M A % I T H 
The firft fix figures from Che right hand are called the 
vnit period, t'ne next fix the million period , after which the 
trillion ; then follows quadrillion, quintillion, fcxtillion, fcp- 
tillion, oElillion, and nonillion, in regular fucceffion ; there¬ 
fore the numbers in the above Table are read as follows : 
Eight trillions, four hundred and thirty-feven thoufand 
nine hundred and eighty-two billions, five hundred and 
fixty-fbur thoufand (even hundred and thirty-eight millions, 
nine hundred and feventy-two thoufand, fix hundred and 
forty-five. And, as the idea of numbers is acquired by 
obferving feverai objects collected, fo is that of fractions 
by obferving an object divided into feverai parts. As we 
fometimesmeet with objects broken in two, three, or move, 
parts, we.may conlidci\any or all of thefe divifions pro- 
rnifcuoufiy, which is the doctrine of vulgar fractions-, and, 
lince the practice of.collecting units into parcels of tens 
•has prevailed univerfally, it has been found convenient to 
.follow a like method in the conlideration of fractions, by 
dividing each unit into ten equal parts, and each of thefe 
into ten fmaller parts; and lo on. Numbers divided in 
:ijiis manner are called decimalfractions. 
SIMPLE ADDITION 
Fs a.rule by which feverai numbers of the fame deno¬ 
mination ara collected together; and the number ariling 
from thofe collections is called the fum. The fign or cha¬ 
racter of addition is 4*1 and is called plus. This charac¬ 
ter is fet between the quantities to be added, to denote 
their amount; thus, 34-6=9, that is, 3 plus 6 are equal 
Vo 9 ; and 24-4rj-6=x3, that is, 2 plus 4 plus 6 are equal 
to 12. 
Rule. Place the feverai numbers under each other, fo 
that units may (land under units, tens under tens, hundreds 
under hundreds, See. and draw a line under the whole. Be¬ 
gin at tine place of units, add up all the figures in that row, 
gnd, if their fum be lefs than ten, fet down that fum 
ftraight below ; if above ten or tens, 
fet down the overplus, and for every 
ten carry an unit to the next row. Add 
up in like manner all the figures in the 
ten’s place, together with the units you 
carried, fet down the overplus above 
the even tens, as before, carry the tens 
to the next row, and fo on to the laft; 
and the figures below the line will be 
the whole fum. 
Proof. Draw a line below theup- 
permoft number, and fuppofe it cut off. 
Add all the reft together, and fet their 
■fum under the number to be proved. Add this laft-found 
.number and the uppermoft line together, and, if the fum 
is the fame as that found by the firft addition, the work 
is right. Or, fubtraCl the numbers fucceffively from the 
fum ; if the account be right, you will exhauft it exaClly, 
and find no remainder. 
The above rule, as well as the method of proof, is 
founded on the axiom, “ the whole is equal to the fum of 
all its parts. 1 ’ The method of placing the numbers and 
carrying for the tens are both evident from the nature of 
notation; for any other difpofition of the numbers would 
entirely alter their value, and carrying one for every ten, 
from an inferior line to afuperior, is manifeftly right, fince 
an unit in the latter cafe is equal in value to ten in the for¬ 
mer. When the propofed numbers are of different deno¬ 
minations, as pounds, (hillings, and pence, or the like, the 
operation nuift be regulated by the value of each, as (hewn 
by the following tables : 
In money, 1 . denotes pounds, s. (hillings, d. pence, and 
q. farthings. Alfo % denotes a farthing, or a quarter of any 
thing; a denotes a halfpenny, or half of anything; and 
denotes three farthings, or three-quarters of any thing. 
4 Farthings — 1 penny; 12 pence, 1 (hilling; 20 (hil¬ 
lings, 1 pound fterling. A groat = 4d. a tefter, 6d. 
half-a-crown, 2s. 6d. a crown, 5s. a noble, 6s. 8d. an 
angel, 19s. a mark, 13s. 4d. a guinea, 21s. a jacobus, 23s. 
M E T I C. 
a Carolus, 25s. a raoidore, 27s. abroad, 3!. XiS. three ua* 
hies, il. and two nobles, x mark. 
Tho Prnce Tables. 
d. s. 
d. 
s. 
d. 
s.d. ' 
d. 
S. 
d. 
12 ~ 1 
72 = 
6 
20 
= 1 8 
70 
— 5 
10 
24. ~ 2 
84 = 
7 
3 ° 
— 26 
80 
= 6 
8 
36 = 3 
96 = 
8 
40 
— 3 4 
90 
= 7 
6 
48 = 4 
108 —■ 
9 
50 
= 42 
100 
= 8 
4 
60 = 5 
120 = 
10 
60 
= 50 
110 
= 9 
2 
Troy Weight. 24 Grains (grs.) = 1 pennyweight 
(dwt.); 20 pennyweights, 1 ounce (oz.) ; 12 ounces, 1 
pound (lb.) By this weight are weighed gold, filver, jew¬ 
els, amber, bread, corn, liquors, &c. by this alfo is tried 
the proportion of gravity in philofophical experiments, 
which any two bodies have to each other; as gold to filver, 
&c. The weight of a guinea in gold is 5 dwts. 9! grs. 
nearly; and of a crown in filver 19 dwts. 8| grs. very 
nearly. The weight of a current guinea is 5 dwts. 8 grs. 
