EXAMPLE III,

Of Numbers of feveral (external) Denominations, viz. of Money:

1. S. d. q.

12326.07.04. 3 The Sum in Ad.

1200. 14. 06. 2 One Numb. gi

ven to be added

The Remaind. 11125. 12. 10. I The Equivalent

of the reft.

EXAMPLE IV,

Of Numbers of feveral (external) Denominations, viz. of Measure.

EXAMPLE V,

Of Numbers of feveral Denominations, viz. of Time.

T. D. H. M.

197. 187. 14. 12 The Sum in Ad.
10.341.06. 20 One Num. given

to be added.

The Refidue 186.211:07. 52 The Equivalent

to the reft.

If

Chap. IV.

Chap. IV.

How to

If more than one Number is to be fubftracted out of the fame greater Number, 7. then it is expedient to add together all fubftract the Numbers to be fubftracted into one feveral Sum, and fo to fubftract the faid Sum. from One. For Inftance.

Numbers

8.

ction by

And this laft Example, compar'd with Example III, both of Addition and Subftraction, is a further Evidence, how the one is proved by the other.

It remains only to obferve, that the The Proof Subftraction of Numbers of one (exterof Subftra- nal) Denomination, may be prefum'd to be rightly perform'd, if the Remainder away 9. of the greater Number be the fame as the Remainder of the other Numbers, (viz. the Number or Numbers to be subftracted, and the Refidue) 9 being caft

cafting

away

away as often as may be. Thus as to Chap. V. Example I, of Subftraction.

Chap. V.

I.

Multiplication, what.

2.

cand,

С НА Р. V.

Of the Multiplication of Integers.

Ultiplication is in Reality no other than a different Sort of Addition : For to multiply one Number by another, is nothing elfe, but to add one Number given to it felf, fo often as the other Number given directs. Thus 4x3=4+4+4=12.

The Number added to it self or multiMultipli- plied, is called the Multiplicand; the Multipli- other, the Multiplicator or Multiplier; cator, and (both these together, the Factors;) and Product, the Number arifing from the Multiplication, the Product.

what.

3.

Of the two Numbers given, either may The first be the Multiplicand or Multiplicator; Rule rela (for the Product will be the fame, viz. 4×3=12=3×4;) but it is better and fo Multipli- more ufual, to take the lefs Number for the Multiplicator, and to place it under the Multiplicand.

ting to

cation.

4.

The fe

ticular

If the Multiplicator confifts of more than one Figure, then the whole Multicond par- plicand is to be added to it felf, first as often as the Right-hand Figure of the Multiplicator fhews, then as often as the next Figure of the Multiplicator fhews,

Rule.

and

and fo on. Thus 421 × 23, is equal to Chap. V. 4213, and alfo 421 x 20.

particular

The Product arifing from each Figure 5. of the Multiplicator, multiplied into the The third whole Multiplicand, is to be plac'd by it Rule. felf in fuch manner, that the first or right-hand Figure thereof may stand under that Figure of the Multiplicator, from which the faid Product arifes. For Inftance:

The Reafon of fo placing the righthand Figure of each particular Product, is in Conformity to the firft general Rule; forafmuch as the right-hand Figure of each Product, is always of the fame Denomination with that Figure of the Multiplicator, from which it arifes. Thus in the fore-going Example, the Figure 2 in the Product 842, is of the Denomination of Tens, as well as the Figure 2 in the Multiplicator. For 1 x 20 (i. e. the 2 of 23)=20, or 2 put in the Place of Tens, or fecond Place.

D

If