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 R I T H M E T I C K. 377 is 35, in which the divifor 7 is contained 5 times. Now vifor 8 below it, fignifying that 1 remains to be divided it is evident, that the fum of the partial qaots, 125, is by 8 ; or this part of the quotient may be confidered as the total quot, or a number exprelling how often the di- a fradlion, whofe numerator is 1, and its denominator 8 ; and the quotient thus completed Ihews, that the dividend 875 contains the divifor 7. From the above example we may learn, that there vidend contains the divifor 7004112 times, and one are always juft fo many figures in the quotient as there eighth part of a t are dividuals; or the firft dividual, with the number of Here obferve, that riot only the laft remainder, but fubfequent figures in the dividend, is equal to the num- every other remainder, muftbe lefs than the divifor ; for if it be either greater or equal, the divifor might have ber of places or figures in the quotient. Hence likewife may be inferred, that no divifor is been oftener got, and the quotient-figure is too little. contained in any dividual oftener than 9 times ; for the And ftiould any one in this cafe attempt to continue the dividual, excluding the right-hand figure, is always lefs operation, the quotient-figures would be all 9’s, the dithan the divifor by 1 at leaft ; and if both be multiplied viduals would prove inexhauftible, and the remaindeis by 10, or have a cipher annexed to each of them, the would conftantly increafe. produdt of the dividual will be lefs than the produd of Hence alfo learn, that if any dividual happen to be lefs the divifor by 10 at leaft ; but no right-hand figure can than the divifor, you muft put o in the quotient, and fupply this defed of 10; therefore the divifor is not bring down the next figure of the dividend ;»and if it be contained 10 times in any dividual, and confequently not ftill lefs than the divifor, you muft put another o in the oftener than 9 times. quotient, and bring down the following figure of the diHere too obferve, that the right-hand figure of the firft vidend, <bc. dividual, and all the fubfequent figures of the dividend, III. Here the divifor confifts 36)789426(21928-54 have a point or dot fet below them, as they are brought of two figures; and becaufe it down ; which is done to prevent miftakes, by diftinguilh- is contained in the two lefting them, in this manner, from the figures not yet brought hand figures of the dividend 72 down. 78, point them off as the firft 1 dp / °4lI28'denom. numer. Examp. II. Here, dividual; and fay, How often 8) ^ 0 36 / ^ ?????(70 becaufe 8 is not con- 3 in 7 ? Anf. 2, and 1 remains; tained in 5, point off which 1 placed, or conceived 334 56 as the firft dividu- as placed, on the left hand of 324 al, and fay, How of- the following figure 8, makes • 032 ten 8 in 56 ? Anf. 7 ; 18 : then fay. Can I have the 102 32 which put in the quo- following figure of the divifor 6 72 tient ; then multiply 7 alfo 2 times in 18 ? Anf Yes.; •8 into the divifor 8, and confequently I get 36 the di306 8 fubtradthe produd 56 vifor 2 times in 78 the divi288 from the dividual; and dual; wherefore put 2 in the as nothing remains, quotient, and multiply that 2 (7s7 ^ bring down the next into the divifor 36, and fuhfigure of the dividend, tradt the product 7 2 from the dividual 7^ and to the 1716 which happens to be a remainder 6 bring down the following figure of the dicipher; and as you vidend 9, for a new dividual: then fay, How often 3 cannot have 8 in o, in 6 ? Anf. 2, and o remains ; again you fay. Can I (0 put o in the quotient; have 6 alfo 2 times in 9? Anf No ; therefore you can and, as multiplying and fubtrading is in this cafe have 36 in 69 only 1 time, which 1 you put in the needlefs, you bring down the next figure of the di- quotient: then multiply and fubtradl as before ; and to vidend 3 ; and as you cannot have 8 in 3, put another the remainder 33 bring down die next figurq 4 for a o in the quotient, and- bring down the next figure new dividual: Then, becaufe the dividual confifts of a of the dividend' 2 : Then fay, How often 8 in 32 ? figure more than the divifor, fay, How often the firft fiAnf 4; which put in the quotient: Then multiply gure of tlje divifor 3 in the firft two figures of the diviandfubtrad; and as nothing remains, bring down the dual 33 ? Anf 9, and 6 remains; which 6 placed on next figure of the dividend 8, and fay, How often 8 the left hand of the following figure 4 makes 64,.: Ain 8 ? Anf. 1 ; which put in the quotient : then mul- gain, fay. Can I have 6 alfo 9 times in 64 ? AnfAcs • tiply and fubtrad,- and as nothing remains, bring down confequently 36 can be had 9 times in 334; wherefore the rxxt figure of the dividend 9, and fay, How often 8 you put 9 in the quotient: Then multiply and fabtrafb; in 9 r Anf. 1; which put in the quotient: then mul- and to the remainder 10 bring down the next figure's tiply gnd fubtrad; and to the remainder 1 bring down for a new dividual: Here likewife,, becaufe tbe dividual The next and laft figure of the dividend 7, and fay, How has a figure more than the divifor, fay, How often 3 in often 8 in 17? Anf 2 ; which put in the quotient: 10 ? Anf 3, and 1 remains; which x placed on the awn multiply and fubtrad, and 1 remains. left hand of the following figure 2 makes 12 : Again fay. TV complete the quotient, draw a line on the right Can I have 6 alfo 3 times in 12 ? Anf. No ; confequentband, and ft the remainder above the line, and the di- ly 36 cannot be had 3 times in 102 ; wherefore try if Vol. I. No. 16. 3 5C you