nominatians. 15. As for Multiplicators of feveral exterof Multinal Denominations, they never occur, plicators of feveral ex- but when the external Denominations are ternal De of various Measures, as Yards, Feet, Inches, &c. And in this Cafe, the Operation may be perform'd, by reducing both the Multiplicand and Multiplicator into one Denomination, as is fhewn, S. 8, Chap. 5, of Reduction. concerning 16. There is also another Method in this Further, laft Cafe, which is called Cross Multiplithe fame. Cation. But this, as well as Reduction, depending on Divifion, it will be improper to speak of it here, before we have Spoken of Divifion. And therefore it Thall be referr'd likewife to Chap. 5; Where it shall be added by Way of Annotation, to the Reduction belonging to this Cafe. The Multipli The best or most certain Way of pro- 17. ving, whether Multiplication be perform'd of proving aright, is (according to the fourth gene- cation by ral Rule) by Divifion, as fhall be fhewn cafting a in the following Chapter of Divifion. It way 9. remains only here to fhew, how the Multiplication of Numbers of one external Denomination, may with certainty enough for common Matters be prov'd by cafting away 9. Namely, 9 being caft away, as often as may be, out of the Multiplicand, and likewife diftinctly out of the Multiplicator, multiply the two Remainders one into the other, cafting away alfo 9 out of what arifes, if it be large enough. The Remainder thence arifing, will be equal to the Remainder of the Product, after 9 is caft away therefrom, as often as may be, if the Multiplication prov'd hereby be rightly perform'd. For Instance, in the first Example of this Chapter, the Remainders will be 8, and in the fifth Example will be 6, as appears by the faid Examples here repeated. CHAP. VI. Of the Divifion of Integers. Do Ivifion fhews, how often the Divifor is contain'd in the Dividend; Divifion, whence the Number found by this Ope- alfo the ration, is called the Quotient. what. As The Dividend, feveral Numbers are plac'd, either and Qnoti Dividend thus, Divifor 3)6(2 Quotient, or thus, Dividend 6 Divifor 3 (2 Quotient. And the O peration begins from the Left-hand Figure or Figures of the Dividend, according to the third general Rule. ent. quot Part What is properly Divifion, is per- 2. form'd by the Quotient's fhewing, how An Alioften the Divifor is contain'd in, or may what. As be taken out of the Dividend; as 3)6(2, alfo Multi and when the Divifor does thus exactly on plication divide the Dividend, it is call'd an ali- ftraction, quot Part of the Dividend. Thus 3 and why requi2 are aliquot Parts of 6. But because it frequently happens, that the Divifor is not exactly contain'd in the Dividend, but after the Division there remains fomewhat of the Dividend therefore in order to know what the faid Remainder is, the Quotient must be multiplied fite to Di. vifion. 5. The first particular tiplied into the Divifor, and the Product wrote under the Dividend, and fubftracted out of it. Thus, 3 is 3)8(2 in 8 twice, and there remains ? 3 If the left-hand Figure of the Dividend be greater than the left-hand FiRule rela- gure of the Divifor, then there must be ting to Di- taken at one Time no more Figures (how vision, many foever they be) of the Dividend, than are equal to the Number of Figures in the Divifor. And if one Operation being perform'd, what remains of the Dividend, be equal to, or greater than the Divifor, than a fecond Operation is to be perform'd; and fo as many Operations, as there is Occafion. Thus in the adjoining Example, becaufe 8 is bigger than 3, there- 387(29 fore only 8 of the Dividend is to be taken the firft Time. Which being divided by 3, gives 2 for the Quotient, and leaves 2 over; which, with the other Figure 7 of the Di 6 27 27 vidend (plac'd by the Remainder 2) ma |