A history of Greek mathematics - Wilbourhall.org

THE TREATISE ON POLYGONAL NUMBERS 517
The last proposition, which breaks off in the middle, is
Given a number, to find in how many ways it can be
polygonal.
The proposition begins in a way which suggests that
Diophantus first proved geometrically that, if
8P(a-2) + (a-4) 2 = {2 + (2ti-1) (a- 2)
}
then 2P = n {2+ (n— l)(a— 2)}.
Wertheim (in his edition of Diophantus) has suggested a
restoration of the complete proof of this proposition, and
I have shown (in my edition) how the proof can be made
shorter. Wertheim adds an investigation of the main problem,
but no doubt opinions will continue to differ as to
whether Diophantus actually solved it.
2
,
: