1802. ] 
4. We may obferve by the way, that 
Ecypt claimed the honour of being the 
cradle of this art, and that, regarding this 
ufeful invention of it as beyond the reach 
of the human intelleét, the Egyptians af- 
cribed it to a beneficent Divinity. Her- 
mes was accounted by them the inventor 
of numbers, calculation and geometry. 
5. All the nations of whom we have 
any knowledge (except the ancient Chi- 
nefe, and a people in Thrace, mentioned 
by Ariftotle) have chofen the fame fyftem 
of numeration, namely, the decuple pro- 
greffion*, and reprefent numbers by the 
Jetters of their alphabets. ‘The different 
periods of tens were diftinguifhed, either 
by accents which affe&ted the numeral 
letters, as among the Greeks ; or by 
different combinations of the numeral 
letters, as among the Romans. Thefe 
methods became very complicated, and 
therefore very inconvenient, when the 
numbers were coniliderable. 
6. The ingenious fyftem of numeration, 
which forms the bafis of eur modern Arith- 
metic, was long familiar to the Arabians, 
before it penetrated into our quarter of the 
world. But the honour of the original 
invention appears to belong to the Indi- 
ans. For Alfephadi, an Arabian author, 
fays, that the Indians boafted of three 
things, namely the bock intitled Golazla 
ve damma (a kind of fables), the method 
of calculation, and the game of chefs.+ 
* It is very probable, that the, arithmetic 
of the ancient Chinefe was analogous to the 
binary arithmetic, For many ages, the figure 
of the Cowa, formed of whole lines ( 
and of broken ones (— —), which they af- 
cribed to their emperor Fohi, was to them 
aninexplicable enigma. But Father Bouvet, 
a learned miffionary, to whom Leibnitz had 
communicated his binary arithmetic, found 
that it explained the Cova of Fohi, which 
appeared to be nothing more than a feries of 
numbers, expreffed according to the principles 
of the new arithmetic of Leibnitz, the whole 
line anfwering to 1, and the broken one to 
our o. As fuch a coincidence could ‘not be 
the effeét of chance, it is probable that the 
binary arithmetic was anciently ufed in 
China. 
The work of Fohi, thus formed of lines 
whole and broken, is intitled the Y-kAing, and 
it makes a part of the five moft ancient Chi- ' 
nefe books, called the Ou-hing. 
The Thracian people, mentioned by Arif. 
totle, he tells us, only counted to four, 
which is apparently to be underftood in the 
fame fenfe in which we may be faid to 
count to ten, that is, by periods of tens. 
+ Ardfchir, king of Perfia, had invented 
the game of trictrac, or tables, by which he 
pretended to seprefent the fyfiem and the 
A Sketch of the Hiftory of Pure Mathematics. 
19 
And Aben-Ragel, an Arabian author of 
‘the 13th. century, exprefsly afcribes the 
invention of this fcheme of arithmetic to 
the Indian philofophers. 
7. It is true, that fome Pythagoreans 
employed nine particular characters in 
their calculations, while others ufed the 
letters of the alphabet, which were the 
ordinary figns; and it appears certain, 
that a mode of notation refembling ours 
was known in the {chool of Pythagoras *. 
But it ismore natural to fuppofethat Pytha- 
goras learned thatinvention from the Indi- 
ans, than that they owed it to the Greeks, 
8. It is faid, that that philofopher car- 
ried the combinations of numbers very 
far, and that he attached myfterious pow- 
ers to certain properties of thofe combi- 
game of the univerfe. The tables were di- 
vided into twelve points, anfwering to the 
twelve, months in the year, and there were 
thirty men, anfwering to the thirty days ina 
month, &c. Ay 
As the Orientals looked upon the difcovery 
of the Perfian monarch as a great effort of the 
human mind, Shechram, an Indian king, 
offered a great reward to any man who fhould 
invent a game, which would bear a comparifon 
with that of trictrac.’”"“The event exceeded 
his expeétations ; for the game of chefs, in- 
vented by Sefla, far furpaffed that of trictrac, 
in the opinion of the wife men. 
* Pythagoras was born at Samos, about 
589 years before the Chriftian era. Improv~ 
ing by the inftruétions of Pherecides, one of 
the feven wife men of Greece, he devoted 
himfelf wholly to philofophy. After the 
death of his preceptor, he travelled in Egypt," 
where he converfed with the priefts, and was 
initiated into their myfteries. He afterwards 
penetrated to the banks of the Ganges, where 
he imbibed from the Brachmans, the doc- 
trine of the metempfychofis. On his return, 
finding his native country groaning under ty- 
ranny,. hechofe a voluntary exile, carried his 
learning into Italy, and there eftablithed his 
celebrated Ichool, in which every kind of 
knowledge, which could contribute to im- 
prove the underftanding and the heart, was 
zealoufly cultivated. In a little timne, Py- 
thagoras was attended by four or five hundred 
pupils. Before he admitted them. to that 
rank, he fubje€ted them’ to a noviciate of fi- 
lence, in which thofe whom he thought 
prone to fpeak, remained at leaft five years. 
His reputation for wifdom, rendered him, the 
legiflator of that country 5 and fome of his 
{cholars became the chiefs of the flourifhing 
fates which compofedit. ‘The moft common 
opinion is, that Pythagoras died in peace at 
Metapontus, in the year 497, before the 
Chriftian zra. His houfe was converted into 
a temple, aydthe philofopher received the; 
honours of a god. The fee of which he 
was the chief, was called the Italian feét. — 
Ds nations 
