[ 2C8 ] 
pen?, that thofe decimals do not terminate, or end, 
with a few figures only ; and fometimes are infinite, 
or never end ; and among thefe are many which have 
one or more figures conftantly recurring ; as in the 
following proportions, viz. 
3:2:: 1,0000, c '§c. : 0,6666, &c. 
and 12:5:: 1,0000, &c. : 0,4166, &c. 
alfo 7:3:: 1,0000, &c. : 0,428571,428571, 
In operations, with fuch recurring decimal frac- 
tions, particularly in multiplication and aivifion, the 
work will either be longer than neceffary, or be very 
inaccurate, if the numbers are not confiderea as cir- 
culating ones : and to come at the true refults of 
fuch operations, fcveral authors have given precife 
rules; and fome of them have fhewn the principles 
upon which thofe rules were founded. 
In the annexed paper thofe principles are, en- 
deavoured to be, exhibited in a different, and in a 
more general and concife manner, than has hitherto 
been fhewn : but the modes of working are not here 
annexed, as they are to be found in Cunn, Malcolm , 
Marjl^ and others ; and may hereafter be fully ex- 
emplified in a treatife of Arithmetic, by the author 
hereof, confidered in a more mathematical order, 
than what has hitherto been appropriated to this moil 
ufeful fcience. 
General Principles. 
. 
■ r 
1. Number is fuppofed to begin at unity, and from 
thence to afeend and defeend : thofe terms afeending 
•above unity, are integers; and thofe delcending be- 
low unity, are fractions. 
When 
