EXAMPLE III, Of Numbers of feveral (external) Denominations, viz. of Money. EXAMPLE IV, Of Numbers of several Denominations, viż. of Measure. The beft or fureft Way of proving, 2. whether any of the fore-going Examples of the Proof of be rightly done, is (according to the 4th Addition, general Rule) by Subftraction, as fhall be by cafting fhewn in Chap. 4. And this Proof is u- away 9, 41 often as niverfal, holding Good in refpect to may be Numbers of feveral (external) Denomi- done. nations, as well as of One. As for Numbers of one (external) Denomination, the Addition of them may be proved with good Certainty enough another Way; namely, having caft away 9, as often as you can, both out of the Numbers given to be added, and alfo out of . (*) The Sum of the Days do amount to 552; of which 365 make up a common Year, and the remaining Days will be 187. If the Sum of the Days arife to four Years, then 366 Days must be allowed for one (viz. the Leap) Year. Ċ 3 the 3. the Sum arifing from thence, if both the Remainders be the fame, it may be look'd upon as fufficiently proved, (at leaft in Matters of no important Concern,) that the Addition is rightly perform'd. For Inftance, 9 being caft away, as often as you can, out of the two Numbers given in Example the First, there will remain 1, or One; and likewife 9 being caft away, as often as you can, out of the Sum, there will remain One. Whence it may be look'd upon as (†) fufficiently prov'd, that the Addition is duly performed in the faid Example. In like manner, 9 being caft away, as Another often as may be, both out of the NumExample of the Jame bers given to be added in Example the Sort of Second, and alfo out of the Sum, the Remainders of both will be the fame, viz. 2. Whence it may with (†) Certain Proof (tt) The Reason why this Sort of Proof is not infallibly certain, (as is the other by Subftraction,) is, because the Remainders in this Cafe will both be the fame, as long as the Figures be the fame, though they be never fo much alter'd as to the Places of them; and confequently, though the Numbers be different from the Numbers given, or the Number to be found. As will appear by comparing the Example here fubjoin'd with Example the Firft. 57896324102 6086417841 ty enough be inferr'd, that the Addition is duly performed alfo in Example the Second. And fo much for the Addition of Integers, or whole Numbers, according to figural Computation. I. CHAP. IV. Of Subftraction of Integers. Subftracti. Subfraction takes the less Number given on, what. 2. lar Rule out of the Greater, and fo finds the Difference between the two Numbers given, or (as it is otherwife called) the Refidue or Remainder or Excefs of the greater Number above the lefs. The general Rules are all along to be A particu- obferved. Befides which it is to be obrelating to ferved alfo, that the greater Number is Substracti- to be plac'd regularly above the lefs. on. 3. Moreover it is to be obferved, that Another although in (*) common Arithmetick the particular Number to be fubftracted, taken all toting to Sub-gether, must be always less than the upAtraction. per Number, out of which it is to be Rule rela fubftracted; yet it often happens, that a Figure (one or more) of the upper Num ber may be less than that Figure of the lower Number, which is to be fubftracted from it. In which Cafe, the faid lefs Figure is to be increafed by adding thereto One taken from the next higher (i. e. following) Denomination, and turn'd in (*) In Algebraick Subftraction this is not neceffary, as may be feen Chap. 9. to |