R U L 



It U I. 



I inch, and under it, in the fecond row, is 1 1 inches, the 

 anfwer to the queftion. 



3. Ufe of the line of t'wiber-meafure. This rcfembles the 

 former ; for, having learnt huw much the piece is fquare, 

 look for that number on the line oi timber- meafure ; the 

 fpace thence to the end of the rule is the length, which, 

 at that breadth, makes a foot of timber. Thus, if the 

 piece be 9 inches fquare, the length neceffary to make a 

 folid foot of timber is 21; inches. If the timber be fmall, 

 and under 9 inches fquare, feek the fquare in the upper 

 rank of the table, and immediately under it are the feet 

 and inches that make a folid foot. Thus, if it be 7 inches 

 fquare, 2 feet 1 1 inches will be found to make a folid foot. 



If the piece be not exaftly fquare, but broader at one 

 end than another, the method is, to add the two together, 

 and take half the fnm for the fide of the fquare. For 

 round timber, the method is, to girt it round with a ftring, 

 and to allow the fourth part for the fide of the fquare. 

 But this method is erroneous ; for hereby you lofe above 

 J-th of the true folidity. See Sliding Rule and Timber. 



Rule, Caliber. See Caliber. 



Rule, Everard's flidinj. 7 c o n 1 



■a /-• ,7 m n- r C See SLIDING Rale. 



Rule, Coggcjhali s fliding. ) 



Rule, Regula, alfo denotes a certain maxim, canon, or 

 precept to be obferved in any art or fcience. Thus we fay, 

 the rules of grammar, of logic, of philofophizing, &c. 



School philofophers diftinguifh two kinds of rules ; viz. 

 theoretical, or rules of knowing, which relate to the underltand- 

 ing, being of ufe in the difcovery of truth ; and pradical, or 

 rules of ading, which relate to the will, and ferve to direct it 

 to what is good and right. 



For the management and application of thefe two forts of 

 rules, there are two diftinft arts ; via. logic and ethics : fee 

 each refpcftively. 



Rules of knowing, regular feiendi, are fuch as direct and 

 affift the mind, in perceiving, judging, and reafoning. 



Rules of a/ling, regulit agendi, are thofe by which the 

 mind is guided in her defires, purfuits, &c. 



Authors are extremely divided abcut the regard to be had 

 to the rules of poetry fixed by the ancients, Ariftotle, Ho- 

 race, Longinus, &c. and admitted by the modern critics, as 

 BofTu, &c. fome contending, that they mutt be inviolably 

 obferved ; others pleading for liberty to fet them alide on 

 occalion. Rules, it is complained, are fetters ; rank ene- 

 mies to genius ; and never religioully obferved by any, but 

 tho'e who have nothing in themfelvel to depend on. Voiture 

 frequently neglefted all the rules of poetry, as a mailer who 

 /coined to be confined by them. 



Tne theatre has its particular rules, as the rule of twenty- 

 four hours, the unities of action, time, and place, &c. If 

 it he true, fays Moliere, that plays conducted according to 

 the rules d • not pleafe, but thofe winch are not, do, the 

 rules muft be naught. For myfelf, when a thing hits and 

 diverts me, I do not enquire whether 1 have done arniis, nor 

 whether Ariftotle'g rules forbid me to laugh. 



Ri lbs of philofophizing. Set Philosophizing. 



R 1 1.1:, in Arithmetic, denotes a certain method of perform- 

 ing particular arithmetical operations, as the rules of addi- 

 tion, fubtraftion, multiplication, and divifion ; which four 

 are called the fundamental rules of arithmetic, all other ope- 

 rations being dependant on one or more ot thefe. See Ad- 

 dition, Subtraction, &c. 



From the combination of thefe rules various others are- 

 derived, and, we mult add, many more than ought to be dif- 

 tinftly characterized. Thus, our writers on arithmetic give 

 us the rules of barter, Ample i-ntenll, brokerage, factorage, 

 rebate and dilcount, exchange, tare and tret, and a valt 

 variety of others, which are, in faft, only fo many example* 



in the rule of proportion (or, as it is commonly called, the 

 rule of three), and ought, therefore, to be included under 

 that gener.,1 term. 



