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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)
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Cap. XC.t.
A L G F B R A.
que in TOFquOE opuS erit Spaciola paralle logramma diridat: Ouorum lingula intelli-
sancur denominationes ferciri d dimensionibus duarum indetinitarum quantitacum.
uEN Cy; ordine procedendo (uc in figura) ab a termino. Ouarum y denoret
radticem extrahendam; et , alteram indetinicam ex cujus porestatibus consticu-
enda C Serics.
Ouando proxonitur Aquacio; Nocat ille cellulas cas seu spatiola, quibus
respondent linguli Aquationis cermini. Regulamque admoret, ut DF, ad duo
aut forre plura spatiola sic notata; quorum unum sic intimum in latere AB, aliud
(aut torie plura) quod Regulam in eo sicu concingat. Acque tum leligit cos
in aequatione cerminos, qui cellulis sie Regulam concingentibus conveniunt, (omif-
sis eis omnibus quae supra Regulam intactam jacent:) acque inde quarir magni.
cudinem in Quocience leu Racice exquirenda ponendam.
Sic, Pro extrahenda Radice y, hujus aequationis, go - 5 ∞ gd + = p - 7a N2 ge
=6a _ = BB~ =0. Cellutis sic ut dictum est notatis; Regulam admoret ad
D (qux elt ima cellula lateri AB contigua,) circa D rorandam (ab A ver siS C)
donec aliam sic nocatam collulam (unam aut plures) contingat. Acque hrie qui
dem continsit Fres; quibus respondene N, X N Y Y, et y. Fx his ergo termi-
nIS g = 7 a a X N. Y Y F 6 a N3, qua =-O, (et porro, li placet, ad hos reductis
25 - 702 + 6 ==0; Doluo y ==~V a X,) quaerendo ralorem y; occurrit ralor
quadruplex; F V a x, = V aN, = V2a N, = V2 a x. Ouorum quiris altumi
Poterit pro primo cermino Ouotientis; prouc aliam aliamre racticem prolequi libet.
Ad hanc Formam; A: quatio Cupra memorara, p + a N y = a ay = N3 - 2. a =0
extribet = 2 a F 2 a ay ) a=0; adeoque v = a proxime. Sumpco itaque a
Pro Primo cermino valoris y; ponendi tunc reliqui omnes =p; adeoque
Poltune hie nonnunguam occurrere disticultates aliquoc; sed quas prudens Le.
Etor Pagacirare lua superare posse credendus elt.
Reliqui termini q, r, s, Cec. paricer inveniri porerune ex aequationibus secunda,
terria, exeterisque sequentibus, uc p ex prima; led majore Pacilirate, uc jam octen-
Cum est.
EX Aquationibus sic reductis in Series Intinitas; exquirit ille Aream tigurarum
currilincarum; Linearum currarum lonsicudinem; masnicudinem ee Tuperticiem
Solidorum; item Segmenta hujusmodi Linearum, Superticierum, et Solidorum;
omniumque Centra CTraritatis.
Idem praestat (sed methodo hac magis adhuc prOmOta) eriam de Curris Me.
chanicis; qua hujulmodi sequationes non admittunt.
Fgus Paemno cutiis casibus accommodata.
Xempla husus Methodi extribet mulca: Ouorum ego aliquor hic tran.
seribo. In quorum quibusdam, pro Seriei inventx Terminis seu Mem
Labris, primo, lecundo, terrio, et sequentibus, (ne Frequenti reperitione opus
SIC) adhibet LiteraS A, B, C, D, ec.
Exemplum L. Dato Sint (recto aut verso,) Arcum invenire. Sit radiusr, Si.
nus rectus a. ArCuS erit
=x F 6ET 40m 112r
3X3X V A
F _c. Hoc est,
SX N N
6X7XrY
1
Ek3XYY
trem; sic Diamerer a; Sinus versus x. AreuS CtH
443+