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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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X1II
X Tium
5
a
L G F. B R
a A P. XXXV
1L
De mutancis Radicibus Lecativis in Affirmativas, es
Affirmativis in Necativas.
X eadem Compositionum inspectione, Pacim liquet, Onam murationem in-
 ducac in siquatione compolica, mutacio lionorum in una vel pluribus Ra-
dicum simplicium; aut in uno vel pluribus membris Aquationum quarum.
vis componencium: mutato scilicet AFirmaciro in Negatirum, aurhoc in illud.
Pater enim, ipso incuicu, in quo membro cujusque termini quaelibet Radix sepe.
riatur; ec quid inde mutationis accideret ex mutato iltius radieis signo.
Patet etiam, speciatim; Si, in ejusmodimembro quoris, Dux, GWacuor, Sex, aut
alius radieum numerus par, membrum illud comporentium, lignum habeane mu-
tacum; nihil inde mucacionis oricurum in signo compolui: (ilam musciplicando
 in F, aut - in -, tancundem fic; ee similiter = in Y, auc F in -: AdCO.
qye guiequid prima mutatione alceratum est, secunda restiruitur; quodque in ter-
EIa mutatur, restiuitur in quarta; e sic semper.) Si verovna, Pres, Ouinque,
aliutre radicum numerus impar, Pionum habeanemutarum: murtatur compolici seu
Facti signum. (Ouipue cum utationes Dux, Ouatuor, Sex, aut alia numero
pares, idem quod ab inicio signum relinquunt; quae supervenit loco impari, illud
mutatum reddic.)
Fe consequenter, li simul omnium ligna utata volumus, (quo radices neza-
cirae tiane affirmatirae, ee altirmatira tiant negatirae;) tiet inde lignorum munario
in terminis Secundo, Ouarto, Sexto, aliisque in locis paribus: (quoniam, in his,
Coefticientis membra singula radices ingrediuntur 1, 3, 5, _c.) Sed in Primo
Tertio, Ouinto, aliisque locis imparibus, (ubi radices sinsula membra componen.
LeS TUnENUMCTO O, 2, 4, _C.) nulla tiec inde tignorum mutario.
Ouodque in uno cujusque Coefticiencis membro contingit, pariter continsit (ob
eandem caulam) in omnihus, adeoque in (membrorum aggresato) Coetticiente,
Adeoque, S in locis sccundo, quarto, sexto, reliquilque paribus, mutentur
Coetticientium signa; led non icem in primos tercio, quinco, reliquisque impari-
bus: Afirmacira qua tuerant radicestiunt Negacirae; ee Nogacira, liune ARIE
matira. (Incellise; si suxpleantur loca omnia, vel ita numerentur quae implen-
tur, acsi implerentur reliqua.) PL, Si raclices su mucatas volumus; tic mucanca
une illa Signa.
Hujusmodi mucationum exempla videas, in Ouacracicarum aequationum casibus Pri-
mo, et Ferrio; et Cubicarum, Primo e Ouarro; icemque Secundo, et P’errio; pariter.
que Nono et Decimo; et in Biquadraricarum Primo et Ouinto, itemque Secundo et
Perrio. Ex Similicer (hresrice perpendacur) in Cubiearum Duinto dt Seprimo, (nem-
De si in alcero incellisatur  b0 tieri ex F b in F C; in alterO Cx = b in =C:)
1.
cem in carundem catu Sexto  Octaro, (sitieri incelligatur = b c, in altero ex L b
in = c. in altero, ex = b in F c.) Lremque in Sexto et Nono catu Biquadratica-
rum, (Facto L cd f ex F C, + a, + f in altero; _ = c af in alterO, ex  C, + d
;aut cum simili aliqua rariatione; quod in aequationitus, ubi desune aliqui
termii, Feri variis modis potest.) Pr (simili suppositione) in Septimo et Octaro
ibidem. Ec (ne plures nominem) idem ubique continget (ob causas jam expo.
Litas) Si singulae radicum simplicium (ipsi a aequalium) Signa habeane, in amo,
contraria eis quae in altero. Verum si ita contingat (ob aliqua Loca tacuas aut
aliunde,) quod aliquarum racticum signa maneane indeterminata (quod modo inti-
nuatum eAt de f66, -=bC; HC d5, = c df; ubi non liquet, num iplaeum b, c,
d s, Signa Tinc F auc -:) idem pariter indeterminacum manebic post mutationem
factam. Ouippe cacenus haec in altero determinantur, quatenus in altero.
Aique hoc pacto (in quacunque aequatione expolica) licebit (ienoris achue ra-
dicum valoribus) radices omnes Astirmacivas in Nexaciras, et Nesaciras En Asir
Cumigue
matiras, MuTare.