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A Treatise of Algebra.

7<j* — 12 ax by the Sum of these two Quantities, andtherefore equal to 20a* -f- <$bc — 7<2* — 12a* ^bc -f-5a 1 , where it appears that the Signs of the three ladTerms are all contrary to what they were given in theSubtrahend.

And the fame Method of Reasoning holds equally inany other Cafe.

Here follow more Examples of Subtraction.

Take 5a*— 2 ca d -f- from 8a* -j- 4 ca — zd

— 3 b x and there will remain za* -f- bca — 3 d —3L*.

_ .- a-\-b , z a 1 -

Take 3V 2a*— Z~~Z ■ kfom 7V 2 ax—

e+b. 5 a»

a — b a z -\-h z

7 + r,“ ;; and there will remain Wax 4- vb __ T ~a'-fA

Take

a ~ , , 3

”7--— za -j-from <a — —~-

V^a 1 + * 6 */a* -f

4 - c and there will remain 7 a — -7^-—— 4 - c—

✓<** +b

_ ,— -JE -— .— ' 2a*

Lastly take vza-** — ZV za*-s- — -=■-■ f rom

___ V 2 e*-}-x*

W 2a 2 — 3\/2a* — ** -fa, and there will remain 8/20*- 2a*

— 4V2a*— x z -—- 4 - s.

" v 2a*-s- x*

Lefore I conclude this Section, I must caution myReader to observe, that, in Addition and Subtraction,all Surds whatever are to be treated as simple Quanti-ties, because their Terms can neither be separated norunited into one by the Addition or Subtraction of otherQuantities, though like and under the same radical Sign.Thus, for Instance, if s/ax was to be added to */b—axthe Sum is to be expressed by b*—ax -f- •/ax, and notby */~b : For this last Value, though it may seem true, isnot the fame with s/b — ax^-'/axi to shew which,let us suppose bz= 100, a — 9 and x=. 43 and then s/ax

— ^36 — 6 and \tb—ax — ^64 = 8; and consequently*/b — ax »i/ax=. 8 + 6=14; but vb is only =10, and therefore less than the Truth by 4.

SECT.