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# Title: [Johannis Wallis S. T. D. Geometriae Professoris Saviliani, in Celeberrima Academia Oxoniensi; Opera Mathematica] Johannis Wallis S. T. D. Geometriæ Professoris Saviliani, in Celeberrima Academia Oxoniensi; Opera Mathematica (shelfmarks Leibn. Marg. 100:1/2, Stück 1; Leibn. Marg. 100:1/2)
# Folio 242, page id 851387705:0262
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D EDICA L1O.
Et propterea V c64 F V CZ = 4 F F =5 =Z. Veletiam, (s principio po.
Ticum cAet =65,) mucaris ubique sionis nueri 65, prorenilter = 4 = F =
Vel sic (immediare ad regulam exisendo:) Aiquacio propolita elt L. C = +2.2
==65. Fr8O3) 12(4 = A. adeogue 64 = A C. FF Z = E7. ade0que 4223 =
229. Et Propieiea
22+ V: 249 - A. c: = 3 = V: 125. - 64: -
E = E.C
Adeoque = Y c64 = Y CF = =4 F L = = 5 = Z.
Postquam has eso Regulas inveneram; nec illis simile quidquam apud eos quostum
videram Analyctas nocareram (Cardanum liquidem non tum videram,) apuc quos
de Aiquationibus Cubicis resolvendis altum erat tilencium: In Carressi Geome-
eriam, (quae Tub id temporis aut paulo serius, Gallice primum prodiit, necdum
enim tunc cemporis exltabat Larine, sed polt annos aliquor,) incidebam. ADyd
quem duas itidem inveni regulas, quas Cardani Regulas appellac, caldem plane cum
nostris, ueut paulo aliter delignatas, nulla tamen demonstrarione munitas, nec vel
lerissimo dato indicio, quo de illarum fundtamento constare postit. Cardanum
tandem nactus, (qui illas Scipioni cuidam Ferreo acceptas retere,) caldem avuc
cum inveni alia quidem methodo demonstratas, (lonsa latis ee perplexa, quaeque
rei originem neuriquam explicat,) quas ego ex Analyleos principiis, uc dictum est
collereram. Oua quidem inreltisatio, s nihil aliud novi in se contineat, Calcem
eonomine Dui Veltra non ingraca torlan ell tucura, quod earum orixinem Da-
retaciat.
Jam ilaque posica aequatione resolvenda, r f 27r = 272: Ouoniam 13, e
27r, eodem signO nOTAntE, pertinehit ea ad regulam secundam. Adeoque cum
sE 3) 27 (9, C6 9XOX9 = 729, ItCM 2) 272 (== 86, e 86X 86 = 7396;
Erit V: 7396 + 229: +86 = 18125+86 = -
Adeoque Y c: V 8125 +86: = Y 13=2 = 2
Adeoque A = E = r:
2
2) 172 (86
486
16
688
7396
+720
N c: 25V 23(= Y 8125) +86:=
A1.
Ergo Aquationis r + 27r f 172, cad. r = F 4 = A - B.
Ex Aquarionisr + 27r = = 272, rad. r = 4 = = A + P.
Et eodem modo de A quationibus hujusce Formae omnibus Ptatuendum: Nulla
enim omnino elt iltius Forma aequatio, quae non unam aliquam radicem habet
realem: Sed et unicam; nam quas expectes dua reliqua, suns rantum imaginaria,
de impostibiles.
Pari mechodo; Si exponatur aequatio re lolvena r3 - 27r = 154. quae, prov.
ter duarum potestacum contraria tgna, ad regulam primam exisenda elt. Adeo.
que cum sIt 2) 254 (27, et 77 X 77 = 5929; iem 3) 27 (9, e 9X9X9 = 729: Exit
77= V: 5929 - 729: = 77 =Y 5200
P. C
c
64. = A c.
AccoquE
17