102 
PYTHAGOREAN ARITHMETIC 
RATIOS GREATER THAN UNITY 
RATIOS LESS THAN UNITY 
3. (a) General 
3. (a) General 
¿Tup-eprys . 1 which ex- 
(superpartxens) ) 
ceeds 1 by twice, thrice, 
or more times a sub 
multiple, and which 
therefore may be repre 
sented by 
m 2 m + n 
1 + 01 . 
m + n m+n 
virerr^ep^ l which ig 
(subsuperpartiens) ) 
of the form o m + W • 
2 m + n 
(b) Particular 
The formation of the names 
for the series of particular super- 
partientes follows three different 
plans. 
Thus, of npmbers of the form 
-i , m 
+ m+ 1 ’ 
, J 
x 3 
¿TriSqaeprys 
(superbipartiens) 
or ¿TTlStTptTOS 
(superbitertius) 
\ 01’ Sto-eTrtrptTOs 
The corresponding names are 
not specified in Nicomachus. 
H - 
¿7ri,rpt/j,epr/s 
(supertripartiens) 
01’ €7rtrptrerapToç 
(supertriquartus) 
or TpwreTrtrerapros 
€7rtrerpap,€p7yç 
* 
' (superquadripartiens) i 
1|- is' 01' €7TtT€Tpa7re/X7rTOS 
I (superquadriquintus) I 
l or TerpaKt(Te7ri7r€/x7rTOS 
&c. 
As regards the first name in 
each case we note that, with 
€7nSi/xep?ys we must understand 
rptrwv ; with ¿TTLrpLfJiepri<s, rerap- 
rwv, and so on.