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Addition and Subtraction. 1:
F they be Homogenal, add or fubtract the ra
tional Part, and to their Sum or Difference join the Surd.
A D D I I IO N.
Ι Τ Ι 7V xy 7xV@c
xVaa+cc 24V xy
3*V ac 4xV aa+cc
SU B T R A CT I ON.
12xV CC 5yv aa+cc
2d. If the Surds be Heterogeneal, add or subtract according to the Signs.
1 + 213iv xy+v nx 4*Vaa+387**
F the Surds be Homogenal, take away the Sign
and it is done ; so the V XyXV xy=xy and V xx+ aax V xx+aa = xx+aa.
If rational Quantities be joined to the Surds, then multiply the rational into the rational, and the Surd into the Surd, and join the Products together.
Divison of Surd Quantities. F the Quantities are pure Surds of the same
Kind, and can be divided off, without leaving a Remainder, divide thein, and to their Quotient prefix their radical Sign.
EX A M P L E.
V xx YY
If Rational Quantities are joined to Surd Quancities of the same Kind, divide the Rational by the Raci nal, if it can be done, and to the Quotient join the Quocient of the Surd, divided by the Surd, with its first radical Sign.
E X A M P L E S. 3dx/xyn
20000 Involution of Surd Quantities.
HEN the Surds are not joined to raticWA
nal Quantities, they are involved to the faine Height as their Index denotes, by taking away their radical Sign.
When Surds are joined to rational Quantities, involve the rational Quantitie: to the fame Height as the lodex of the Surd denotes; then multiply the involved Quantities into the Surd Quantities, after the radical Sign is taken away, as before.
The fint brings each side of the Equation to an entre Piaction.
Tie fecond, brings Equations into Integers, by notipiying al:ernately the Numerator of each Side into the Denominator of the other.
The third, brings by Transposition the several M.mbers of the unknown Quantities to the fame Side of the Equation, (viz.) to that Side, which after Tranfpofition, will render them Afirmative.
The fourth, transposes all loose Quantities from the side of the unknown, to the other side of the Equation.
The fifth, finds the unknown Quantity, by dividing the whole Equation by iis Coeficient.
E X A M P L E.
5 2 X 3
12x + go 2x + 36 =
5 3 X 5 14 10x + 180 = 12x + go 4 10x 5 130 = 2x + go
5 - 90 6
90 = 2x
ܐ ܀ 6
17 45= *
+ 5 = * + 2
6 2 X 4 3
20% + 48 3* + 20 =
18x + 120 = ?Ox + 48 4
5 120 = 2* + 43 5-4 8 16
72. 2x 71 36 = x
N. B. The three Dots in the Margin fignify Consequently.