N U M 
B E II. 
801 
Arabians, according to Sylveftre de Sncy, counted no 
farther than four hundred, or twenty .(bares, before the 
fixth century of the begin, which correfponds to about 
the middie of the eleventh century of the'Chriftian sera. 
To denote nine hundred, they had recourfe to the clumfy 
expedient of doubling the alphabetic-charaCter of'four 
hundred, and joining to it the character of one hundred. 
The inhabitants of the province of Bifcay, and of Ar¬ 
morica, people defeended from the ancient Celts, are 
faid to reckon like-the Mexicans, by the powers of twenty, 
or the terms of progreffive (cores 
But it is high time we fliould begin to (peak of the in¬ 
troduction of the Arabic numerals, which produced a to¬ 
tal revolution in the fyftem of arithmetic. Mr. Leflie is 
of opinion, that the ingenuity and varied refources of the 
ancient Greeks, were the main caufes which diverted 
them from difeovering our fimple denary fyftem. Having 
attained a diitinCt conception of the powers of the geo¬ 
metrical progreftion, and even advanced 'fo far as to em¬ 
ploy thc-ir finall o to fill the breaks of a period, nothing 
feemed wanting hut to difmifs the punCluated letters and 
thofe for tens and for hundreds, and to retain merely the 
direCt fymbols for units, that is, the firft third part of 
their alphabet. Here, however, thofe matters of fcience 
were (topped in their career; and the Eaftern Empire p_re- 
fents a melancholy picture of the decline and corruption 
of human nature. Ingenuity had degenerated into po¬ 
lemical iubtlety, and the manly virtues which freedom 
infpires, were exchanged'for meannefs and felf'-abafe- 
ment. 
Some writers, milled by very fuperficial views of the 
fubjeCt, have yet aferibed the invention of the modern 
numeral characters to the Greeks, or even to the Romans. 
Both thefe people, for the fake of expedition, occafion- 
ally ufed contractions, especially in reprefen ting the 
numbers and fractions of weights or meafures, which, to 
a credulous perufer of mutilated inferiptions, orancient 
blurred manuferipts, might appear to refemble the forms 
cf our ciphers. But this refemblance is merely cafual, 
and very far indeed from indicating the adoption of a 
regular denary notation. The moll contracted of the 
Roman writings were formed by the marks attributed to 
Tiro or Seneca, whilethofeof the Greeks were mixed with 
the fymbols called Jig Ice; both of which have exercifed 
the patience and fkill of antiquaries and diplomatifts. In 
the latter fpecies of characters, were kept the accounts 
of the revenues of the emprefs Irene at Conflantinople. 
But the modern Greeks appear likewife to have fome- 
times ufed a fimpler kind of marks, at lead for the low 
numbers. The continuator of Matthew Paris’s Hiftory 
relates, that “in the year 1251 died John Bafingftpke, 
archdeacon of Leicefter, who brought into England the 
numeral figures of the Greeks, and explained them to 
his friends.” It is fubjoined, that they confided of a 
perpendicular ftroke, with a ftvort line inferted at differ¬ 
ent heights and at different angles, fignifying units on 
the left, and tens on the right fide. The figures them¬ 
felves are (crawled on the margin of the text. But they 
are evidently fo different in their form, and fo diftinCt 
in their nature, from the modern ciphers, that one 
cannot help feeling furprife, to fee an author of any 
diicernm.ent refer the introduction of the latter to Ba¬ 
fingftoke. 
It cannot be doubted that we derived our knowledge 
of the numeral digits from .the Arabians, who had,them¬ 
felves obtained this invaluable acquifition from their ex¬ 
tended communication with the Eaft. Thofe deferving 
people, who, under the name of Moors or Saracens, had 
for many centuries cultivated Spain, were moft ready to 
acknowledge their obligation to the natives of India, 
who, according to Alfephadi, a learned Arabian doftor, 
boafted of three very different in ventions : the compofi- 
tion of the Gotaila Wadamna, or Pilpay’s Fables; the 
game of chefs; and the nine digital characters. Still much 
Vol. XVII. No. 1178. 
