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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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Cu. LCil.
a  t dad
honc speculationem incerrupiste. Cumque eam Post relumpturus crat, circa an
num 167F; animo cdendi ca quae hac de re inveltisarerat; una cum Nora ejus
De Refractione Luminis Theoria: Alia cum accicterune, quibus hoc impectiium
est
dixhibet ille (in his Liceris) non cancum Approximationes mulcas parriculari
buo calitus accommodatas; sed generales Methodos Regulalre, calibus innumeris
Facile applicabiles: Inde deduet portinc ad libirum hujusmodi Series seu Pro.
prectiones incerminata; ec quidem magna varietate pro eodem catu. Specimina
fimul exhibens quomodo accommodari possine hujulnodi Progreltiones; Pio re
Etiticandis Fineis Curris (Geometricis, ec Mechanicis;) Pro quadrandis Piguris
Currilineis; Pro invenienda longitudine expolici ArcuS, ex dacis Chordis, Sini
butre Rectis aut Vertisz _ horum paricer ex caris Arcubus; Pro Loparichimis ad
Numeros accommodandis; et his ad illos; Aliisque in Macheti inquilicionibus
latis perplexis.
Oua in re ucicur ille non rancum Divisione in Speciebus (ut lupra ostentum
est.) Sed in Speciebus itidem Fxcractione Radicum, Ouadraricarum, Cubicarum,
consequentiumque Poreltarum, de Incermediarum; cum in simplicibus s quario
nibus, cum in Afectis.
Ouomodo hanc achibuerie Mechodum pro seriebus Incerpolandis; jaur supra
ostentum elt. Indicando Oncias (quas vocant) seu numeros praetixos pocelta-
cum Membris, d Radice Binomia procreatarum, (quarum poreltarum respectirum
Esponencem vocat m,) oriri ex hujusmodi concinua mulciplicatione,
0. m + m 2 m 3 m 4 , ecc.
Oui quidem procellus; ( m (exponens porestatis) sit numerus Integer; se.
iplum decerminabit, polt certum loeorum numerum cuique porestati conrenien-
cem; redeunte r, unde inceperat. Sed, _ m sic Fractio; crantibitur in intini.
tum per numeros neratiros.
Contequenter ad hac: Cum invenerit numeros ei poceltati consruentes, quam
per V4 designare Colemus (cujus exponens ct. m = 5) hos ette,
5. + 16. = 130. - 3 = c.
Hlos accommodat, exempli gratia, ad meam illam seriem (pro quacrando Circulum
ejusre Duadrancem) V: R R = c5. Vel (polIIO R = L;) V: L = cc. Invenic.
que Y: P - 66: = x- 38C= 50 = 1s5 c. Dux quidem, in se mulciplicata,
restituit X =56. Or ex subjecto procettu liguer.
2 = cc (4, = 266, = 60, - 60, ac
F BC5-
ec. .
s
cd
3∞ c
dc.
dec
el-
AEque ex hoc procestu (aliisque contimilIS nACIITX) hoc Theorema dedue,
pro hujusmodi ExcractionibuS;
3
M-- n
A
ec
∞ + ~81m -∞ 
rectas inde Formanda, aut Radix ejusmodi Porestatis extrahenda: P CA primus ter-
minus ejulmodi expolica quanitalis. Z, ett reliduum ejuldem per e diritum.
Vbi L. F 2 elt expolica Glasenao Cusito Lacs eut extranenda, aut aliqua PO.