NOTATION. 
number, made of that number the denominator of a fraCtion, 
Cc. 
of which =~ was the numerator : a 
I 
y= =, ae =» pra! == —— &c. but the frac- 
64 121 
tion 4 had a oie character, as C, or <, or C’, or 
f 
When the numerator is not unity, the denominator is 
placed as we fet our exponents. 
T ao 
Thus, ad , reprefented 15%, or = ; 
64 
and gine reprefented gi2t, oF — 
: Ay apes __ 331776 2033544. 
eee = 203544 = 3531776 * 
this laft fra@ion is found in Diophantus, book iv. quef- 
As it was only our intention, in this place, to convey to 
the reader a comes and general idea of the notation of the 
0° 59! 8" 17! 13% 12" grt 
now remains for us to do, “ by a few 
(lowing extracts 
wample ix narra —From Eutocius, theorem 4 of the 
eesti of the circ 
ape 847 3921 
gz. nv 60 8400 
yn. Brne go8 2321 
— 
lings and pence ; but it is more fim 
e co base ratio of 10 between any character and the fuc- 
eee on 
E ae in as —Eutocius, theorem 3 on the mea- 
fure of the circ 
0. yxar 9 3636 
B.yu § 2 3409 
Coxe 7 0227 
This example alfo is fo fimple, that the reader will find no 
difficulty in following the operation, by proceeding from 
right to left, as in our fubtr action, whack method feems fo 
i 
ployed in their multiplication; but it will not be cas i 
pr 
sileca pega rl and fimple, that one can hardly con- 
e why the fhould ever proceed in the contrary 
— though t bee are many inftances which makes it evi- 
dent that they did, both in sds and fubtraQion, work 
aa pe to right. 
multiplication, they moft commonly proceeded in their 
operations from left to right, as we do in multiplication of 
algebra; and their fucceflive products were placed without 
uch apparent peak as is evident from the following ex- 
amples. But as each 
of their charaGters retained always 
aie in whatever order they ftood, the 
is was that it rendered the addition 
\ ome. 
e to the me ini to retain in mind the 
value of all the Greek characters, we have, for the eafe of 
the reader, in the os cea ee made the fubttitutions 
as below, by which means their operations will be the more 
readily comprehended. 
For « 6 y 3, &c. we write 1 
2° +o] Cc a) ro] 2 i] 9 
ere oe 
Ps &c oes 1! 2 Wop tt 6" gt SB! " 
i ° & ° yi oan om a mw" Li "yf ai 
eBy hy &e 2 3h git st ON 7 BN g 
And the ai are reprefented by ™, placed above the 
number of 1 
Thus, 1° 2° 3, &c. have their proper value. 
1! 2! a ne will reprefent ie: 20, 30, &c. 
i oY! 9%. Ss — 100. 2 
zit git att 
uw 
O, 300, &c. 
a4 1000, 2000, 3000, &e. 
i are Pet be fo many ‘myria iads. 
After which, it will be extremely eafy to follow the work 
in all the fucceeding examples, 
pry r"g' 3 
P v ¥ rau 5! a 
O.te i git 
E B d p U Ce ait 5” 1" S| 
spvé ai" so 
This example may be far a illuftrated thus: by begin- 
ning on the left hand, we hav 
p X p== a, Or 100 X 100 = 10000 = 1” 
pxXvu=t Or 100xX §50= §5000= _ gill 
pXy=t Or 1TOOX 3= 3oo= 3! 
Again: 
vu xX p= f Or 50 X 100 = 5000 = mt 
vx u= BG, or 50 x S0O= 2500= Ql! gilt 
vuxX y= pv, or sox 3= 150= i” ¢! 
Alfo: 
y X pt Or 3 xX IOO= 3" 
yxu=pv, Or 3X SOo= ms! 
yxy=% or 3x na 9 
Whence by addition we have evidently 27 3!" 4" 9° 
The above example ie exaGtly copied from 2 
and is Cufficient to indicate the method that the Greeks e 
efent 
