16 A Treatise of Algebra.

In the Examples hitherto laid down all the Productsare affirmative, the Quantities given to be multiply’dbeing so; but in those that follow some are affirmativeand others negative, according to the different Cafes spe-cify’d in the latter Part of the Rule j of which the Rea-sons shall be explained hereafter.

The Product of tox by — 11 y, or of — zo* by > i y is

_ 3 _

— 220 xy. Also the Product of 3 t/a-^b by "J/ax is

b x J ax ; for the Prdduct of / a-\-b by t/ax_ 3 —

is t/a -f- b x /ax ; which multiply’d by 21, the Pro-duct of the Coefficients gives 21 x/a-\-b x/ax or zi

- 3 _

t/a -fix sax.

Moreover the Product of — "I 0 / 0 * + x z by —

3 _ _ 3 -

6 b/a z — x z is 42 ab/a z -\-x z x/a z — * 2 j for the Pro-

- 3 -

duct of the Species is here a/a z -\-x z x b/a z — * 2 ;which, by what is proved in the preceding Lemmas, is

- 3---

equal to a x b x /a z x z X /a z — x z or ab/a z -s- x z3_

x t/a z — x z (for the Surds may be considered as simpleQuantities, represented by single Letters) and so in otherCafes.

2°. When a FraWton is to be multiply’d by a Quantity•which is not a FraSiion, the Product will be had by mul-tiplying, the Numerator of the FraSiion by the given Mul-tiplier and making the Produft a Numerator to the givenDenominator.

Thus the Product of ° by c will be —; and that ofb b

3 “ by 2 td will also that of by -

b b c -J- a

T/ax will be l f ab / ax . ■ lastly, that of 2 ab by ■

c-\-d Va z -\-x~