40 GREEK NUMERICAL NOTATION 
written in full, e.g. yvpidSe? fivorj kui = 22780912 jq 8 , o 
(ib. 17. 34), To express still higher numbers, powers of taken 
myriads were used; a myriad (10000) was a first myriad number 
(vrpcoTr] yvpids) to distinguish it from a second myriad (Sevrepa consistir 
yvpidd) or 10000 2 , and so on; the words 7rpoorai, yvpidSes, (100000 
Sevrepai. yvpidSes, &c., could either be written in full or g. a ^ e 0 £ 
expressed by M, MM, &c., respectively; thus Sevrepai yvpidSes 'period 
o ' _ first pt 
iq TrpcoTOU [yvpidSes) M = 16 2958 6560 (Dio order 
phantus, Y. 8), where M = youdSes (units) is inserted to period 
distinguish the the number of the ‘ first myriads ’> 01 P. 
froiji the ,<r0£ denoting 6560 units. second 
/TG 0 P.10 lc 
(i) Apollonius’s c tetrads on ; the 
The latter system is the same as that adopted by Apollonius ^ le 111111 
in an arithmetical work, now lost, the character of which is, (100000C 
however, gathered from the elucidations in Pappus, Book II; um ^ 
the only difference is that Apollonius called his tetrads (sets ft rs ^ or< ^ i 
of four digits) yvpidSes arrX'ai, SnrXaL, rpnrXa?, &c., ‘ simple from P 1 
myriads’, ‘double’, ‘triple’, &c., meaning 10000, 10000 2 , period ol 
10000 3 , and so on. The abbreviations for these successive on, the 
powers in Pappus are y a , //, y r , &e, ; thus y jev£(3 taxi itself, en 
koI y <$v = 5462 3600 6400 0000. Another, but a less con- is descrit 
venient, method of denoting the successive powers of 10000 myriad-r 
is indicated by Nicolas Rhabdas (fourteenth century a.d.) yvpiaKia-y 
who says that, while a pair of dots above the ordinary yvpidSey) 
numerals denoted the number of myriads, the ‘ double nothing 
myriad ’ was indicated by two pairs of dots one above the other, 
the ‘ triple myriad ’ by three pairs of dots, and so on. Thus 
^ = 9000000, $ = 2 (10000) 2 , ¡1 = 40 (10000) 3 , and so on. 
(ii) Archimedes’s system (by octads). 
Yet another special system invented for the purpose of 
expressing very large numbers is that of Archimedes’s 
Psammites or Sand-reckoner, This goes by octads: 
10000 2 = 100000000 = 10 s , 
and all the numbers from 1 to 10 8 form the first order; 
the last number, 10 8 , of the first order is taken as the unit 
of the second order, which consists of all the numbers from 
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