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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 268, page id 851708439:0292
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L. C F B R A.
ap. L. XII.
impolsibiles, pro raria politione datorum  myn; adeoque, Ila  las Lact
ces inutiles.
28,) hincpatet. Ouoniam, ubicunque hoc conmeru alter duorum m, n, CIl IC
In casu ZI _ ZII, propter cranelcentem c (adeoque ac, 66, 66,) erit l=aa
M = = bb, n = ab = VIm. HIOC aurem, cum in expolitis numeriS 16, 27, 18, (prO
BM, n) nON ConcinSat; certum CA, CaTUS COS, PFOUE jaM ExPONUINEIE L, M, M, Im-
poltibilese.
am a (3 25) ejulque ricarius e(S20) insrediuneur aequationem principalem
dice plana; qualis est illa 5 26. Sed ex illis, nunc hi, nunc illi casus, cradunt
223. Ouod autem polteriores calus quatuor, Proce fas ponuneur l, M, n, (16,
27, 18,) sine impossibiles, (adeoque, qa cos spectat agualio, secle Lepolta 527
dius prOxOrtIOnALI HILeL CII  h n cuos reliquos: Nimirum, In Calu IZ e X
propter cranescentem b, (adeo que ab, 66, 60,) exit l = aa, n = 66, m = ac = V In
F24. Hinc igitur, ubi caluum horum aliquis continei, (hoc elb, utri vel l, M, n
vel hn m lunt Conue Proporcionales,) exvedita paret methodus pro inveni
endis an b, c. Slt enim in omnibus aa =; adeoque a = F VI: Adeoque II
T25. Sed ec rerum clt, si = Vnn, (hoc elt, lim, n, line continue propor-
m = VIn, exIL B =O, 6=VN: SIn = VIM, Crib = VN, C=O.
tionales,) unus crium eranelcet; nimirum, inus vatoruum aa =-0. (adeoque
a = + 0, a= = 0, erunt duo ex duodecim valoribus a.) Sed hic calus non cle
Iltam non insrediuntur b, c.
vac aequationem ad alciorem gradum, (quod Faciunt B == F0, 80 = = =,) quoni
T26. Nam quandocunque hoe concingit (quod sic unus ratorum aa = 0,) erit
ec = 2 aa = 0 unus raloru e  aa  Ca G29,
=51C + 9It 8 = 71II e = 2 P =0
obie3FBH 4b0sb0
ut 2M 16
betur ee eraneleant, quancum ad hunc ralorem,) prodibit terminus absolutus
212 -= 4.VImn F2mmnn =0. Quod sempertc, in omni aequatione, ubi id
dicis unus valor =0. (Fonimirum quod terminus absolutus est factus a continua
mulciplicatione omnium ralorum inter sc; quorum SI unus lic on etiam o erit qui
Factus est.) Adeoque de ejus semissis 1 = 2 IImn = mmnn -0. Hujusque la
tuS quadraticum IV = m n = O. FF VI = mn. Adeoque Y =V m n. lE propterea
(eximenco ex quacraciea ralorem ee =0) aequatio ad cubicam redtisetur (dirsils
Md
ET proxcerea (eum sit unus valorum ex = 0; adeoque omnia memibra quibus ha-
omnibus per ee) 
e = 51 et + 9It e
M H + 5lm 1
127. FF (C Conver(O) C 1 = Vmn: tm II = mn; e I1 = m n = 0; d
deprimitur, reliquos tres valores ee continentem; ut (upra( 53, 5
ig 33. ub sulteleca
si duo ralores ee sic craneleant; redisetur ad quadraticam. L. L HC POH1.
728. Pro hoc ratore an = = ee =9; valoteS B_G reperTUMCL U PTIUO, LMIIIH.
rum (per S XY) B =m a + V: 8M a = 12 In a a. + m a + 4 11
Prex eranelcentem an clli Luis mulcixlis omnibus) b=
etiam (ut S +23, 124, 125;) Propcex eranescenem a ladeoque aa, ab, a5,) exic
M == bb, n = ec; ad eo jue b = V m, c = Y n. (Dui quidem ralores indisterenter
Cumi poltunc astirmatiri auc negacivi, b = = i m, c = Va ac poltularerit occa
(i0.) Idem aurem urroris moco prorenic valor: pulas  = V m. hoc et (ductis
verisque
EL Propteres
A - 2.7 Lmn. + mm n n = C, C. Z. l = 4. bL Mn = 2. mm n n = C
cranelcente termino ultimo, carerilque per ee dirisis) biguadrarica in Cubican
Vat