Page:Encyclopædia Britannica, first edition - Volume I, A-B.pdf/465

 A It I T H M E T I C K. 3% are extremes, and of the fame kind, viz, both oP by the firH: term, and the quot 15 is the anfwer, of the terms them men. fame name with the middie term, viz. L. Sterling. And becaufe the divifor happens to be the extreme in It is obvious that the an- Men. days men, fwer muft be lefs than the mid- 16 : 12 : : 8 the fuppofition, the proportion is direft. Quest. 3. If 13 yards of velvet coft L. 21, what dle term; for 16 men will do 8 the work in fewer days than 8 will 27 yards cod at that rate ? men; and therefore, by Rule 16)96(6 days. Anf.r. l. r. # II. the greateft extreme, viz. 96 If 13 : 21 :: 27 Rem. 4s. 16, is the divifor ; which 27 12 place on the left hand, and the <P) other extreme on the right, as 13)48(3 d. M7 39 When there hap- directed in Rule III. Then multiplying the fecond and42 — pens to be a remain- third, and dividing their produdt by the firft, the quot 13)567(43!,. Rem. 9 d. der, it may be redu- comes out in days; that is, of the fame name with the 4 ced to the next in- middle term. 52 — ferior denomination, And becaufe the extreme found in the demand hap13)36.(2^ and *the operation pens to be the divifor, the proportion is inverfe. 47 26 continued, as in the Quef. 2. How much plulh of 3 quarters wide will 39 — margin ; and in this line a cloak that hath in it 4 yards of 7 quarters wide ? Rem. 10 f. cafe the quot will' Rem. 8 L. yds. 9. confirt of two or Here the arrfwer mull be : 4 :: 7 20 greater than the middle term; more parts. T for the, plulh being narrower 13)160(12 s. than the cloth of which the 3) 28 (9yards. Anf.. 13— cloak is made, will require 27 L. s. d. r 30 Jnf. 43- 12. 3 24t more length. 26 Queft. 3. If 36 yards be a rood(1)of mafon-work, at 3 feet high, how many yards will make a rood at 9 feeta Such remainders are always of the fame name with high ? the preceding part of the quot. Thus, the firft remainFeet. yds. feet. der 8, and the firft part of the quot 43,-are both pounds ; 9 : 36 :: 3 and the fecond remainder 4, and the fecond part of the 3 quot 12, are both {hillings; and the third remainder 9,, and the third part of the quot 3, are both pence; and 9)108 the. fourth remainder 10, and the fonrth part of the quot 2, are both farthings. Anf. j2 yards.. As we have no money under farthings, the laft remainder cannot be reduced any lower;' fo there remains Sect. II. The Compound Rule of Three. 10 farthings to be divided by 13 ; that is,‘there is wanting to complete the quot, the thirteenth part of: 10 far- The Compound Rule of Three, from five given numthings, or the thirteenth part of every remaining farthing; • bers finds a fixth, or from feven given numbers finds an that is, ten thirteenth parts of one farthing; fo you fet eighth, or from eleven finds a twelfth, <bc. the remainder 10 aboye, and the divifor 13 below a line This rule eafily and naturally admits of fubdivifions, drawn between them, in the form of a fraftion, of which which, from the number of the terms given, may be dethe remainder ia the numerator, . and the divifor the de- nominated the rule of Five, the rule of Seven, the rule of Nine, the rule of Eleven, nominator. Queftions in the Compound rule of three are alfo refolved into two parts, viz. a fuppofition and a demand. II. The- Simple Rule of Three Inverfe. If five terms be given, three- of thefe are always found Quest, i. If 8 men can do a piece of work in 12. in the fuppofition, and two in the demand; if feven ■ days, in how many days will 16 men do the fame ? terms be given; four of thefe are in the fuppofition, and In this queftion the fuppofition is, If 8 men do a piece three in the demand; if nine terms are given, five of of work in 12 days, and the two terms contained in it thefe are in the fuppofition, and four in the demand; if are 8 men and 12 days: The demand lies in thefe words. eleven terms be given, fix of thefe are in the fuppofition, In how many days will 16 men do the fame-? and the- and five in the demand, <bc. only term contained in it is 16 men. and demand being dillinguilhed, proThe number fought here is the days in which 16 men ceedTheto fuppofition flate the queftion; that-is, to put the terms in will'do the work, and the term in the fuppofition of the due order for operation, as the following rules diredh feme kind is 12 days; wherefore I place 12 days as the Rule I. Place that term of the fuppofition which is middle term, according to Rule I. the two remaining of the fame kind with the number fought, in the middle. The-:
 * Rem. 4 s.