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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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A L C F B R A. C ap. I. XXV
Adeoque; Cuborum iltorum intinica series, eric = m III: Bars quarra coridem
maximo aequalium.
Acquetime intertur; Parabolocidis Cubiea complementum este, a Parallelogramt
mi circum seripei: Iplamque isicur Paraboloeidem, & ejusdem Parallelosrammi. A.
liaque similia
Similiter; Ouoniam Series Biquadratorum, aliorumque ascendentium ad pocelta-
tem Onintam, Sextam, Seprimam, sc. Pune plusquam 5, 5, 7, 3 _c. Seriem totidem
maximo xqualium; Ped excectus continue decre(eit prout ausetur numerus termino-
rum, e tandem eraneseit: Sune isitur series illae, si supponantur in infinitum con-
tinuatae, 3,5,  e ec. cocidem maximo aequalium.
Nimirum; Deo Biquaceacis, si series sinica sie, Aeerexacum est = m H . f. 3= ma
+
SM mb. HoC Cs = + 3 +
dem maximo aequalium.
T2. n nB
qualium.
2
+
=
Teriei cori-
Z21
ero Sexranis (hoc est Ouadratis Cuborum, seu Cubis Ouadratorum) ABBrCSA-
cum cs = mF j- 5 mI + m V-
143
gnr
zunn
p1-
genun
42. n n B n H
mF. Seu (Posito I = n, ) : mV + 2 m B + 3 m B = , m B = i- m V + 42 m 1:
(dt pariter in aliis.) Hoc ett, =-
an hnn hmun aennuu a nmun
ipEUS m P, leu Periei tocidem maximo equalium.
Et pro aliis porestacibus similiter; ue ibidem docetur.
Obi maniteltum est, quod (prout numerus terminorum creteic) exceltus su-
Pras 33 2 5, 6, 7 (e lic de exeteris) ita concinue decreseit uc tandem tiac quoris
altignabili minor, adeoque si in intinicum concinuetur eraneleit.
Hoc est (univertim) Ot F, ad exponentem respectivae potestatis (sen numerum
dimentionum) uno auctum: Sic est bujusmodi insinita series pro ea potestate, ad
seriem totidem maximo aequalium.
Duod incellectum relim, non cancum de (expositorum drichmetice proporrio.
nalium) Ouadraris, Cubis, caeterisque poreltaribus ascendentibis: sed de Corun-
dem radicibus Ouadrarieis, Cubicis, dec. item de Compotiris ex his auc illis aut
uerisque; e horum omnium Reciprocis. Intellisendo, per Exponencem Lateris,
Ouacrati, Cubi, ecc. numeros inceeros, 1, 2, 3, Scc. Radicum vero Ouadraricarum.
Cubicarum, ecc. numeros Fractos, Z, Z, _c. FF Compolitorum; puta, Radicum qua
dracicarum Cuborum, Radicum cubicarum Biquadratorum, _tc. 3, 3, c. F.L Rcci.
Procarum,
Hinc ibidem intertur: Ouadratura Parabolarum et Parabolocidium omnium;
Magnicudo Spaciorum Spiralium; Trem Figurarum incerminatarum, quarum Lon-
gicudo supponacur intinica sed Area tinica; Kigurarum icem solidarum incermina-
TaruIM. Aliaque hujusmodi mulra.
Vel etiam (mittis nominibus Ouadtratorum, Cuborum, _c.) idem sic exponatur
simplicius, et univertalius. Series maenicudinum seu quancitatum (numero infi
niearum) in ratione simplan Duplicata, Triplicata aliasve mulciplicata, Arithme
iice proportionatium 0, L, 2, 3, 4, dec. (incellectis rocibus Duplicata, Priplicara
Mulciplicata, ecc. eo tentu quo detiniunrus ab F velide, 50 det. lib. 5. quo vocibus
jam ulitatis Ouadraci, Cubi, ee caererarum porestatum aequipollent:) aut Subdu-
plicata, Subtripticata, aliasve Submultiplicata; aut Subduplicata triplicatae vel
Subcriplicatae, aliasve composita; aut in barum quarumvis Reciproca; aut in (eo
rundem 0, 2, 27 3, 4, 8c.) ratione sic a numeris inteeris, fractis, surais, vel neca
tivis denominanda: est ad seriem totidem Srimo aequalium; ut 2, ad seriei expo-
nentem uno auetum.
Potestares.