7. How to fubftra&t feveral If more than one Number is to be subftracted out of the fame greater Number, then it is expedient to add together all Numbers the Numbers to be fubftracted into one from One. Sum, and fo to fubftract the faid Sum. For Inftance. 8. of Subftra Remains 1200.14:06.2 And this laft Example, compar'd with Example III, both of Addition and Sub. ftraction, is a further Evidence, how the one is proved by the other. It remains only to obferve, that the The Proof Subftraction of Numbers of one (exterction by nal) Denomination, may be prefum'd to cafting be rightly perform'd, if the Remainder away 9. of the greater Number be the fame as the Remainder of the other Numbers, (viz. the Number or Numbers to be fub. ftracted, and the Refidue) 9 being caft away away as often as may be. Thus as to 10992221893 :...I 1134587692 And thus much for the Subftraction of Integers. CHAP. 71. I. CHAP. V. Of the Multiplication of Integers. Malcipli- Multiplication is in Reality no other cation, than a different Sort of Addition : what. for to multiply one Number by another, is nothing elfe, but, to add one Number given to it felf, fo often as the other Number given directs. Thus 4*3=4+4+4=12% 2. cand, Mul The Number added to it felf or multiMultipli plied, is called the Multiplicand; the tiplicator, other, the Multiplicator or Multiplier; and Pro- (both thefe together, the Factors ;) and duct,what the Number arifing from the Multiplicátion, the Product. particular 3: Of the two Numbers given, either may The first be the Multiplicand or Multiplicator; Rule rela- (for the Product will be the fame, viz. ting to Mul 4*3=12=3*4;) but it is better and fo tiplicatimore ufual, to take the lefs Number for the Multiplicator, and to place it under the Multiplicand. on. 4. The fe ticular If the Multiplicator confifts of more than one Figure, then the whole Multicond par- plicand is to be added to it felf, first as often as the Right-hand Figure of the Multiplicator fhews, then as often as the next Figure of the Multiplicator fhews, Rule. and and fo on. Thus 421×23, is equal to 4213, and alfo 421×20. . The Product arifing from each Figure Rule. 5. of the Multiplicator, multiplied into the The third whole Multiplicand, is to be plac'd by it particular felf in fuch. manner, that the first or right-hand Figure thereof may stand under that Figure of the Multiplicator, from which the faid Product arifes. For Instance: The Reafon of fo placing the righthand Figure of each particular Product, is in Conformity to the first general Rules forafmuch as the right-hand Figure of each Product, is always of the fame Denomination with that Figure of the Multiplicator, from which it arifes. Thus in the fore-going Example, the Figure 2 in the Product 842, is of the Denomination of Tens, as well as the Figure 2 in the Multiplicator. For 1x20 (i. e. the of 23)= 20, or 2 put in the Place of Tens, or fecond Place.) 6. If either of the Numbers given have The fourth one or more Cyphers at the Right-hand, particular the Multiplication may be perform'd with Bule out taking Notice of the Cyphers, 'till the Product of the other Figures, be found: To which are to be prefixt, on the Right-hand, the Cyphers before not taken Notice of. For Inftance : 7. If the Multiplicator has any Cyphers The fifth intermixt with its other Figures, they particular Rule. need not be taken Notice of at all. Thus, 8013 5006 48078 8. 40065 40113078 In Multiplication it is of great Ule, Of the Mul- readily to know what is the Product of #plicati02 Table. any two of the nine Figures, otherwise called Digits. To which End there is drawn up a Table, from its Ufe, called the Multiplication Table. This is fo con triv❜d, |