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# Title: [Johannis Wallis S. T. D. Geometriae Professoris Saviliani, in Celeberrima Academia Oxoniensi, De Algebra Tractatus; Historicus & Practicus. Anno 1685 Anglice editus; Nunc Auctus Latine. Cum variis Appendicibus; Partim prius editis Anglice, Partim nunc primum editis] Johannis Wallis S. T. D. Geometriæ Professoris Saviliani, in Celeberrima Academia Oxoniensi, De Algebra Tractatus; Historicus & Practicus. Anno 1685 Anglice editus; Nunc Auctus Latine. Cum variis Appendicibus; Partim prius editis Anglice, Partim nunc primum editis (shelfmarks Leibn. Marg. 100:1/2, Stück 2; Leibn. Marg. 100:1/2)
# Folio 394, page id 851708439:0418
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l L G E B K
1D. X
RE SOL V FFO.
Fermini omnes, ex eodem aequationis latere consistentes, aequentur nihilo, et ipsa-
rum y ec y diguicates (s opus sic) exalcentur rel deprimantur, sic ur carum indi-
ceo nec alicubi negaciri sine, nec tamen altiores quam ad hunc effectum requiri.
tur; _ SIE L ~ terminus intimae dignicaris corum qui neque Der y neque Per ejus
Auxionem ; neque per earum dignicacem quamvis mulciplicantur. Sic L 2 qe y ter.
minus alius quilibet, ee omnes ordine terminos percurrendo collige ex lingulis seor-
sin numerum . l te sic, utcoc habeas ejulmodi numeros quor sunc cermini.
Florum numerorum maximus rocetuer, ec ~ eric dignitas primi termini SerieiPro
ejus coetticiente ponatur a, ee in xquatione quae resolvenda dicitur sexibe a s prOy, et
va Z = = prOy; ac termini omnes resultantes in quibus 2 ejuldem est dignieatis
ac in cermino k2, sub propriis signis collecti, ponantur aequales nihilo. Nam haec
aquatio debire redicta dabic coetticientem a. Sic habes a ~ cerminum primum Sc.
riei.
OPER A F IO S F CV N D A.
ero reliquis omnibus hiujus seriei cerminis nondum invenris pone p, et habe.
bis Aquationem y = a _ + p, e inde eriam per Prob. L. A quationem y = va 2 - 
LP. In resolrenda, proy de y seribe hos eorum ralores et habebis Resolvendam
noram, ubi posticium praeltat ipsiusr: et ex hac Resolrenda primum exerates
cerminum Seriei peodem modo aique terminum primum seriei cociusy = a ~ = P
ex Relolrenda prima excraxisti.
OPFRATIO TERETA ET SEQDENTES.
Dein tertiam Relolvendam eadem ratione invenias acque secundam invenisti, de
ex ea terminum tertium Seriei corins extrahes. Ex similiter Resolvendam guartam
invenies, ee ex ea quartum Seriei terminum, et hic in intinitum. Series aurem AC
invena erit radix Aiquationis quam exiratiere oporcuit.
E. Z E M P L V M
Ex Aquatione g2 2 = 2 y - d d 2 2. + d 2 V =0, excrahenda sic radix y.
Ponc B = L, e Aquatio cradet ge - 2 y - d d f 22 = 0, quae est Resolvenda.
sam vero cerminus intimus in quo nec y neque y reperitur, ett a d, qui iphi k2
aquatus dac a = 0. Ferminis relignis p, = 22 y pone J2HaB qualem successi-
re de inde in primo calu habebis p. = 0, a. = 2, B = 0, et in iccundo v. = 2.
a =0 _B = F. Ec hinc =  F  EC in primo casu o, in secundo = +. Unde
a.f
vell o, et a3 der a = LTunc a A O; quarum ultine dua a e 0 in Retolrenda
PEOy D i scripie, produenne aa. f. 0 ~ = dd. L d2; de cermini a a de - dd in
quibus index dignicatis & Mt a seu 0, posici aquales nihilo danc a = d. Unde pri
mis Seriei terminus a 2 cradic d.
OPERATTO SECONDA.
Proterminisreliquis pone p, et habebis aequationem y = d. + p, et inde (per
Prob.