R СНАР. Х. of Reduction. Eduction is the Turning of a Quantity Chap. X. I. of one Denomination, into an equi- Reductivalent Quantity of another Denominati- on, what. on. It is manifold. on of In The Reduction, which fhall be here 2. first spoken of, is that of an Integer of Reducti one external Denomination into ano- tegers into ther. It is two-fold, Defcending and equivaAfcending. lent Inte gers, two Reducti greater Defcending Reduction, is that, whereby fold. an Integer of an higher or greater Deno- 3. mination, is turn'd into an Equivalent of Firf, Defcending a lefs Denomination. And this is done Reductiby multiplying the Number to be reduc'd on, or the by fo many Units of the lefs Denomination of Inon, as are Equivalent to one Unit of the tegers of a greater Denomination. Thus, Pounds Denomi are turn'd into Shillings by multiplying nation, inby 20, Shillings into Pence by multiply-valent of ing by 12, Pence into Farthings by mul- a lefs Detiplying by 4: Because, 4 Farthings=1 Pence, and 12 Pence = Shilling, and 20 Shillings 1 Pound. So Yards are turn'd into Feet by multiplying by 3, and Feet into Inches by multiplying by 12: Because, nominati on. Chap. X. Because, 12 Inches 1 Foot, and Afcending Reducti lower De = Yard. I Foot, and 3 Feet 4. Afcending Reduction, is that, whereby Secondly, an Integer of a lower Denomination, is Reducti- turn'd into an Equivalent of an higher on, or the Denomination. And this is done by dion of In- viding the Integer to be reduc'd, by fo mategers of any Units of the lower Denomination, as nominati are equivalent to one Unit of the Higher. ons into Thus, Farthings are turn'd into Pence by an Equi- dividing by 4, Pence into Shillings by an Higher. dividing by 12, and Shillings into Pounds by dividing by 20; for the Reason before affign'd in defcending Reduction. So Inches are turn'd into Feet by dividing by 12, Feet into Yards by dividing by 3; for the Reafon likewife affign'd in defcending Reduction, valent of These two Sorts of Reduction are of The Ufe of Ufe in Multiplying or Dividing Integers the fore of feveral external Denominations. For duction, if the Multiplicator or Divifor consists of illustrated. many Figures, then each Operation is going Re best perform'd by Reduction. For Inftance: Suppofe there were an 120 Perfons, to each of which was to be paid 10%. 12 s. 6 d. 3 4. And it is required to know, what Sum will pay them all ; that is, what Sum 10. 12s. 6d. 39, multiplied by 120, amounts to. Now in order to multiply the Integers given in Pounds, Shillings, Pence, and Farthings, they they must be all reduc'd into One, viz. Chap. X. the lowest Denomination, i. e. Farthings. Which, according to the Method of defcending Reduction defcrib'd, §. 3. is thus done. It being thus found, that 107. 125. 6 d. 3 q. is equal to 10203 Farthings, I multiply 10203 by 120, the Number of Perfons propos'd. 10203 Farthings. 120 204060 10203 1224360 Farthings. Hence Chap. X. Hence, I learn, that the Sum requir'd to be known, is equal to 1224360 Farthings. It remains therefore to turn the faid Farthings into Pounds, Shillings, and Pence, by afcending Reduction. Which, according to the Method of the fame defcrib'd, S. 4. is thus. 93 Chap. X 55 40 150 140 107 100 7 Shillings. And thus it is found at Length, that 6. to pay Iol. 12 s. 6 d. 39, to each of The Proof 120 Perfons, I must have in all a Sum of of the fore12751. 7 s. 6d. And whether no Error going Reduction.. is committed in the foregoing Operati ons, may be tried by working again Backwards, i. e. by dividing 1275 1. 75. 6 d, by 120, and feeing if the Quotient will be (as it ought) 10l. 12 s. 6 d. 37. In order whereunto, 1275 1. 75. 6 d. must be reduc'd all into Pence, Thus, 1275 |