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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 190, page id 851708439:0214
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sL L G F. B R A.
Cap. XL. VIC
Policoque Ve = V 13. Maniteltum est, f minus ese quam L. Nam 13 V L3
=e V e plus est quam EF V L3: quod FOret minus.
Sumpro isitur f = Z: Elabetur ff fC V C = 8V 13.
Duod Subductum ex LF V 13 = 35V 13:
Relinguit 28V 13 = 3aaf Y e = 3aaf V 13 = 3a a V 23.
Adeoque 13 =3a a. 22 = aa. 3 = a.
Tdeoque aaa = 3 a ff0 = 133 +13 =3 = 40. OT opOrtuIE.
Ergo YC: 40 = V 1573: = a = f V C = 3 F ZV 13.
Ec aequacionis radia, r = h + Z V 23, plus, 3 = = V 13, =5.
C A P. XL VIII.
Idem extenditur ad Radices cre ditas Tnexplicabiles.
Ddo Porro; Ouod haec methodus extendit se, non tantum ad catiis A.
quationis ZIT; aa a + 3bb a = f 2600: eosque Aquationis XTIY
L aca = 3bba = + 256C caluis, ubi B minor est aut aequalis ipli c. Sed
ad cos eriam ( qui pro deploratis haberi Tolent) ubi b major est quam c. 2de0.
que V: 5066C6 = bbbbbb; Ceu V - ddddad; Radix quadratica Negacirx
Ouancitatis.
Ouamris enim, uriusque Radicis membrum, VC: c0c = V - d a d d dd; &e
NC: 66C- V= dddd dd; inrolrere rideatur Aiquationem Quadraticam Im-
pessibilem, proxier inexplicabilem radicem Ouadrati Negatiri V = d d d d d d, (de
quo Tarriotum incellisendum puto, cum eam dicit (Seect. 6. pr. 13.) Impossibi-
tem, propter Tneaplicabilitatem radicis V - a a a d d d.) Non tamen Impoltibilis
eAt ea Aquatio; Led Radicem Reatem habet. Ouod ante oltenderat TParriotus ad
prop. 2 et 4. Sectionis 5. Dux radix, non alia est ab ea quam hac nocatione de-
Signat,
YC. c0c = V - a d a d ad. = VC. c00 -Y - d a d d a d.
Ouodque tingulis membris videtur impossibile, mutua connexione destruitur.
Sic in Aquatione Cubica . . . . . rrr - 63r = 162.
Obi b = V 3 = Y 2F, major est quam c = VC. 157 = YC. 8T. (Ouod patebit Oua-
drando BT, ee Cubando 27.) Radix aurem (per eas regulas)
r = YC. 8E = Y (656E -9262 =) = 2.700. = VC. 8F - Y = 2700.
HOC CA VC. 8F + 30Y - 3. = VC. 8F - 30Y -- 3.
Padicum Cubicarum torma, a = f V = e.
Et quadrarum ipsius fY = e, cst - ft e.
Iptiusque a + fY -e
Cubus aaan = 3a afV = e, = 3a55e, - f5FeY = c.
Iptinsque a - fV = e,
Cabus aaa = 3aafV = e,
Adeoque, in praetenti casum
3assen  ffer=
aa a = 3 af f0 = BL. acque 3a a fV = e, = sCY B= 30V
FOC Cst, POsicO V = e =V. = 3; Tumptoque f = L;
34af -f550 = 34a - e = 3a a - 3 = 30.
r = YC: 40 = Y (+600 - 27 =) 2573: +. YC: 40 = Y 2573.
Hoc clt VC: 40 F ZFV F3: F VC: 40 = EEV 13.
Adedque