299 
N U M 
and female numbers, was ftyled “the number of the 
world.” Repeated any-how by an odd multiple, it al¬ 
ways re-appeared; and it marked the animal fenfes, and 
the zones of the globe. Six, or the hexlad, being com- 
pofed of its feveral factors, was reckoned perfedt and 
analogical. It was likewife valued, as indicating the 
fides of the cube, and as entering into the compofition of 
other important numbers. Seven, or the heptad, formed 
from the junction of the triad with the tetrad, has been 
celebrated in every age. Being unprodudfive, it was de¬ 
dicated to the virgin Minerva, though pofl'efled of a maf- 
culine character. It marked the feries of the lunar 
phafes, the number of the planets, and feemed to modify 
and pervade all nature. Eight, or the oftad, being the 
firlt cube that occurred, was dedicated to Cybele, the 
mother of the gods, whofe image in the remotelt times 
was only a cubical block of (lone. Nine, or the ennead, 
was efteemed as thelquareof the triad. It denotes the 
number of the Mules ; and being the laffc of the feries of 
digits, and terminating the tones of mufic, it was in- 
feribed to Mars. Ten, or the decod, from the important 
office which it performs in numeration, was, however, 
the moll celebrated for its properties. Having completed 
the cycle, and begun a new feries of numbers, it was aptly 
ftyled apocattftafiic, or periodic ; and therefore dedicated to 
the double-laced Janus. The cube of the triad, or the 
number 27, expreffing the time of the moon’s periodic 
revolution, was ftippofed to lignify the power of the lu¬ 
nar circle. The quaternion of celeftial numbers, one, 
three, five, and (even, joined to that of the terreftrial 
numbers, two, four, fix, and eight, compofe the number 
36, the fquare of the fil'd perfect number 6, and the fym- 
bo! of the univerfe, diftinguilhed by wonderful properties. 
But it would be endlefs to recount all the vifions of 
the Pythagorean Ichool ; nor lliould we defeend to notice 
inch fancies, it, by a perpetual defeent, the dreams of 
ancient philofophers had not, in the adtual Hate of focie- 
ty, dill tindtured our language, and mingled with the 
various inditutions of civil life. Not to wander in fearch 
of illudration, we feethe prediledlion for the number Jeven 
flxongly marked in the cudomary term of apprentice- 
fitips^ in the period required for obtaining academical de¬ 
grees, and in the legal age of majority. Lefiie's Phil, of 
Arithmetic. 
The Chinefe appear, from the remoted epochs of their 
empire, to have entertained the fame admiration for the 
ntydical properties of numbers that Pythagoras imported 
from the Ead. Diltinguiffiing numbers into even and 
odd, they confidered the former as terredrial. and parta¬ 
king of the feminine principle Yang; while they regard¬ 
ed the latter as of celedial extraction, and endued with 
the mafeuiine principle Yu. The even numbers were 
reprefented by (mall black circles, and the odd ones by 
fimilar white circles, varioufly dilpoled and connected by 
draight lines. See the annexed Engraving, fig. 1. The 
funt of the five even numbers, twm, four, fix, eight, and 
ten, being thirty, , was called the number of the Earth; 
hut the fum of the five odd numbers, one, three, five, 
fieven, and nine, or twenty-five, being the fquare of five, 
was dyled the number of Heaven. The nine digits were 
likewife grouped in two different ways, termed the Lo- 
chon, and the Ho-tou. The former expreffion fignifies the 
“ Book of the River Lo,” or what the Great Yu faw de¬ 
lineated on the back of the myfterious tortoife which 
rofe out of that river. It 
may be conceived from this ar- 
rangement: 
N ir.e 
_ 
Four 
Two 
Three 
Five Seven 
Eight 
Six 
One 
Nine was reckoned the head, ana One the tail, of the tor- 
B E R. 
toife ; Three and Seven were confidered as its left and 
right (houlders; and Four and Two, Eight and Six, were 
viewed as the fore and the hind feet. The number Five, 
which reprefented the heart, was alfo the emblem of Hea¬ 
ven. We need fcarcely obferve, that this group of num¬ 
bers is nothing but the common migic fquare, each row 
of which makes up fifteen. 
As the Lo-chou had the figure of a fquare, fo the Ho- 
tou had that of a crofs. It is what the emperor Fou-hi 
obferved on the body of the horfe-dragon, which he faw 
fpring out of the river Ho. The central number was 
Ten, which, it is remarked by the commentators, ter¬ 
minates all the operations on numbers. Each way it 
counts 31. 
Seven 
Two 
Five Three Ten Four Nine 
Five 
One 
Six 
Thus much of the allegorical notation of the Chinefe. 
In their regular calculations, they have, from the remoteft 
ages, ufed an inftrument called the fwan-pan, or compu¬ 
ting-table, fimilar in its ffiape and conllruftion to the 
abacus of the Romans, but more complete and uniform. 
The fyftem of meafures, weights, and coins, which 
prevails throughout the Chinefe empire, being entirely 
founded on the decimal fubdivifion, the fwan-pan was 
admirably fuited for reprefenting it. The calculator 
could begin at any particular bar, and reckon, with the 
fame facility either upwards or down wards. This advan¬ 
tage of treating fractions exadlly like integers, was, in 
practice, of the utmoft confequence. Accordingly, thofe 
arithmetical machines, but of very different fixes, are 
conllantly ufed in all the drops and booths of Canton and 
other cities, and are faid to be handled by the native tra¬ 
ders with fuch rapidity and addrefs as quite to aftoniffi 
the European faflors. 
But the Chinefe have alfo contrived a very neat and 
fimple kind of digital figns for denoting numbers, 
greatly fuperior, both in precifion and extent, to the me¬ 
thod pradfifed by the Romans. Since every finger has 
three joints, let the thumb-nail of the other hand touch 
thole joints in fucceffion, palling up the one fide of the 
finger, down the middle, and again up the other fide ; and 
it will give nine different marks. On the little finger, 
thofe marks fignify units, on the next finger tens, on 
the mid-finger hundreds, on the index thoufands, and 
on the thumb hundred thoufands. With the combined 
pofitions of the joints of the one hand, therefore, it was 
eafy to advance by figns as far as a million. To illuitrate 
more fully this ingenious pradlice, we have copied, at fig. 
2, from a Chinefe elementary treatife of education, the 
figure of a hand, noted, at the feveral joints of each fin¬ 
ger, by charadters along the inlide correlponding to one, 
two, and three; down the middle by thofe anlwering to 
four, five, and fix ; and again up the outfide by charadlers 
expreffing feven, eight, and nine. It is faid that the mer¬ 
chants in China are accufcomed to conclude bargains 
with each other by help of thofe figns; and that often, 
from felfiffi or fraudulent views, they conceal the panto¬ 
mime from the know ledge of by-llanders, by only leeming 
to feize the hand with a hearty grafp. 
As the Chinefe had conltrudted the fwan-pan on the 
principles of the Roman abacus, fo they had likewife, at 
the remotelt epoch of the empire, framed a lyltem of nu¬ 
merals in many refpedts fimilar to thofe which the Ro¬ 
mans probably derived from their Pelafgic anceltors. 
This will appear from the infpedtion of the charadlers on 
a larger lcale, at fig. 3. It is only to be obferved, that the 
Chinefe mode of writing is the reverie of ours ; and that, 
beginning at the top of the leaf, they defeend in parallel 
columns to the bottom, proceeding, however, from right 
to 
