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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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2. Sic, in Exemplorum ance positorum uno;
Pro V392, Tubltituo T4V2.
Cap. XI. V.
VC. 20 = V 392:
Hoc est, PrO VBba Substituo BV a.
(Fademque merhodo mor in Radicum Surdarum Addirione e Subductione.
Onde Catim liguer, num line commensurabiles, Beenc. VE in V FX7 = V 52
hoc ClL ZVFZ = 2V23: quas commenturabiles esse Ptatim liguer; carumque Tum-
mam esse, 5N 2Z; ditterentiam F V 23: Led in V 24 = V 18, hoc cA 2V6 = 3V2
incommenturabiles eas esse liquet; quia sIC LuNE V6 _ YZ; adeoque in LOrMZ
Binomii aue Apocomes connectendas.)
Reducto autem, ut dictum est,
VC. 20 =V392. ad V C. 20 = 24V2.
manifestum est radieis Binomix (siqua sic) parrem unam este, vel V2 vel hu-
jus mulciplum per numerum rationalem. (Ouippe sI V2 non ingrediatur Ra-
dicem, neque insrederetur Cubum.) Duam radicis partem axpellabinus Ve, aut
fV e; reliquam a.
Cum itaque Radix sit in hac Forma
Cubus erir
a = V e:
aaa =3 a ave + 3ac= eY c.
Obi aaa = 3ac est aes rationalis; _ 3 a a V e = ev e, irrationalis.
FIOc. Cst (in prasentI CaTuI) S una pars radicis sit
Tum est
Adeoque
VC = Y2.
3aaV C + eV e = 3a a Y 2 + 2V2 = 14V 2.
3a a V 2 =12V2. 3aa = 22. aa = 4. a = 2
Ft consequenter, pars rationalis,
aaa = 3a c = 8 f 12 = 20.
Ouod cum hypocheli conreniat, radicem habeo;
a = V e = 2 = V2.
Adeoque YC. 20 f V 392. = VC. 20 - Y 392. = 2 + Y2 pluS 2 - 12. = 4
Si vero hoc non LuCCeITBEE tenLameM; tm, PrO V 2, Substimistem f Y2
dando ipsi f majorem auc minorem ratorem quam L, prour tentamen illud
indicarerie.
2. Paritex in exemplorum altero YC. Y +8252 + 135. HOC et, VC. 78Y3FY35.
Polito Y3 =V a; iplaque radice dV a = e.
Cubus eries
Fxirque
adda Y a = 3d dac = 3decV a = eec.
aa d ava + 3dceY a = 78V3 = 3d d d V 3 = 3d cCV 3.
HOc eAt (posito a = L:) 78 = 3 + 3C6. 75 = 3C0. 25 = ec. 5 == c.
Et pars rationalis,
eec + 3ddac = 125 + 45 = 170.
Ouod cum nimium sic, (Foret enim +35,) Batet d sumprum este justo minorem.
SuMptO Itaque d =2. adeoque dV a = 2 V3.
ExIE addava t3dec Y a = 24 Y 3 F 6ec Y 3 =78Y 3.
Adeogue
24 + 6c0 = 78. 6ce =54. ec = 9. e = 3.
EE pars racionalis cec = 3dd ac = 27 + 508 = +35; ut oportuie.
Radix ergo ct
2V 3+ 3.
Adeoque YC: Y 18252 + 135: = YC: Y 18252 =235:
scu YC: 78Y3 + 135: - YC.: 78Y3 - +35: = 21 3 + 3, minus, 21 3- 3, =6.
Si in secundo hoc tentamine, pro 235, provenittet adhuc numerus major:
pateret sumprum raloremr d este adtue julto minorem, adeoque sumendum ad.
huc majorem.
Sin pro 235, provenistet numerus minor; pateret valorem d = 2, ette julto
majorem: sed d =r, julto minorem; adeoque sumendum incermedium a = 13
Duo Tumpco, s res non recte successeric: Pateret inde, expolui Cubi Bino-
miam radicem, qualis quaeruue, nullam eAfe.
cute