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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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6.9
on
13.
1.8
Cap. L. XTI.
A L G F B R A.
Adeoque a = x7, 4 26, 540, 14 F L BB = O. F22, 618,0
B0=- L. 416, 240, 14 a0 - 16. 877,382,0
aa f b0== 26.
Bb + ac = X7.
202. FL, POsItO b - -- 3,936,854,0.
Exit c=
26 - a a = b0 = - 2. 4. 76, 140, 14
D
= - 3.936,854,03
Sed ca = 26. 355,290, 4
ab = T. 462,546,0
co tabl = 18) = 24833, 41
=0. 359,713,65.
Adeoque a = 17. 456, 240, C4 ELBB = 25. 438, 8F9,7 Sed 66 = O. 129,59,,
b0= =L. 426, 140, 14 ab +L. 50L, L8613
aa F B= 16.
bb. + ac = F7.
ab - 16. 429,5349
c6 + ab(= 18) =. - 26. 300, 14 5, 0
703. Tandem, sumpio (Der 572) quarco ralore aa = 16. 030, 145, 44:
Adeoque a = 4. 003, 766, 4; e 26a = 64. 060, 262,5; et ad = 64. 180, 957, 8:
Frie 26a = a = = 0. +20,695, 3 = 17b - B3.
204. Fabemus aurem (per 575) valorem unum b = 0.907,099.7: Cujus ope,
sic deprimitur aquatio cubica ad quadraticam:
Puta
b - 0007,099, 7 =0)
)63 - 27B =0. 720,695,3 =0 (4
 (38-0007, 099, 74 b - 26. 999,94 d, d = 0.
bb = Cb - D = 0.
205. Cujus duae radices sunt F ZC = V: Z C9 + D: = b.
HOC est, b = + 0.003,549, d =L 4. 123, 1O2, 2.
Hloc est, b = + 4. 226, 651, L; e b = - 4. L 29, 552,3.
Tnucilis utraque.
206. Nam, polico B = 4. 126, 65F,0;
Exic 26 = a a = bc = - 0.030, 445 + = - 0007,305,1. = c.
b = = 4. +26, 65F, C
Adeoque a = 76. 030, T45, 44. FLBB = 17, 029, 248,
B5- 0. 030, 145,44 ac = 0. 029, 248
au Fb0 = 26.
Bb + ac = 27.
107. EE, Polito B = = 4. 179, 55T,3:
16 -- aa = b6 = - 0. 030, 145, 4 = + 8.007,317, 7 =6.
B = - 4. +79, 55L,3
Adeoque a == 16. 030, 145, 44 FL Bb -= 26, 970, 702,
66 = 0. 030, 24544. ac = 0. 029, 298
au + B0 -- 16.
Bb + ac - 17.
ab - 10. 4.93,721,
cc +at (= 18) = 26. 493, 677,6
208. Constat igitur, ex jam octentis; sumpeo quoris ralore a (primo, secundo,
certio, quarcore,) ralorem b (sire per quadracicam, sive per cubicam aequatio
nem, quaesicum,) nonnisi unicum este, (cum radices religuae sine inuriles:) Et
consequenter, ralorem c, unicum item este: Et propterea, potiorem else procel.
Tum per quadratieam (ue simpliciorem) quam per cubicam aequationem.
209. Sed pro valoribus aan (qui omnino quatuor sunt, et uiles omnes;)
manitestum est eguationem principalem (quae quaestionem universaliter com
plectitur, in omni sua rarietate) limpliciorem esse non posse quam biquadra-
ricam; (uc est ea in 529, et 35: nulla enim, hac simplicior, quatuor radices
continet.
T10. Constat porro; equationis hujus biquadratieae, oportere, raclicem planam
cAte (hoc eltu duarum dimentionum) ur elt aa: quo pollic a in singulis du-
Dlicem
A6 = 0.000,053,4
ab- 16.52.2, 146,7
6c + ab( = 18) = 16. 522, 200, 1
dell C0= 0.000,053,4