NOTATION. 
Thus, for example, to Sper the truth of the eo 
in the following exam 
noe igs 
pateag 3 Gao Proof, 
eeoke, rem. 7 ME 
2225238 a 
phase oe = @ 4 
canes is divifible by 4, the w 
43 if the three laft digits be divifible by 8, mber is 
divifible by 8; and generally, if the x - digits i divifible 
by 2”, the whole number is divifible by 
eg 7 raped — in 5 or . is of one of the 
for + 0, both of which oe are 
evidently yale by by . oe the latter by 10 
very number may be expreffed by A x 10" +B, 
where B ie the x laft digits: a - example, 
846144 = 784614 x IO + 7 10° + 44 = 
Lb 6 na 4 aa nd fine ere is divifible by 2, 
deine t be divifible by 2” 
; Prov. VI. 
To alae eo operations by means of the duo- 
denary {cale o 
Rule. ee rm Pe number of feet, if above iat into 
the duodenary “Teale, and fet the inches and part 
Then multiply as in common arithmetic, except carrying 
for every 12 inftead of for every 10, a3 in the common 
operations, and in the refult = — the integral 
part of the produ& into the denary {ca 
Exam. 1.—Multiply 17 ft. 3 in. 4! by 19 ft. 5 in. 11° 
73 4 = 153 
2 Proof by 11: 
13908 
7248 ay 2 
garg. 4 
1534 
336 ft. gin. 6! 88! 240°9688 anfwer. 
Exam. 2—Find the folidity of a cube, whofe fide is 
13 ft. 7 in. 7. : 
77 = 13°79 7 
ny 
—_—— Proof, 
7751 
7751 SS 
1197 , 5AS 
1177 , 3 
135°g76r 
11°97 
tf 
9049867 3X5 
9049867 4 
1359761 
1359761 
ea = 2533 ft. 2in. 8a" gt xv 9” anf, 
ppirneetiea was firft publifhed by the writer of this ar- 
ticle, i in Nicholfon’s Journal, vol. xxv. and it appears to ee 
fefs confiderable advantage over the common rule, both o 
account of the facility of operation, and the accuracy of the 
refult, as likewife that it may thus be fubmitted to proof, 
the fame as common multiplication, which it is not poffible to 
apply to the old method, In the above examples, the proof 
of 11 is only made ufe of; but it is obvious that it might 
alfo be proved by 13, according to the rule in Prop. 5. 
me manner, any other arithmetical operation, 
{uch as divifion, extraGting the {quare root, a is performed 
with as much faci lity as in common number 
Eva ven the area of a Soa equal 1 to 174 
feet 11 inches, at its length 15 feet 7 inches; to find ite 
breadth in feet, inches, &c. 
174 ft. 11 in. = r26°y, and 15 ft. 7 in. we 13°97 
137) 126*y(y°2841 
1235 
Proof by it. 
S 
ay not be amifs to fay h 
it i ea » which is this; from the fum of the digits in 
the dividend, take t in the remainder; then the re. 
mainder from the di 
the remainder onfidered as the produc arifing 
from the siairichiceden of the dividend and quotient 
X 2 
HAN 