At a time when arithmetic and geometry formed almoft 

 the only fubjefts of a mathematical education, long fpun-out 

 treatifes of arithmetic, and extenfive elementary works on 

 geometry, were at leaft excufable ; but fince the improve- 

 ments that have been made in analyfis, the two former fub- 

 jefts form but a very fmall part of what is neceffary to be 

 known, tor a perfou to have any pretentions to the character 

 of a mathematician ; and it is, therefore, atlomlhing that 

 writers on thofe fubjefts, particularly thofe on arithmetic, 

 have not thought of contracting their works, by coiidenfing 

 under one head a number of different rules, now given under 

 diftinft titles, and transforming others, fuch as pofition, alli- 

 gation, &c. to introductory treatifes on algebra, to which 

 branch they more properly belong. By a judicious arrange- 

 ment of this kind, the two fubjefts of arithmetic and ele- 

 mentary algebra might be very well condenfed into the 

 ufual fize of an arithmetic, and a boy be made to acquire a 

 competent knowledge of both fubjefts, in lets time than is 

 ufually employed in taking him through arithmetic only. 



Rule of Three, or Rule of proportion, by fome former 

 writers called alfo the Golden Rule, is one of the molt ex- 

 tenfive and ufeful rules in arithmetic, teaching how to find 

 a fourth proportional to three given numbers. 



The rule of three has commonly been divided into two 

 cafes, direS and inverfe, a diftinftion, however, which is to- 

 tally ufelefs, and which has been avoided by fome of our 

 heft modern writers ; it may not, however, be amifs to ex- 

 plain, in this place, the difference that was formerly under- 

 ftood between the direft and the inverfe rule of three. 



The rule of three direel, is when more requires more, 

 or lefs requires lefs, as in this example. If 3 men will 

 perform a piece of work, as, for inilancc, dig a trench 48 

 yards long in a certain time, how many yards will 12 men 

 dig in the fame time ? Here it is obvious, that the more men 

 there are employed, the more work will they perform ; and 

 therefore, in this inltance, more requires more. Again ; if 

 6 men dig 48 yards in a given time, how much will 3 men 

 dig in the fame time ? Here lefs requires lefs ; for the 

 lefs men there are employed, the lefs will be the work done 

 in the lame time. And all queitions falling under either of 

 thefe cafes are faid to be in the rule of three direft. 



The rule of three inverfe, is when more requires lefs, or 

 lefs requires more, as in this example. If 6 men dig a cer- 

 tain quantity of trench in 14 hours, how many hours will it 

 require for 12 men to dig the fame quantity I Or thus : If 

 6 men perform a piece of work in 7 days, how long will 

 3 men be in performing the fame work ? Thefe example? 

 are both in the inverfe rule ; for in the firlt, more requires 

 lefs, that is, 12 men being more than 6, they will require 

 kfi time to perform the fame work ; and in the latter, the 

 number of men being lefs, they will require a longer time. 

 All queitions of this clafs are faid to be in the rule of three 

 inverfe. Thefe two cales, however, as we before obferved, 

 may be included under one general rule, as follows. 



Rule. — Of the three given terms, fet down that which i* 

 of the fame kind with the anfwer towards the right hand ; 

 and then confider, from the nature of the quell ion, whethei 

 the anfwer will be more, or lefs, than this term. If the an- 

 fwer is to be greater, place the lefs of the other two termi 

 on the left, and the remaining term in the middle ; but if it 

 is to be lefs, place the greater si I lie two given quantities 

 on the left, and the lels in the middle ; and in either cafe, 

 multiply the fecond and third terms together, and divide by 

 the firlt term for the anfwer, which will always be of the 

 fame denomination as the third term. 



4 T 2 Mrt 



