(3) 
couftt of in my EngUPf Algebra j and /cmiewhat more fully in 
the L^fi» Edition: where 1 give an Jiccount alfo of Mr. Rap&^ 
fin's Method; which^neelnot here repeat, becaufeit is to 
be feen there. 
Since which time, Monfieur De Vagny hath publifted his 
Method of Approximation^ principally for fingle Equations, 
or Extra<aing the Root of a (ingle Power. 
And Mr. HaUey bath iince improved this Method, with a 
further Advantage f efpecially as to AfFeded Equations. 
But I need not repeat either of them, becaufe they are 
both publi/ht. That of Z)^ L'^^w/ in a Treatife by it (elf; 
and that of Mv.HaUey^ in tho PbtloJ. Tranfa^. Numb. 210, 
for the Month of May^ 16^^, 
Thefe may all, or any oi them, be of good ufe (each in 
their own way) for making more fpeedy Approaches, and 
by g eacer I/ aps^, in many cafes, than Viet<i\ Method (pro- 
fecu.ing (he Exnadion in Decimal Parts ) purfued and impro- 
ved by Mv.Ougkred and Mv. Harriot of our own, and by o- 
the.'S abroad ; e/pecially as to Sin pie Equarions^ if we (iip- 
pp(e (uch Extradions to be pursued to the full exrenr. 
As lor . inliance, if we would Extra<Sl: the Root of an im» 
per fed: Sur(()I id^ (or a Power o\ five Dimenfions ) to hav^ 
its Rcsot true as far as tha lixth place of Decimal Parts. In 
order to this, we are to add (or (uppofe to be added) (ix 
Pundradonsof Cyphers, (or, fix times five Cyphers, that is 
Thirty Cyphers) beyond the place of^ Unites in tlie Number 
propofed. If now we puriue the whole Operation to the 
utmoft of thofe Thirty places, the Work would be long and 
tedious. 
But if we make ufsof Mr. OAf^^/r^/s Expedient, (forMuI- 
tiplication, Dlvifion, Extraction of Roots, and other like 
Operations,) by neglecting fb much of this long Procefs, as 
is afterward to be cur off and thrown away as ufelefs, (which, 
I think, is generally pradifed) the Work will be much ab- 
bridged, and the Advantage of the other Methods much lefs 
confiderable. 
That is. If (for afcertaining the fixth place of Decimal 
Parts) we add fix Cyphers (inftead of thirty) and one or 
two more ( the better to (ecure what from the confequent 
places may in theOperadon be tranfmitted hither ;) and pur- 
fue the Operation thus far, negleiSting the following places^ 
(which 
