AL'L' 



' IF botli Ri-ealcr and kffer extremes he not plural, tlay 

 may be linked lo differently that fcvcral differences may be 

 taken and a variety of anfwers may be made to the queftion, 

 yet aU true ; but if one of the extremes be llngJe, there can 



h< but one anfwcr. ,,,.„- r . 



The numbers being linked, take the difference of each 

 from tlie mean or common price ; and place this difference 

 ajraiiift the luimber it is linked to, alternately. 



Everry number, hnked with more than one, muff have all 

 tlie differences of the numbers it is linked to, fet againft it. 



Thefc differences rclolve the queftion, when the price of 

 every one of the ingredients is given without tlieir quanti- 

 ties : and the demand is, to mix them fo as to iell a certain 

 quantity at a mean rate. 



Exalnble I. A perfon would mix wheat at 4^. a bulhel 

 with rye at 2s. 8</. fo as to fell the mixture at 3^. 6d. a 

 bulhel,' how much of each mull he take ? 



Thus : (1. 



48110 bufliels of wheat.j A„f,,.„. 

 ^ 32I 6 bufliels ot rye. j 

 Esamph 2. A vintner would mix Malaga, at Js. 6?/. a 

 gallon, with Canary at 6.r. 9</. and white wine st 4--. 3^/. fo 

 as to fell the compound at 5s. 2d. a gallon : what quantity 

 of each muft he take ? 



d. 



00 -"x 



62 



"y 

 5^^ 



I ! 

 I I 



19 



1 1 Malaga, I 

 1 1 Canary, |. Anfwcr. 



^ .28 47 VHiite wine. ) 

 N.B. The difference between 62 and 51 is 11, which is 

 fet againft 81, and alfo againft 90: the difference between 

 62 and 81 is 19, placed againft 51 : the difference^between 

 62 and 90 is 28, which is alfo fet againft 51. Th-.-ii 19, 

 added to 28, is 47 : and therefore the differences required 



are II, II, 47- , , . ^ . , 



But, in .AlUgattoii partial., when the quantity 01 one, witli 

 the price of all the ingredients, is given, and the demand is 

 to know the quantities of the other ingredients ; then, the 

 rule of three is to be ufcd. 



Say, as the difference ftanding againft the price of the 

 given quantity is to the given quantity, fo are the feveral 

 other differences to the refpeftive quantities required. 



Example 1. If it be defired to mix 10 bufhels of wheat, 

 at 5^. with rye at 3s. 6d. and barley at 2s. \d. fo as to fell 

 the mixture at 4J. per bufliel, how much rye and barley mull 

 be taken J 



r Wheat, ^o''^ 



48 ] Rye, AzJ] 



I Barley, 28--^ 



6.20 

 12 

 12 



26 



12 



12 



White wine, il— ^ 



12 

 21 

 18 



9 



21 



12 



ALL 



"Tlien, the quantity -of Canary being given, fay, by the 

 f:; iT. irethod 21 : 24 : : each difference : its rcfpeftive quan- 

 tity : that is, 



1 3i gall. Malaga, 

 As 7:8:: -I 18 : 2C4 Sherry, 



White wine. 



Then 26 : 10 : : 12 : 4-^- bufnels of 176 and of barley. 

 Example 2. How much Isfalaga at -,i.(id. a gallon, Sherry 

 at 5^. white wine at 4J-. ^d. muft be mixed with 24 gallons 

 01 Canary at 6j-. ^)d. fo that the whole may be fold at 6j-. 

 per gallon \ 



r Malaga, 



\ Canary, 



72 -J Sherry, 



(. White wine, 



Or thus : — 



Malaga, ^^'V. 



Canary, ^^A 1 



Sherry, 6ciJ J 



f 1 2 : 13! 

 4 18 : 2oi 



I 9 : lof 



Or, ty the 



As 12 ; 24: : p' : 

 Or .: 2.:|J: 



1 



Anfwc 



Or, ty the fecond method : — 



42 gall. Malaga, 



18 Sherry, 



36 White wine. 



And, in Alhgahon total, when the price of eveiy ingre- 

 dieu". Is given, without any of their quantities, and the de- 

 mand is to make up a certain quantity to be fold at a mean 

 rate ; then all the differences added together will be the firfl 

 iTun-.ber in tlie nile cf three ; the whole qui.ntity to be 

 mixed, the fecond number ; and each difference apart, the 

 feveral third numbers ; snd fo many forts as are mixed, fo 

 many operations muft there be of the rule of three. 



Example I. A goldfmith would mix gold of 24 carafts 

 with fome of 21, and with another fort of 19 carafts fine, 

 and v.-ith a due quantity of alloy, fo that 190 ounces might 

 be of the fiaenefs of 17 caiafts ; how much of each loil 

 muft be taken >. 



iJ. B. Alloy is reckoned at o caraft. 



_., , C 17 : ?o^-'- of the three forts of Kold. 



Then 64: 190:: jj^.^sllofailoy. 



Exami)le I. A mixture of wine is required to be made of 

 130 quarts from 5 forts, whofe prices are 7^. 8^/. \cd. 14^/. 

 and I ?(/. a quart refpettlvely, and the whole is to be fold 



of each is neceffary ? As 



and ijt/. a qua: 



at 12(7. a quart; how much ot eacU is nece 



there are five quantities, they will admit of feveral alterna' 



tions. 



F'lrjl Method. 



r 



I 



12 ^ 



2 

 3 



Second Method. 



r i5-\ 



12 <i loj) ) 



L 





Method. 



[ 



2.4.5 

 2.4.5 

 3-2 



3-2 

 3-2 



II 



1 1 



5 

 5 



37 



The operation by the laft method is as follows 



r 1 1 : 38if quarts of wine at 15^/. and J^d. 



1 5 : «7tf 



21 ■■ »30 



at lod. 8(/. and jJ. 

 The 



