184 THE ELEMENTS DOWN TO PLATO’S TIME 
extracts from Eudenms and Simplicius’s amplifications ; then 
came the critical text of Simplicius’s commentary on the 
Physics edited by Diels (1882), who, with the help of Usener, 
separated out, and marked by spacing, the portions which they 
regarded as Eudemus’s own. Tannery, 1 who had contributed 
to the preface of Diels some critical observations, edited 
(in 1883), with a translation and notes, what he judged to be 
Eudemian (omitting the rest). Heiberg 2 reviewed the whole 
question in 1884; and finally Rudio, 3 after giving in the 
Bibliotheca Mathematica of 1902 a translation of the whole 
passage of Simplicius with elaborate notes, which again he 
followed up by other articles in the same journal and elsewhere 
in 1903 and 1905, has edited the Greek text, witli a transla 
tion, introduction, notes, and appendices, and summed up the 
whole controversy. 
The occasion of the whole disquisition in Simplicius’s com 
mentary is a remark by Aristotle that there is no obligation 
on the part of the exponent of a particular subject to refute 
a fallacy connected with it unless the author of the fallacy 
has based his argument on the admitted principles lying at 
the root of the subject in question. ‘ Thus ’, he says, ‘ it is for 
the geometer to refute the (supposed) quadrature of a circle by 
means of segments (77477/4 arcor), but it is not the business of the 
geometer to refute the argument of Antiphon.’ 4 Alexander 
took the remark to refer to Hippocrates’s attempted quadra 
ture by means of lunes (although in that case T/xrjy a is used 
by Aristotle, not in the technical sense of a segment, but with 
the non-technical meaning of any portion cut out of a figure). 
This, probable enough in itself (for in another place Aristotle 
uses the same word Tyrgm to denote a sector of a circle 5 ), is 
made practically certain by two other allusions in Aristotle, 
one to a proof that a circle together with certain lunes is 
equal to a rectilineal figure, 6 and the other to ‘ the (fallacy) of 
Hippocrates or the quadrature by means of the lunes ’. 7 The 
1 Tannery, Mémoires scientifiques, voi. i, 1912, pp. 339-70, esp, pp. 
347-66. 
2 Philologus, 48, pp. 836-44. 
3 Rudio, Der Bericht des Simplicius iiber die Quadraturen des Antiphon 
und Hippokrates (Teubner, 1907). 
4 Arist. Phys. i. 2, 185 a 14-17. 5 Arist. De cado, ii. 8, 290 a 4. 
? Anal. Pr. ii. 25, 69 a 32, 7 Soph. El. 11, 171 b 15.