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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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=VAE, et
A E G F B R A.
= = Y -. Nam, BOlico, verbi Gracia A = bb, _ E = 5f: exI
isitur V A = VBB = b, _ VE = YFf = f: AdeoquC, ut A XF.:
sic (radices) VAKNE = bF = V BBFF = VAE. Pariterque
= V =. EE similiter in aliis quibulris Radicibus Homogeneis. VE, Si A = Bbb,
e E = fFF: tum est AE = BBBFFF, _ YCARVCF = Bf = V cbbbfff
=VCAL. FE SC de CXTETIS.
Ideoque radicem Curdam Ouadrare aut Cubare (ee similiter de aliis porecta-
tibus,) est porestatem iplam quadrare aut cubare, retenta eadem Radicalicatis nOta.
PaTa, O: V3: = V3XV3 =19 = 3. EFC: V3: = VZRVZXV3 =V: 3X3X3:
V27. Vel etiam (cum tieri potelt) bisecando aut trilecando exvonentem
radicalitatis. Or G: V993: = V93 = C: V9993. Et quidem, s imperata
Pocestas, parem habet denominationem cum radicalicare, delendo nocam radica-
litatis. Or G: V43: = 3. Et C: VC3. =
Contra vero, Surda radicis (numerire similiter norari) radicem quadraticam,
cubicam, aliamre extrahere; M radicalicaris exponentem duplare, triplare, alial-
ve (prout imperatum est) mulciplicare. Sic iplius V 92, vel Vc3, radix, qua-
dratica ct V 992, vel Vcc3. Aur (ubi tieri porelt) ex ipla poceltare cui
praetisitur radicalicatis noca, radicem imperatam exirahere, retenta quae erat radi-
caliraris nota. Sic iptius V C 9, radix quadrarica est Y C3. Nam S ipsius V C3
quadratum, hoc cAt V c3X V C3, tic (ut oltentum cAt) V c9; erit hujus qua-
dratica radix V CZ
Si Radices hujulmodi (numerire ad radicum Formam notati) Feterogenex
lint: reducendae prius erunt ad idem genus, quam insticuatur ca Mulciplicatio
aue Dirisio. VF 2V 3 Tcu 2 X V 3, hoc cA V 4 x V 3, cAt V (4 X3:
T2. FV
2V C3, Teu 2 X V c3, hoc cA V C8xV C3 =VC (8x3 =) 24. EC V92XVC3
=V9g98XVCCO = Y99972 = VCC72.
Ouehtredus radices heterogeneas ad idem genus reducendas docet, Dividendo
indices seu exponentes utriusque potestatis propositae, per maximam eorum com-
munem mensuram: es multiplicando tum indices per alternos quotos, tum ipsas
potestates in species alternis quoris coenomines. Sic V gqA X V CCB9 = Y cCCC
ACXVCCCCBgq = VccCCACBgq. HlOc cst VA AXVSB9 = VZACXVEB49
V2 ACB99. Nam 2) 4 (2, 8 2) 6(3. Trerumque 4X 3 = 12 = 2X6: Cu-
busque (seu certia poreltas) iptius A, elt AC; et quadratum (seu secunda po.
celtas) iptius B4 est B99:
2) V A X V B9 = s2 A Cx Vu B94 = p AcB49.
Sic Y44 FOXVCC7 = V cCCCLOOOKVCCCC4O = Y cccC 40000.
Similiter Faciendum est, Si Radlix (tive lurea Fit sire non Curca) sic duplanda,
dimidianda, auc alias mulciplicanda rel diridenda, per numerum ettabilem, in.
cegrum vel tractum;
VE 2YC32 = 2aY C32 = V CBRVC32 =V c256.
Ec ZNC32 = = 2 V C32 = Y CSRVC32 = Y C8 =YC4.
Sed in hujusmodi catibus; malim exo (niti cum ratio particularis contrarium
Tuadeac) partem rationalem seu estabilem servare separatam, ex radicalicaris liea
(quam vocant) exempram. Adeoque pro V c 256, malim seribere 2. V c 32, vel
achuc pocius 4. V c4.
Acque in hunc tinem poteltatem soleo diridere per (quam postum) maxi-
mum iltius generis numerum tiguratum; (hoc est, per maximum quadratum, (I
Tic radix quadratica; auc maximum cubum, si cubica; alque in aliis similiter,)
Muscnsile
aP. XAV