[ 2i 3 ] 
Hence it appears, that, in common multiplication, the product of a cir- 
culating number, by its proper denominator, in g’s, will be deficient of the 
true product by that circulating number. 
Thus o,6 x 9 = 5,4; then 5,4 -\- ,6 =: 6. For 4. = 0,6 
0,06 x 99 = 5,94 ; then 5,94 + 0,06 — 6. For JL. = 0,06 
0,625 X 999 = 624 ,375 ; then 624,375 4- 0,625 — 625,0 
Hence. Any finite number is in proportion to the fame number re- 
curring, as the proper denominator of the circulate is to that denomina- 
tor increafed by unity. 
• « 
Thus 9:10 : : 6 : 6. For 6x9= 6x10 
• • • • 
99 : 100 : : 25 : 25. For 25 x 99 = 25 x 100. 
SCHOLIUM. 
If to the preceding articles, be joined the compendiums of multiplying 
and dividing by any number of 9’s, they will confiitute the whole of the 
theory, upon which depend all the operations with circulating numbers : for 
as thefe have 9’s for their denominator, wanting unity in the lowed; place to 
make them io’s ; therefore unity for every 9 is applied in fome additions and 
multiplications: Or, the circulating parts being reduced to finite number ; 
then working with them by the common rules, will give finite refults ; which 
refults are to be reduced to circulates by contrary operations to what were 
ufed to reduce the circulates to finites. 
XXXIII. A 
