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7109 To this 7109, I bring down another Figure of the Dividend, viz. 2, and then it will become 71092 ; then I consider how often 7 can be taken from 71, &c. (just as at the first Operation,) and find it may be taken 9 times, therefore I set down g in the Quotient, and with it multiply the Divisor, setting down and Jubtracting their Product, as before ; Then the Work will stand
Thus 7563) 590624922 (7809
(00000) Here the Work is ended, and I find the Quotient to be 78094, being the true Multiplicand of the proposed Example of Multiplication, Page 18.
Tbat is, 7563 is contained in 590624922 juft 78094 times, &c.
If the Work of this Example be considered and compared with the Rule (Page 22.) the whole Business of Division will be easy; for indeed the only Difficulty (as I said before) lies in making choice of a true Quotient Figure, which cannot well be done according to the Common Method of Division, without Trials, yet those Trials need not be made with the whole Divisor (as appears by this last Example) for by the two First Figures of the Divifor all the rest are generally regulated ; except the Second Figure chance to be 2, 3, or 4, and at the same time the Third Figure be 7, 8, or 9, then indeed respect must be had to the Third Figure, according as the Rule directs.
However, if those Trials are thought too troublesome, they may be avoided, and the fame Quotient Figure may both easily and certainly be found by help of such a small Table made of the Divisor, as was of the Multiplicand in Page 20.
EXAMPLE 4. Let it be required to divide 70251807402 by 79863. See the Example of Multiplication, Page 20, and as there directed make a Table of the Divifor 79863, Thus,
Divisor. Dividend. Quotient. 1179863) 70251807402 (879654 2159726 638904.... The Work of this Operation 3239589 636140 I presume may be easily under4 319452 559041
stood. For those Figures in the 5399315
Table are the Product of the Di6.479178 _718767
visor into all the 9 Figures; con7559041
sequently those Figures in the 8638904
small Column do thew what
Figure is to be placed in the 101798630
431260 Quotient; without any doubtful
'EX A MPLE 6. Again, Let it be required to divide 43789 by 67. 67) 43789 (6538the true Quotient required.
Remains (38) How such Remainders thus placed over their Divisor's (which are indeed Vulgar Fractions) may be otherwise managed, lhall be shewed farther on,
N. B. When the Divifor happens to be an Unit, viz. I, with a Cypher or Cyphers annexed to it, as 10, 100, 1000, &c. Division is truly performed by cutting off with a Point or Comma, so many Figures of the Dividend as there are Cyphers in the Divifor ; then are those Figures so cut off to be accounted a Remainder, and the rest of the Figures in the Dividend will be the true Quotient re« quired, because an Unit or I doth neither multiply nor divide.
EX A MPLE 7. Let it be required to divide 57842 by 100. The Work may Atand thus, 100) 578,42 the Quotient required, or thus 100) 57842 (578.467 the same as before. - Hence it follows, that if any Divifor have Cyphers to the Pright-hand of it, you may cut off so many of the last Figures in the Dividend, and divide the other Figures of the Dividend, by those Figures of the Divifor that are left when the Cyphers are omitted. But when Division is ended, those Cypher's fo omitted in the Divisor, and the Figures cut off in the Dividend, are both to be restored to their own places.
EX AMPLE 8.
5400) 675469 (125
uncher in Milimanner o elient is 125 tune Remaine
Remains (4) But the true Remainder is 469.Consequently the true Quotient is 125543%.
As to the manner of proving the Truth of any Operation, either in Multiplication or Division, I presume it may be easily understood, by what is delivered in Page 21, compared with the three firft Examples of Division; for from thence it will be easy to conceive, that if the Divifor and Quotient be multiplied together, their Product (with what Remains after Division being added to that Product) will be equal to the Dividend. As in the Fifth Example, where the Dividend is 379, the Divisor is 5, the Quotient is 75, and the Remainder is 4.
I say,' 755=375, to which add the Remainder 4, it will be 379.
Again, in the Sixth Example, the Divisor is 67, the Quotient is 653, and the Remainder is 38.
Then 653x67343751, and 43751+38=43789 the Dividend, &c.
There are several useful Contractions, both in Division and Multiplication, which I have purposely omitted until I come ta treat of Decimal Arithmetick. Also I have omitted the Bufiness of Evolution or Extracting of Roots, until further on; and so shall conclude this Chapter with a few Examples of Division unwrought at large, leaving them for the Learner's Practice.
45007) 23884044718 4530674.
356) 244572000 (687000.
79) 282016 (356925.
CH A P. III. Concerning addition and Subtraction of Numbers of
different Denominations, and bow to reduce them from
Note, When I. s. d. q. are placed over (or to the Right-hand of) Numbers, they denote those Numbers to fignify Pounds, Shillings, Pence, and Farthings.
l. s. d. q. As 35 10 6 2. Or 35 l. 10 s. 6įd. Either of these do signify 35 Pounds, 10 Shillings, 6 Pence, 2 Farthings.
The same muft be understood of all the following Characters, belonging to their respective Tables, viz. Of Weights, Mec. Jures, &c.
2. Troy Weight. The Original of all Weights used in England, was a Corn of Wheat gathered out of the middle of the Ear, and being well dried, 32 of them were to make one Penny Weight, 20 Penny Weight one Ounce, and 12 Ounces one Pound Troy. Vide Statutes of 51 Hen. III. 31 Edw. I. 12 Hen. VII.