NUMBER. 
81)7 
The New Multiplication-Tulle. 
I 
2 
3 
4 
5 
6 
7 
2 
2 
4 
6 
IO 
12 
J 4 
l6 
3 
3 
6 
I I 
x 4 
17 
22 
25 
4 
4 
IO 
x 4 
20 
24 
30 
34 
5 
5 
12 
17 
24 
31 
3 6 
43 
6 
6 
*4 
22 
30 
36 
44 
52 
7 1 7 
| 1 
: 
34 
43 
5 Z 
61 
“ The laft line of this Table is thus fpoken: Seven ones 
are feven; feven twos are min fix; feven threes are two 
min five; feven fours are three min four; feven fives are 
four min three; feven fixes are five min two ; feven fevens 
are fix min one. 
“ He who will take the pains to fet down i, 2, 3, 4, 5, 
6, and 7, and multiply them alternately by 2, 3, 4, 5, 6, 
and 7, daily, will be a complete odtarift in a month ; which, 
without practice, he cannot be, as a mere fpeculative 
knowledge of it will not be fufficient. He will then prove 
his work by divifion, and enumerate each line.” 
To convert the Old Arithmetic into the New .—The Rule, 
of courfe, mull be the fame w'e have already given, with 
an Example: namely, to divide continually by 8, till the 
quotient is lefs than the divifor, and to preferve each re¬ 
mainder, whether figure or cipher; and the laft quotient, 
or remainder, is to be afiumed as the firft figure of the 
number required. We (hall, hcnvever, annex another 
Example, that we may farther explain the notation, and 
introduce the rules for fradlions and mixed 
numbers, let the number to be reduced into 
odlaries be 1817. By the procefs in the mar¬ 
gin, the figures will be 3431, which Mr. 
Richardfon pundluates, and reads thus: 
34-31 2= 3 min, 4 minor, and 4 min 1. And 
he adds, “ If we either double or halve thofe numbers 
twelve times fucceftively, we (hall find the immenfe benefit 
of the new arithmetic.” 
To reduce a Vulgar Fraction to an O Sari an FraSion .— 
Odlalife both numerator and denominator, and the bufinefs 
is done. 
Example.—Reduce to the odiary notation. 
8)52 8)365 odt. dec. 
64 = 
365 
8)1817 
8)227 
8)78 
3 
614 
06 
45 
J 5 ' 
o 5 
555 
To reduce a Mixed Number ; or a Whole Number and a 
Decimal TVadZitm.—Reduce the whole number by divifion 
in the ufual manner. Then reduce the decimal by mul¬ 
tiplication, oblerving to increale the produdl one place in 
each multiplication ; thus: Let the number to be reduced 
be 9-123, 
123 
8 
8)9 
'I'll 
01 i 
e. 11, or min one. 
0 
984 
8 
7 
872 
8 
6 
976 
The decimal fradlion will feldom odlalife perfectly, or the 
odlal fraction decimate. Exchange 6)976 for 7, as nearelt 
the truth, and you have, 11,077 odl. =£ 9-123 dec. 
Example 2.—Reduce 11-125. 
8 )n 1 125 V 
8 11-125 dec, = j 3j x 
11 } 
A comparifon of the 1 odlal and decimal fradlions will 
Ihow this fyftem in a favourable light. 
i. e. eight and »ir. 
twice eight and five, 
three eights and four, 
four eights and three. * 
five eights and two. 
sir eights and one. 
OBal. 
Vulgar. 
Decimal Fra&ions. 
h 
1 
* Integer divided by two eighteen times 
* ? successively. 
,4 
1 
2 
•5 
,2 
1 
4- 
•25 
,1 
I 
g 
•a 25 
,04 
^1 _ 
i 6 
•0625 
,02 
. f 
3 ? 
•03125 
,01 
i 
6 4 
•015625 
,004 
I 
128 
•0078125 j 
,002 
See. 
*00390625 
,001 
&c. 
•001953125 
,0004 
•0009765625 
,0002 
•00048828125 
,0001 
•000244140625 
,00004 
•0001220703125 
,00002 
•00006103515625 
,00001 
•000030517578125 
,000004 
•0000152587890625 
,000002 
•00000762939453125 
,000001 
•000003814697265625 
In a communication to Mr. Snart, of a date fo recent 
as laft month, (April,) Mr. Richardfon fays, “ I am now 
preparing a work for the purpofe of farther explaining 
odiary arithmetic, in which I produce the new table of 
time, fpace, and long-meafure, (all three being one and 
the lame,) in a feries of columns moving by 64. This 
cannot fail of being underftood, and performs precifely 
the fame thing as the odlary arithmetic. 
Universal Taele. 
£ d 
E 
E g 
6 
G 
3 G 
> .5 
0 2 
c c 
6 
G 
a 
> 
0 
G 
w 
<r- U, 
^ a. 
P* 
C3S 
2 
S « S'! 
Pi 
1 . 
. 00 . 
. 00 . 
. 00 . 
,. 10 . 
. 00 . . 
00, 00 
1 
63 
..63 
..63 
..63 
..63 . 
. 63 , 63 . 
or 13. 
64 parvum fradtions one ftandard or unit, 64 units one 
minor, 64 minors one parvum, 64 parvums one primo, 
64 primos one minor primo, 64 minor primos one parvum 
primo, 64 parvum primos one bino. 
“ I now place a unit under the right-hand cipher, and 
fubtradl, and have the following remainder, which is thus 
fpoken : Sixty-three parvum, fixty-three minor, and fixty- 
three primo. Sixty-three parvum, fixty-three minor, and 
fixty-three. Sixty-three parvum fradlion. 
“ I think it impolfible for any human creature to mif- 
underftand this; for, as the extent of the equator is known, 
the length of every other name in the table may be 
known therefrom. The (Indent will alfo learn to break¬ 
through his prefent habit of numerating in triples; and, 
when all this is become familiar to him, he will eafily 
learn to tranflate this table into odlary arithmetic, which 
is precifely the lame thing in another drefs, only changing 
the word ten, or ty, which occurs at every other place in 
the table, for the word min in the odlary arithmetic. I fet 
down fixty-three, and divide it by eight, thus: 
This divifion is performed in the common way, - 
except that the 7 quotient is placed under the 7-7 - 
6, and the 7 remainder under the 3. The perfon who 
performs 
