mathematico,Diss. Berlin, 1914, and Die fünf platonischen Körper(Philolog. Untersuch. Heft 24), Berlin, 1917; E. Hoppe, Mathematik und Astronomie im klass. Altertum, pp. 133 ff.; Rudolf Eberling, Mathematik und Philosophie bei Plato,Münden, 1909, with my review in Class. Phil. v. (1910) p. 114; Seth Demel, Platons Verhältnis zur Mathematik,Leipzig, with my review, Class. Phil. xxiv. (1929) pp. 312-313; and, for further bibliography on Plato and mathematics, Budé, Rep.Introd. pp. lxx-lxxi.

3 Plato is perhaps speaking from personal experience as director of the Academy. Cf. the hint in Euthydem. 290 C.

4 i.e. the mathematicians already feel themselves to be independent specialists.

Creative Commons License
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.

load focus Notes (James Adam)
load focus Greek (1903)
hide Places (automatically extracted)

View a map of the most frequently mentioned places in this document.

Download Pleiades ancient places geospacial dataset for this text.

hide Dates (automatically extracted)
Sort dates alphabetically, as they appear on the page, by frequency
Click on a date to search for it in this document.
1929 AD (1)
1917 AD (1)
1914 AD (1)
1910 AD (1)
1909 AD (1)
hide Display Preferences
Greek Display:
Arabic Display:
View by Default:
Browse Bar: