A treatise of Algebra. iji

Terms of a decreasing geometrical Progression, the Sumof that Progression infinitely continued, or the Value ofp, will, according to this Supposition, be truly repre-a z e z a 1 !

fented by-- or-- (see p. 72 .) whence we

ae — be z a — be

( pd V

—- I

a 1 -j- pbf

pb

Now though the Suppontion, by virtue

a -f- ~

1 a ■-

whereof this Conclusion is derived, is not strictly true,yet when the Value of e is small, which is here supposedto be the Case, the pirror arising therefrom will be very

a z e

inconsiderable, since the Expression- takes in the

a — be

two first Terms of the Series intirely and participates ofthe rest. But if you would have a Theorem whichshall take in the three first Terms,"fa’s. then let the said

are . - , b z e*

Expression-, cr it's E^ual qr -s- He 2 -j-fa’s. be

a — be , a

subtracted from the given Expression ae -j- be 1 -j- rr3,' ' hz

(3c. and the Remainder c -x *3, (3 c. will Ihew how

a

a z e , _ a z e

much-is below the Truth ; that is-[*

a — be 1 a — be

b z J 2

f- X e3, £sV. — p But, since c — — x *3 13c.

a a

a z e

appears to be very small in respect of-, and e is

a — be

p p

found above to be nearly —-or — ( which last

Value is sufficiently exact for our present Purpose) letp z

be substituted instead of f 2 , in that Expression, andI, a our