Chap. I. Period of the faid fecond Period; hence it is known also, that 22 muft ftand in the two first Places of the second Period, i. e. in the 7th and 8th Places from the Beginning, and confequently must have fix Cyphers fet before it, (namely, to fill up all the fix Places of the first Period, which in this Number is void of fignificant Figures,) to make it denote twentytwo Millions; which is therefore denoted thus, 22 000 000.

32.

And thus much for Notation (Literal Integers as well as Figural) of Integers or whole or whole Numbers. Where it is to be observed, and Frac- that Numbers are fo called, when the

Numbers

tions,

what.

Things number'd are confider'd as fo many whole Things; whereas fhould the fame Things be confider'd as Fragments or Parts of any Thing elfe, then the Number is call'd a Fraction. For Example: Ten Shillings confider'd by themfelves, or as so many whole Shillings, is efteem'd a whole Number; but ten Shillings confider'd as ten Twentieths, or the Half of a Pound, is esteem'd a Fraction.

CHA P.

CHA P. II.

Of Computation, and the four Primary Operations of Arithmetick

in general.

PRO

Chap. II.

1.

pute or

Roceed we now to the fecond and much larger Part of Arithmetick, To com called Computation. To compute then, or caft Ac(as it is commonly called) to caft Ac- count, count, is to find a Number fought, having two or more Numbers given.

what.

Operations

And this is done, either fingly by ad- 2. ding together the Numbers given, or by ComputaSubstracting one from the other, or by tion diftinguishable Multiplying or Dividing one by the into fimple other; or elfe, laftly, by fome two or or primary more of these Operations jointly. Hence and comthis fecond Part of Arithmetick is diftin- pound or Secondaguishable into fimple or primary Operations, and compound (viz. of the Simple, two or more) or fecondary Operations, The fimple or primary Operations are Four, viz, Addition, Subftraction, Multi- The primaplication, and Division.

ry.

3.

ry Operations Four.

4.

In like manner, the fecondary Opera. tions are reducible to Four in general, The feconviz. Reduction, fuch as relate to Propor- dary Opetion, Evolution, or Extracting the Roots of likewife Powers, and Equation.

As

rations,

reducible to Four iss

general

Chap. II.

Operations

As it has been obferved, (Chap. i. Sect. 22.) that figural Notation is much 5. fhorter and quicker than Literal; fo it is The primary and obvious to conceive from thence, that Secondary figural Computation is much more eafy to be po- than Literal: Infomuch, that though liken of, on- teral Notation is still used in fome Cafes, ly in refeyet literal Computation is quite laid Figural afide, excepting only as to its Algebraical and Alge- Ufe. For this Reafon it will be needful Computa- to fpeak of the primary and fecondary Operations of Arithmetick, only in reference to Figural and Algebraical Computation.

rence to

braical

tion.

or Signs of

6. To begin then with the four primary of the Operations, with reference (*) to figural Characters Computation. Computation. Each of the faid Operathe four tions is expreffed in fhort by a certain primary Character. Thus + is the Sign of AddiOperatition, of Subftraction, + of Multiplicacation, and.) (.or (. of Divifion. To ÷ which add the Sign of Equality. Hence,

ons.

2+4
6-4
4+2

8

2)8(4 or (4

denotes in words

thus much, viz.

Two added to Four, is equal to Six.
6 when 4 is fubft. from it, is equ. to 2.
Four multiplied by Two, is equal to 8.
Eight divided by Two, is equal to 4.

(*) What is here faid, does in good Measure relate alfo to Algebraical Computation, as is fhewn Chap. 9.

7.

Having fhewn the Characters or Signs Chap. II. whereby each of the four primary Operations is denoted in fhort, I proceed General now to lay down fuch Rules, as relate in Rules regeneral to the four primary Operati- lating to

ons.

the four

primary

8.

Rule the

ist.

Numbers of the fame (whether (†) in Operations. trinfecal or extrinfecal) Denomination must be placed directly one under ano- . ther; as Units under Units, Tens under Tens, &c. Pounds under Pounds, Shillings under Shillings, Pence under Pence,

c. Yards under Yards, Feet under Feet, Inches under Inches. Years under Years, Days under Days, Hours under Hours,

c.

The particular Sum of any Denomination is always to be refolved into as many following or higher Denominations, as may be. Thus 24 Units are to be refolved into two Tens and four Units, and each Figure to be fet in its proper Place according to Rule the 1ft, viz. 4 under Units or in the first Place, 2 under Tens or in the fecond Place. In like manner, 59 Farthings are to be refolved into

C

9.

Rule the

2d.

(+) By intrinfecal or internal Denominations, are meant fuch as belong to Numbers confidered in themfelves, as Units, Tens, Hundreds, &c. By extrinfecal of external Denominations, are meant fuch as belong to the Things numbered, as Pounds, Shillings, Pence, &c.

3

FarChap. II into 1 Shilling, 2 Pence, and things; and the Figure 1 to be placed under Shillings, 2 under Pence, and 3 under Farthings.

IO.

Rule the 3d.

4th.

II.

Addition, Subftraction, and Multiplication begin at the Right-hand Figures, and go on to the Left: Divifion on the contrary.

The (beft Proof of Addition is by Rule the Subftraction, of Multiplication by Divifi on; and on the contrary, Subftraction is beft proved by Addition, and Divifion by Multiplication. For what Addition and Multiplication join together, Subftraction and Divifion disjoin again. For Example: Because 3+4=7, therefore 7-4=3, or 7-3-4. And in like manner, because 2×3=6, therefore 2)6(3, or 3)6(2. And thus much for what relates to the four primary Operations in general, proceed we now to speak of each in Particular.

(II) For there are other Sorts of Proof, among which the more ufual is by cafting away 9, of which I fhall give an Inftance in each Chapter, belonging particularly to the several Operations.

С НА Р.