NICOMACHUS 
101 
deficient {kWinris), and perfect (reAeio?) numbers respectively. 
The definitions, the law of formation of perfect numbers, 
and Nicomachus’s observations thereon have been given above 
(p. 74). 
Next comes (cc. 17-23) the elaborate classification of 
numerical ratios greater than unity, with their counterparts 
which are less than unity. There are five categories of each, 
and under each category there is (a) the general name, (b) the 
particular names corresponding to the particular numbers 
taken. 
The enumeration is tedious, but, for purposes of reference, 
is given in the following table:— 
RATIOS GREATER THAN UNITY 
RATIOS LESS THAN UNITY 
1. (a) General 
1. (a) General 
7roAXa7rA.rx<Ttos, multiple 
(multiplex) 
vTTOTroXXoLTrXdcno 1 ;, submultiple 
(submultiplex) 
(b) Particular 
(b) Particular 
StTrXacrtos, double 
(duplus) 
TpavXd(nos, triple 
(triplus) 
&c. 
vTroStTrAacrtos, one half 
(subduplus) 
vTTOTpiTrXdaios, one third 
(subtriplus) 
&c. 
2. (a) General 
2. (a) General 
imp-dpios ) 
(superparticularis) I a num ' 
ber which is of the form 
i , 1 n+1 
1 + or , 
n n 
where n is any integer, 
VTre-TTLpiopLOS (subsuper- ] , 
particularis) j" t e 
n 
fraction , where n is 
n+1 
any integer. 
(b) Particular 
(b) Particular 
According to the value of 
n, we have the names 
T7/xtoAtos = 1-| 
(sesquialter) 
ETUT/Oiros) = l-g- 
(sesquitertius) 
eTTirerapros — 1^ 
(sesquiquartus) 
&c. 
VcfiripUoXLOS = § 
(subsesquialter) 
VTrtTTLTptTOS — ^ 
(subsesquitertius) 
V7re7TLT€.TOipTOS = 3- 
(subsesquiquartus) 
&c.