1 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. That is, 7563 is contained in 590624922 just 78094 times, &. E2 If 3025 To this Remainder 3025, I point and bring down the last Figure 2 of the Dividend, which makes it 30252; then praceeding in all respects as before, I find the Quotient Figure to be 4, with it I multiply the Divisor, setting down and fubtracting their Product as before, and then the Work will stand Thus 7563) 590624922 (78094 52941 61214 60504 Chap. 2. Of Divifion. Thus 7563) 590624922 (780 61214 7109 27. To this 7109, I bring down another Figure of the Dividend, viz. 2, and then it will become 71092; then I confider 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 fet down 9 in the Quotient, and with it multiply the Divisor, setting down and fubtracting their Product, as before; Then the Work will stand Thus 7563) 590624922 (7809 52941... 61214 HH (০০০০০) 71092 68067 30252 30252 60504 71092 If the Work of this Example be confidered 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 Divifor (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 Divisor 79863, Thus, Divifor. Dividend. Quotient. 179863) 70251807402 (879654 2159726 638904... 3239589 636140 4319452 559041 5/399315 770997 6479178 718767 522304 9718767 479178 The Work of this Operation I prefume may be easily understood. For those Figures in the Table are the Product of the Divisor into all the 9 Figures; consequently those Figures in the fmall Column do shew what Figure is to be placed in the Quotient; without any doubtful Trials of the Divisor, with the 319452 Dividend, as before. 319452 (○○○○○○) This Method of tabulating the Divisor may be of good Ufe to a Learner; especially until he is well practised in Division; yea, and even then if the Divisor be large, and a Quotient of many Figures be required; as in refolving of high Equations, and calculating of Astronomical Tables, or those of Interest, &c. Hitherto : Hitherto I have made choice of Examples wherein the Dividend is truly measured or divided off by the Divisor, without leaving any Remainder, being exactly composed of the Divifor and Quotient. But it most usually falls out, that the Divifor will not exactly measure the Dividend; in which case the Remainder (after Division is ended) must be set over the Divisor, with a small Line betwixt them adjoining to the Quotient. EXAMPLE 5. Suppose it were required to divide 379 by 5. the Remainder. 5) 379 (75 the Divifor. Again, Let it be required to divide 43789 by 67. 67)43789(653 the true Quotient required. 402. 358 335 239 201 (38) 2 Remains How such Remainders thus placed over their Divisors (which are indeed Vulgar Fractions) may be otherwise managed, shall be shewed farther on. N. B. When the Divisor happens to be an Unit, viz. 1, 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 Divisor; then are those Figures so cut off to be accounted a Remainder, and the reft of the Figures in the Dividend will be the true Quotient required, because an Unit or I doth neither multiply nor divide. EXAMPLE 7. Let it be required to divide 57842 by 100. The Work may stand thus, 100) 578,42 the Quotient required; or thus 100) 57842 (578 the fame as before. Hence it follows, that if any Divifor have Cyphers to the Right-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 Cyphers fo omitted in the Divisor, and the Figures cut off in the Dividend, are both to be restored to their own places. EXAMPLE 8. Suppose it were required to divide 675469 by 5400. 5400) 675469 (125 (4) But the true Remainder is 469. Consequently the true Quotient is 125. 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 first Examples of Division; for from thence it will be easy to conceive, that if the Divisor 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 Divifor is 5, the Quotient is 75, and the Remainder is 4. I fay, 75×5=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 653×67-43751, and 43751+38=43789 the Dividend, &c. There are several useful Contractions, both in Divifion and Multiplication, which I have purposely omitted until I come ta treat of Decimal Arithmetick. Also I have omitted the Business of Evolution or Extracting of Roots, until further on; and fo shall conclude this Chapter with a few Examples of Divifion unwrought at large, leaving them for the Learner's Practice. ! 45007) 23884044718 (530674. CHAP. III. Concerning Addition and Subtraction of Numbers of different Denominations, and how to reduce them from one Denomination to another. T SECT. I. 1. Of English Coin. HE leaft Piece of Money used in England is a Farthing, and from thence arifeth the rest, as in this Table. Note, When 1. s. d. q. are placed over (or to the Right-hand of) Numbers, they denote those Numbers to fignify Pounds, Shillings, Pence, and Farthings. As 35 10 6 2. Or 351. 10s. 6d. Either of these do fignify 35 Pounds, 10 Shillings, 6 Pence, 2 Farthings. The fame must be understood of all the following Characters, belonging to their respective Tables, viz. Of Weights, Meafures, &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. But |