HISTORY OF THE PROBLEM 
245 
by actually quoting the proof and the epigram, which are the 
genuine work of Eratosthenes. 
Our document begins with the story that an ancient tragic 
poet had represented Minos as putting up a tomb to Glaucus 
but being dissatisfied with its being only 100 feet each way; 
Minos was then represented as saying that it must be made 
double the size, by increasing each of the dimensions in that 
ratio. Naturally the poet ‘ was thought to have made a mis 
take’. Yon Wilamowitz has shown that the verses which 
Minos is made to say cannot have been from any play by 
Aeschylus, Sophocles, or Euripides. They are the work of 
some obscure poet, and the ignorance of mathematics shown 
by him is the only reason why they became notorious and so 
survived. The letter goes on to say that 
‘Geometers took up the question and sought to find out 
how one could double a given solid while keeping the same 
shape; the problem took the name of “ the duplication of the 
cube ” because they started from a cube and sought to double 
it. For a long time all their efforts were vain; then Hippo 
crates of Chios discovered for the first time that, if we can 
devise a way of finding two mean proportionals in continued 
proportion between two straight lines the greater of which 
is double of the less, the cube will be doubled; that is, one 
puzzle (a,7r6pr]/j.a) was turned by him into another not less 
difficult. After a time, so goes the story, certain Delians, who 
were commanded by the oracle to double a certain altar, fell 
into the same quandary as before.’ 
At this point the versions of the story diverge somewhat. 
The pseudo-Eratosthenes continues as follows: 
‘ They therefore sent over to beg the geometers who were 
with Plato in the Academy to find them the solution. The 
latter applying themselves diligently to the problem of finding- 
two mean proportionals between two given straight lines, 
Archytas of Taras is said to have found them by means of 
a half cylinder, and Eudoxus by means of the so-called curved 
lines; but, as it turned out, all their solutions were theoretical, 
and no one of them was able to give a practical construction 
for ordinary use, save to a certain small extent Menaechmus, 
and that with difficulty.’ 
Fortunately we have Eratosthenes’s own version in a quota 
tion by Theon of Smyrna: 
‘ Eratosthenes in his work entitled Platonicus relates that,