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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. XCIII.
A L G F B R A.
datium E; Sirque Currx Ca natura, ut ducta vicunque applicata BC, junctaque recta
AC; item deleripro Semicirculo a B P. diametro, cujus circumterenEIX OCcurTAF DH
recta normalis rectae A F ab ejus medio puncto D excitata, recta juncta F B Faciac
ansulum P B A aequalem ansulo B A C. Ouaritur dimentio spatii ABC sub qu2-
buS reCtS A B, BC, SE CUEra AC comprehenti. Si A D vel DF. VOCCTT C. AB
i BC, L.; EX nacura Cueva invenierur A quacio ad illam, C. L. 3 f s. = X = C X3.
sive L = VC
aur in Canonis Forma L. = C 3 XX C. + X 3, ubi B = Ci2, K
1
oe
=2, 5 = 1, N =  M - ; Cumque P) = Et numerus inteser et posicirus, Series
genio suo intinica abrumpicur, et quidem post cerminum secundum, cum P +
Cicbinacius; ee tieouiae valor exprimerur cerminis numero siniis. Siquidem drea
per supra teripium Canonem interius demonstrandum aequalis sic C f X] 2 in:
C  XX, = EKCLACI: dempio -  n C 2. Hoc elt aequalio Y C + X. i:
FF 2
F313
3C2X - 3C3]: + 3C Sive Area aqualis 3 Y C X = 3C, X2 F4C] + 3C
In pracedencibus exemplis Series in Canone intinica, quam Pactorem Univerta-
lem apvellaris, post primum aut secundum terminum abrumpitur; in sequente vero
ad tertium exeurrit. Si D5F, 3 = P ZXI- C3X, live in tormula Canoni
apta L = = urC: F.  X = C 1, ubi B =  0 R = 2, 5 = F, N = 1, M-:
R q 1
Cumque hic etiam = = Sic inceser d posicirus, Figurx ralor terminis numero Li.
nicis exprimi poreric; erit urique per supraseripiam seriem L. = X = C, p in:
2X2
OC3X
27Cr
27 cr1C
20DF2 35D Fa 140 D F6 2g0D F6
Postea ostenditur quomodo haec eadem series inserriat, si contingat M esse n-
merum incesrum se policirum; monstracque sumendum elte supra seriptae Seriei ter.
minorum numerum aequalem M F F, de quancicatis S X. + 
expantae
sire eroluca primum cerminum in omnes L’actoris Onivertalis cerminos allumpros
ducendum, sccundum in omnes dempro ulcimo, tertium in omnes dempro ylrimo
et penulcimo _c. In isto ehim catu ubi M, elt numerus integer et potitirus, Sc.
ries non abrumpitur, sed ii termini qui ex ulteriori quam quae praeseripra est mul.
ciplicatione oriuntur, craneseunt.
Proponatur in exemplum figura in qua L. = N X. X2 f A, exie per seriem supra-
Seripram Area aequalis X2 F A) 3 X 2 + 2A X 2 - 38 A X  + _c. Sed
tric ralor minus consruere videtur huie tigura, cum sE quodammodo intini.
csus quia Serieo Factoris Onivertalis non ur in exemplis praecedentibus abrumpicur
per mechodos camen lacis notas, L iBurA aguOuT Z X + 3 2X., Sed si Seriei fi-
Drateripex sumantue cermini duo, quoniam M. F F et binarius, e tiac pu)t.
plicatio ut dictum, producetur verus atea ralor: ec quae ex lublequenium ter-
ininorum mulciplicacione oriuntur quancicates se inricem collune, nt ex ipta ope
ratione institura patet.
Cnoni subjunaitur modus achmodum nacuralis illum invehiendi. Factor enim
universalis, sive Series illa in cujus lingulos terminos ducenda elt quancitas Hxec
SXn F m = E facillime invenitur, divicendo nea valorem intinita Serie
signiticatum (quem per nostram Mechodum in Lxercicatione anno 1084 edita in-
venire proelioe est) per hane quanticacem S X. f  m F 2 eriam in seriem
infinicam retoluram. Pacet enim ex mulciplicatione Lactoris Oniverlalis sie in.
venii