Republic Book 7 (235r – 240v)


This book has much about what came to be called the Quadrivium, geometry and astronomy  Stereometry is added on, a bit self-consciously and awkwardly, as if Plato were talking in an aside to his friend Archytas.   I believe we can locate some parallel asides, to his other friend Philip of Opus, curiously at a time when he and Plato had already collaborated on LAWS, Book 12 (end) and he himself under a name alluded to at 527e2, will have been in the role of teacher to young Aristotle, in Athens.    The verb SWQHNAI ( σωθῆναι : 527e2 ) will have been recognised as the first factor in this Socrates’s name, as the accompanying word  ‘kreitton’  [same phrase in  e2] is an allusion to its other factor.  More analysis is needed of this point, along with points about the specialist terms ‘prosrhma’ and ‘proseipein’, concepts of ‘setting forth in speaking’, to be found both in relevant passage of REP. and in the final book of LAWS.  Thesleff has located the late Plato style that draws on independent evidence to link these two works tightly.

There is a great rarity of wording in the final chapter of the final book of Euclid’s ELEMENTS.   This is the famous Five Platonic Solids segment or chapter, also the final one in the entire work of 177,328 words, counting all words such as ‘AB’ in the phrase ‘the line AB’.    This is a word Aristotle would find extremely familiar, being a variant of the word very common in his Analytics: “apodeiknu-‘  This is the root word of Kant’s word ‘apodictic’ and many related words in and out of technical vocabulary of specialists.  Here is a thought-experiment, based upon a near-hapax double occurrence, just within this final section — the one closest linked to Plato — in all of Euclid:


Eucl 13, 14-16, sunapodeiknumi, both quasi-hapaces r2



Republic, Book 7

Chapt 1:  514 a1

Chapt 2:  515 d9


Chapt 3:  517 a8

Chapt 4:  518  b7


Chapt 5:  519 e1


Chapt 6:  521 c1

Chapt 7:  522 e1


Chapt 8:  524 d1


Chapt 9:  526 c7


Chapt 10:  528 d1

Chapt 11:  529 c3

Chapt 12:  530 c6


Chapt 13:  532 b6


Chapt 14:  533 e3

Chapt 15:  535 a3


Chapt 16:  536 d4


Chapt 17:  539 a5