Chap. 14. Resolution of Arithmetical Questions-) &c. 6 3

Chap. XI V.

Various Arithmetical Questions Algebraically rcjvwsi* , wrjerwymost of the Rules hitherto delivered are exercis’d , in the In -vention and Resolution of pure or simple Equations .

I-Eolations may be divided into two kinds, viz. Adsected or^Compounded. <2^ <

sniohr* ^ P ure 0r ^ lm P^ e Equation is of two kinds, viz,. First, when the quantity QfcttJb . 2when th ex P re ^ b y a simple Jtloot only, as a-, as in this Equation, 6<®== 12 : secondly,thicP he .st uant ‘ i y fought is exprest by a simple Power only , as aa, or a«a,tk c. as in

Equation, 34^ — 24 ; likewise in this, 2 aaaa '•= 3 2 , and such like. -

^ 1E An adfected or compounded Equation is that, wherein there are two or more QrC-e/b, 3^ierent Degrees orj Powers of the quantity sought; as in this Equation , aa 6 ar- z 7 , where aa and a express two different Degrees or Powers of the quantity (ought,e one signifying a Square, and the other its Root or side: also in this Equation,aaa -\- 6 aa — 2 a — 28, there are three unlike Powers or Degrees of the quantity (ought,t0 Wit, aaa, aa, and a.

IV. The Invention and Resolution os Pure or Simple Equations is copiously iliu- Q/&. C/tr:strated by Arithmetical Questions in this Chapter, as also in the second and third Books

oi my Algebraical hlements . and the Resolution of Adfected or Compound Equationsin Numbers is handled in the is, ■ 6 , and 17. Chapters of this Book, as also in the 10, andj 1. Chapters of the second Book. But how Algebraical operations are applicable tothe solving ok Geometrical Problems, I shall shew in my fourth Book of AlgebraicalElements.

V. When an Arithmetical Question is proposed, the number sought must first of all q/saAA'- Soth™ 11 ^ ° r ^PP 0 ^ t0 be known; and you may represtnt it by the litter -r, or any

er Vowel-, you may likewise represent the given numbers by Consonant-, as, b,c,d.Scc.

c 'j*#? ^ CS ^ ar . tes P utS forgiven Quantities the former letters of the Alphabet, as, a > b,

rentes bul tor Quantities fought the latter letters, j,x &c. Then With the letters

sobtractin 11 ^ "umbers given and sought, an orderly process must be made, by adding,

at length^ ' multiplying or dividing, &c. according to the import of the Question, until

°f it amfs ^^"on be sound out between the number sought or some Power or Powers

a Pure or Simole F* - r or numbers given: Lastly, when the Equation so found out is

in the foresoin?, ^^'oo,rhe number fought may be discovered by some of the Reductions

Pounded fE a r> r f 3 and 13. Chapters - but when the Equation is Adfected or Com-

the R'solwm thereof beUgs either to the 3

tlc I0 >and it.Chanters,i.»r ‘

, < Chapter of this first Book, or

...._ tmiu w u.c 1 5. v^napici v

Chapters of the second Book. . , . . . pn j

VI. In the Resolution of every Question , I proceed from the beginning toFy steps numbred in the Marpin bv i a 3 4 ,1 And because Numeral ^Alge-

,S more easie for Learners than the Literal , (though not soue u Operation be-dsore given in Sett. 8. Chap. , to I have in stony Questions exprest the Operation De

on png to every step in both kinds of Algebra, that the of* 3 . /Thekffer numberbo in the second step of the Resolution of the followingfirstQuestion,^^ er n “

sovigbtis exprest by Numeral Algebra thus, *6--; but by. LtterdAlgb,rat hr

Also, in the fourth step, the Equation by numeral Algebra ls — 26 _ 8 , but byliteral Algebra it is 2 a — b~c. „ , , .

VII When an Equation is found out in any of the following Onions take it

for granted that the Reader knows how to reduce it, if need be, according to the Rules ut

t 1 he , i « re g° in g r r,t r,and 13. Chapters,.that I may avoid tedious repetitions of wi

hath been already explain’d. These things premised, I proceed to the Queitthemselves.

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