Apothecaries Weight. 20 Grains = 1 fcruple 
( 9 ); 3 fcruples, 1 drachm (3); 8 drachms, 1 ounce (§); 
12 ounces, 1 pound (it). By this weight apothecaries 
compound their medicines, though they buy and (ell their 
drugs by avoirdupoife weight. Apothecaries weight is the 
fame as troy, having only fome different divifions. 
Avoirdupoise Weight. 16 Drachms (drs.) = t 
ounce (oz.); i6ounces, 1 pound (lb.); i4potmds, 1 ftone 
(ft.) ; 2 (tones or 28 pounds, 1 quarter of a hundred (qr.) ; 
4 quarters, 1 hundred-weight (cwt.); 20 hundred, 1 ton; 
191 hundred, 1 fotherof lead; 7A pounds, igailonof oil. 
By this weight are weighed all things of a coarfe or droffy 
nature; fuch as butter, cheefe, flelb, grocery wares, See. 
all metals, except gold and filver. The pound troy is to 
the pound avoirdupoife as 14 to 19 ; but the ounce troy is 
to the ounce avoirdupoife as 56 to 51 ; therefore it is evi¬ 
dent that the pound avoirdupoife is greater, and the ounce 
lefs, than thofe of troy weight. Mr. Ward, in his Ma¬ 
thematician’s Guide, fays, that by a very nice experiment 
,he found, that ilb. avoirdupoife is equal to 140Z. 11 dwts. 
1 if grs- t r °y ; and 1 oz. = 18 dwts.. 5^ grs. troy. 
Wool Weight. 7 Pounds avoirdupoile = 1 clove; 
2 cloves, 1 ftone; 2 ftones, 1 tod; 6^ tods, 1 wey; 2 weys, 
1 fack ; 12 facks, 1 laft ; and a pack of wool is 12 fcore lb. 
Long Measure. 3 Barley corns (b.c.) = 1 inch (in.); 
12 inches, 1 foot (ft.); 3 feet, 1 yard (yd.); 5 feet, 1 
pace; 2 yards, 1 fathom; 5^ yards, 1 pole, rod, or perch; 
4 poles, 100 links or a land-chain ; 40 poles, 10 chains or a 
furlong; 8 furlongs, 1760 yards or a mile; 3 miles, 1 
league; 60 geographical, or 69A Englilh, miles, 1 degree; 
360 degrees, 1 circle ; 30 degrees, 1 fign ; 12 (igns or 360 
degrees, 1 revolution of the zodiac. Each degree is di¬ 
vided into ftxty equal parts, called minutes; and each mi¬ 
nute fubdivided into fixty equal parts, called feconds; and 
each fecond divided into fixty equal parts, called thirds; 
and fo on to fourths, fifths, lixths, See. by an equal fub- 
divifion of fixty. 
Square Measure. 16 Square quarters of an inch, x 
fquare inch; 144 fquare inches, 1 fquare foot; 9 fquare 
feet, 1 fquare yard; 30^ fquare yards, 1 fquare pole; 40 
fquare poles, 1 rood of land; 4 roods, 1 acre; 640 fquare 
acres, 1 fquare mile ; 7 fquare yards, 1 fquare rood of wall¬ 
ing ; 100 fquare feet, 1 fquare of framing in carpenter’s 
work ; 43 fquare yards, 1 bay of dating, but, when coun¬ 
ter meafure is allowed, which is commonly half a yard at 
the eaves, then 50 yards is 1 bay. 
Solid Measure. 64 Solid quarters of an inch = 1 
folid inch ; 1728 folid inches, 1 folid foot; 27 folid feet, x 
folid or cubic yard, or 1 load of earth ; 40 feet of unhewn, 
or 50 feet of hewn, timber, 1 ton or load. 
Cloth Measure. 2A Inches = 1 nail; 4 nails, 1 
quarter; 4 quarters, 1 yard; 5 quarters, 1 ell Englilh; 3 
quarters, 1 ell Flemilh ; 4 quarters i t inch, 1 ell Scotch ; 
6 quarters, 1 ell French. 
Corn Measure. 2-Pints = 1 quart; 2 quarts, 1 pot¬ 
tle; 
34578 
37 50 
87 
.■Example. 328 
*7 
327 
Sum 390S7 
4509 
Proof 39087 
- " -t* 