obfeurity hangs over the whole fubjeCt. Two diftinCt in¬ 
quiries naturally prefen-t themfelves: 1. At what-period 
did the Arabians firft become acquainted with thofe cha¬ 
racters ? and, 2. What is the precile epoch when the know¬ 
ledge of them was .imparted to the Chriftian nations of 
Europe ?• 
1. Gatterer, the late ingenious and very learned Pro- 
. fefi'or of Hiftory at Gottingen, in his “Elements of Uni- 
verfal Diplomacy,” maintains that our ciphers were only , 
primordial letters, invented by Taaut, or Theut, and 
known to the ancient Egyptians and Phoenicians, being 
■(till diftinCrly obferved, as he afferts, in the inferiptions 
painted on the coverings of the oldett mummies; and 
that afterwards, along with other branches of fcience, 
they patted to the oriental nations, among whom they 
. were preferred, till the victorious arms of the Mufl'ul- 
men penetrated to India, and brought hack thofe pre¬ 
cious monuments of genius. But we cannot believe 
that a contrivance fo very fimple, and fo eminently ufe- 
ful as that of the nine digits, if once communicated, 
could ever again be loft or negleCted. Pythagoras and 
Boethius merely contemplated the properties of numbers, 
and feetn not, in their calculations, to have gone beyond 
the ufe of the abacus. Au early intercourfe had, no 
doubt, fubfilted between the people of Egypt and of In¬ 
dia ; and a linking refemblance maybe traced in their 
cuftoms, their buildings, and their religious rites. But 
the characters exhibited on the Egyptian monuments 
bear no indication of the decimal fyftem-; and are, like 
the Roman and Chrnefe numerals, abridged reprelenta- 
tions of objeCts, rather than arbitrary figns. 
That the occupiers of Hindooftan and the nations com- 
. municating with them, have for ages been acquainted 
with the ufe of the decimal notation, cannot be difputed. 
But was this an .original difeovery, or at what diftant 
epoch was it firft introduced among them ? The eafy 
credulity of European vifitors encouraged the Brahmins 
to fet up very lofty pretenfions relpeCting the antiquity of 
their fcience. Among other .treafures, they boafted the" 
poffefiion, from time immemorial, of an elementary trea- 
tife on arithmetic and menfuration, compofed in Sanfcrif, 
and called Lilnwati, offuch ineftimable value, as to be af¬ 
eribed to the immediate infpiration of Heaven. But the 
refearches of our ingenious countrymen, in exploring that 
facred language of India, have difpelled foine i 11 li fions, 
and greatly abated the admiration of the public for fuck 
eaftern learning. From what we have been able to gather, 
the Lilawati is a very fhort and meagre performance, 
loaded with a filly preamble and colloquy of the gods. 
It begins with~the numeration by nine digits, and the 
lupplementary cipher, orfmall o, in what are called the 
Devanagari characters; and it contains the common 
rules of arithmetic, and even the extraction of the fquare 
root as far as two places of figures ; but the examples are 
. generally very eafy, fcarcely forming any part of the 
text, and only written on the margin with red ink. Of 
fractions, whether decimal or vulgar, it treats not at all. 
The Hindoos pretend, that this arithmetical treatife was 
compofed about the year 1185 of the Chriftian era.' The 
date of a manufeript, however, is always-very uncertain. 
We know befides, that the oriental tranferiber is accuf- 
tomed to incorporate without fcruple fuch additions in 
the text as he thinks fit. Nor wiil any of the criteria 
which might al'certain the age of a manufeript apply to 
the eaftern writings, where the compofition of the paper, 
the colour of the ink, and the form of the characters, have 
for ages continued unchanged. 
It appears, from a careful infpeCtion of the manuferipts 
preferved in the different public libraries of Europe, that 
the Arabians themfelves were not acquainted with the 
denary or decimal numerals before the middle of the 
thirteenth century of the Chriftian £Era. They cultiva¬ 
ted the mathematical fciences with ardour; but feldom 
afpired at original efforts, and generally contented them- 
+ H felves 
