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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. LXXXVI. A L C F B R C
nunguam praestabie m = m =0; sed (hoc praetermitso) cransibitur ad numeros nC.
sacires, in intinicum procecuros.
Cum igicur, pro serie V: PR =cc: numeros habeamus (modo InVentOS)
=5. = a3. = 362. + 36,3. _c. Dui sic itidem lune exprimendi,
2.
2 X 4. 2 X 4 X6 2X4. X6XB 2X4X6XBXFO
dec
Oui locos suppleuri sunc Numeracorum pro membris quaesuae seriei intinica: Oui
bus Denominatores jam ante habuimus 1, 3, 5, 7, 9, FF, ecc. in progrettione A-
richmerica: Intinita igitur series pro quadratura Ouadrancis Circuli, (cujus Ra
dium ponimus = r, adeoque Onadratum ejusdem = +, e de reliquis Poceltarit1s
similiter, ne operam nobis Facellar dirisio per R, R R, _C.) Polico SignO - l0c0
secundo (propter RR - cc connexum per lignum =) et, volt, alterne   nisi
cum signum- in numeris modo inrentis commutet L in -; (unde reaple contin-
sic signa post primum omnia esse =,) Faliserit,
243 2X4XG 2X4RBX7 2RAXBKBKO REHNSNBLIONFF
ec.
Eademque convenit ipsi V: R R F CC: (quae Hyperbolam spectat:) cum hoc
Cola divertitate, quod (prOpter R R F CC connexam SignO F) Signa qude ante
Fuerane alterne F -, jam line omnio f futura; nisi cum, propier - in numeris
modo inventis, mucanda sine in -. Onde provenie, pro H perbola,
c + 223 224 45 2X4 X6~Z ZKAROKBKO ZKAROKBKEOKEF 
Adeoque, ut prior illa series est ad F, sic Onadrans Circuli ad R R, AuL Oua-
grans Fllipleos ad circum seriptum Parallelogrammum.
Fr, ut series Polterior cst ad X, sic quadrans Hyperbola (externa) Rectangula
aeguilatera (cujus intercepra diamerer aequalis elt semisti diametri crantrerlae, scu
R = Z T,) ad R R (inscripcum quadratum;) vel (si Fyperbola non lic aequila-
cera et rectangula) ad (inscripcum) paralselogrammum, cujus latera lunt Conju-
Baca Semidiameeri.
Simili mechodo, altignari porest Intinita Series pro Ascregato omnium V: d7
ad: aliilque similibus. Similes que hic adhibenda sune accommodationes, prout
supra inlinuatum est, pro Sesmenris; ubi non cousque procedius ut (I d==,
auEC= R.
Comautem perspexerit ille, hujusmodi procestus, per Interpolationem, Operotos
esC: porius existimarie, alias methodos achibere, ope Diritionis, de Exeractionis
Radicis in Speciebus; De quibus polt dicendum exii.
Aique hinc oricur (qui jam dicitur) procectus per Series Insinitas ( quas inero.
anxie Neretonus) ejusque lingulis membris applicaca nostra Srithmetiea Infinito-
rum Ouadraturas exhibet Fisurarum omnium quae sic reduei postune ad Seriem
Infinicam. Sed et aliarum Inquiticionum Aesresatum, simili ordine proceden-
cium, peut Fieuras Geometricas non specten. Duippe Fieurarum Quadratura
non est nili Ciasus parsicularis tub illa Generali Inquititione.
F
Methodus Approximandi, secundum c.
SF alia methodus approximandis speciarim pro Circulo, (led qua alS
 Curris aecommodari potelt, lic mutata, ue cujusque Currae natura postu-
Llatu) jam olim ab Achimede aclhibica; quam L’an Culen, Snellius, aliique,
PrOMOVETUNE: Per continuam Areus Sectionem, et Chordarum Tansentiunque
accommodationem ad eas Peripheriaxe portiones.
Secundum