142 
PYTHAGOREAN GEOMETRY 
a longer fragment including the same passage is now available 
(though the text is still deficient) in the Oxyrhynchus Papyri. 1 
The story is that one Bathycles, an Arcadian, bequeathed a 
cup to be given to the best of the Seven Wise Men. The cup 
first went to Thales, and then, after going the round of the 
others, was given to him a second time. We are told that 
Bathycles’s son brought the cup to Thales, and that (presum 
ably on the occasion of the first presentation) 
‘ by a happy chance he found . . . the old man scraping the 
ground and drawing the figure discovered by the Phrygian 
Euphorbus {= Pythagoras), who was the first of men to draw 
even scalene triangles and a circle . . ., and who prescribed 
abstinence from animal food ’. 
Notwithstanding the anachronism, the ‘figure discovered by 
Euphorbus ’ is presumably the famous proposition about the 
squares on the sides of a right-angled triangle. In Diodorus’s 
quotation the words after ‘ scalene triangles ’ are kvkXov eirra- 
/xijK7]{eTrTafi^K€’ Hunt), which seems unintelligible unless the 
‘ seven-lengthed circle ’ can be taken as meaning the ‘ lengths of 
'seven circles’ (in the sense of the seven independent orbits 
of the sun, moon, and planets) or the circle (the zodiac) com 
prehending them all. 2 
But it is time to pass on to the propositions in geometry 
which are definitely attributed to the Pythagoreans. 
1 Oxyrhynchus Papyri, Pt. vii, p. 83 (Hunt). 
2 The papyrus has an accent over the e and to the right of the 
accent, above the uncertain tt, the appearance of a X in dark ink, 
A. 
thus KnLKVKXovey, a reading which is not yet satisfactorily explained. 
Diels (VorsokratiJcer, i 3 , p. 7) considers that the accent over the e is fatal 
to the reading. enrayvKii, and conjectures ml kvkXov eX(im) 
vrjCTTeveiv instead of Hunt’s ml kvkXov €Tr[Tap,T]Ke’, rjde VTjarevetv] and 
Diodorus’s ml kvkXov (UTayrjKo 8i8n^e vrjcrreveLV. But kvkXov eXtKa, ‘ twisted 
(or curved) circle’, is very indefinite. It may have been suggested to 
Diels by Hermesianax’s lines (Athenaeus xiii. 599 a) attributing to 
Pythagoras the ‘ refinements of the geometry of spirals ’ (eXUoov my-fya 
■yecoyerpiris). One naturally thinks of Plato’s dictum (Timaeus 39 a, b) 
about the circles of the sun, moon, and planets being twisted into spirals 
by the combination of their own motion with that of the daily rotation ; 
but this can hardly be the meaning here. A more satisfactory sense 
would be secured if we could imagine the circle to be the circle described 
about the ‘ scalene ’ (right-angled) triangle, i. e. if we could take the 
reference to be to the discovery of the fact that the angle in a semi 
circle is a right angle, a discovery which, as we have seen, was alterna 
tively ascribed to Tbales and Pythagoras.