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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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Malto.
2-
rst
Cap. XIVII. A L G F B R A.
Ouipue valor ipsius a in hoc negorio, semper ese debet, vel numerus in-
Eeger; vel salcem inceori dimicius, quon seminatus, tiac integer.
EF (ne vasa conjectura multiplici Opus TIc) semper ele debet aliquora pars
iltius numeri qui praetigicur surdae radiei, qui hie ett 78. Ouippe 78 = dada t3 dec,
est dirisibilis per a. Ft Tunilicer in aliis casibus.
3. Pariter; in hoc alio; ubi pars utraque surda est.
YC. Y5408 = Y5400. HIOC est VC. 52V2 = 30V6.
POlito aVa pro membro majori; et fV e, Pro minori;
Radix exit av a =fY e,
Adeoque Cubus d dav a =3 d d a YC +3 aff e a =555 et c.
Tum, Dotito Va =Y 2, et V e = Y6. Sumptoque f = +:
Eric 3ddafVC + fff ev e = 3 d d aV6 + 6Y6 = 30V6.
Adeoque 3dd a V6 = , 24V6. 3d da = 24. ad a = 8.
RE (PFOPTCF a = 2,) d d = 4. d = 2.
Ideoque membrum alterum; addav a = 3 affeN a = 16Y 2 f 36Y2 -=52Y2. uE OportuiE.
Ergo Radix Cubica, dV a = fV C = 2V2+16 = V8=V6.
Et YC: V5408 F V5400: = VC: V5408 - V 5400: = V8. + V6 plus
V8 - 16 = 2V8 = V 32.
Vel etiam, ordiri licuistet ab V a = V 2. Sumproque d = +, Foret
addava + 3 asser a = ara = 3ffer a = 2V2 +3f er 2 = 2V2 + 18f(V2 =52V2.
Adeoque 18ff 12 = 5012. 28f5 -50. 28 = ff = 23: f =
Hoc aurem (praeterquam quod nec sic inteser, nec incesri dimidius)
Extriberet (sfeY e = 3d d afV e = 3116.
Dui nimius est: (Foret enim 30 V 6.) adeoque sumptus est a justo minor.
Sumpeo itaque (secunda vice) a = 2,
habebitur addava = 3afseY a = 1612 + 36ffY2 = 52Y2.
Adeoque 36ffV2 = 36V2. e f5 = 2 = ].
Ideoque memibrum alcerum; f5 5 erc + 3 d daf Y e = eY e = 3 ad aY e = 616
= 24 V 6= 30 V6. ut oportuit.
FrsO, radix aV a = fV C = ZY 2 = V6. Caeteraque ut prius.
4. Similicer, si proponatur aeguatio rrr + Or = 270.
Oui casus est A.quationis XII. F jusque Radix, per has regulas,
r = YC: = 85 = V (7225 + 27 =) 9252: - YC: - 85 + Y7252.
Hoc est, rC: = 85 = F4. V 37: - VC: - 85 + 24 V 37.
Posico jam Ve = 137, Tumproque f = 2; toret eV e = 37 V 37:
Ouod fieri non porell. Ouipre non plus habetur quam 24V 37.
Sumpco ilaque f. = 3. (Est urique E, semistis incegri.)
Eric Ss feV C = 38 V 37. Duod subductum ex 24. V 37 = 25 V 37:
Relinguie, 3 V 37 = 34a fV0 = 3 aa f Y 37 = 2a a V 37.
Adeoque 23 = 3 a a. 2Z = a a. 3 = a.
Ideoque aaa = 3 asse = 135 f 38 = 8 = 85. VE OpOrtuiE.
ErGO VC: 85 = V 7252: = a = fY e =3 = = V 37.
Ex Ractix aequarionis r = + 3 = 3 V 3D minus = 3, F 3 V 37, = 5.
5. Similiter, Ei proponatur aequatio;
rrr-Or =80.
Dui et calus Fxplicabilis, squationis XII. Ejusque radin,