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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 174, page id 851708439:0198
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A F. G F B R A.
(Fanique hac M re, sed Tubobseure, sequitur Cartesins.)
Verbi gratia; S Occurrat aequatio
Oux rite dispolita, haec erit
Sed, quo fractiones ritentur, mulciplico terminos
; Tubtticuo que Cut commodius) e P1O an
Gecque
Ohi valores iptius e dupti erunt ralorum a. Fisque invencis, corum seniltes e.
runt radices a quaelica.
Sa, PrO
HIOC Cst pro
aa a F a a V 3 = 28V 3.
aaa + a a V 3 +04 = 23V 3.
Mulciplico cerminos respectire per I, V 3, 3, 3V 3, ec.
tlabeoque
eec +3e0 +00 =20.
Ec in aliis similiter.
Ci A P. XLIII.
De Aaditione  Subductione radicibus lenotis facien-
da; adeoque auserendo secundo termino.
Ocet proxime; Radicum adhuc incognitarum ralores Augere auE Minue.
re, Addica rel Subducta data quantitate.
Et consequenter (si id opus Sit) Negatiras (vel aliquas vel omnes)
Acirmatiras reddere; aut Astirmatiras reddere Negatiras.
Sed Radices Imaginarixe, neque per Mulciplicationem aue Divisionem (ut in
Capice praecedente,) neque per Addirionem aut Subductionem Cut in hoc capite)
tient Rcales.
Ft vice rersa; quamris AFirmatirae in Negatiras, aut hae in illas, mutari pol-
sune; (adeendo scilicet aut Tubducendo, sed non mulciplicando aut diridendo:)
Realestamen, sire AFirmatirae sire Negatira, neurro modo tient Imaginaria.
Hloc Artiticium (quamris e alias usui (IL) in hunc praecipue tinem introduxit
Fharriotus, ue terminorum intermediorum unus aue plures tollantur, (praeserrim
Secundus:) auc etiam (si id requiratur) lupplCantur.
(Onem _ hac etiam parte sequitur Cartestus.)
Exempla (quibus res melius incelligatur, quam praeceptis,) haec extribet FLarriotus:
I. In Aquarione,
a a a -- 3b a a =- + C66.
Si valorem radicis aminutum velit (verbi gratia) magnitudine B (tercia parte Co.
efficientis;) aut aliam substituere racicem e = a -- b:
Ponit
c+ B= a.
Et consequenter ee + 2b c + Bb = a a.
Et. eec + 3bec + 3bbc + bbb = 444.
Adeoque Aquationem ad hanc Formam redueics
eec + 3bec + 3bBC + B0B = + a4a 2 = = C66.
(36CC- 6bbc = 36bb = -364a
HOc est (deleris quae le muruo destruune, reliquisque rite ordinatis,)
eec = 36bc = +c00. + 2BbB.
Cujus Radix e = a -- b. Hoc est; Ouilibet ralos racteis en in hac aequatione,
aequar resrectirum ralorem a = b in praecedente.