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# Title: [Ps. 1] (shelfmarks Leibn. Marg. 178, Stück 1; Leibn. Marg. 178)
# Folio 356, page id 175905688X:0378
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=175905688X&page=378
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 42 lines, status machine
# Lines: 42 recognised, mean confidence 0.88
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356
APPENDLX DF CUBTCARUM
F quibus liquet cubum erientis quanciraris cognicae penultimi
cermini majorem esse quadrato semissis ultimi, aC prOPterCAFa-
dicem aequationis juxta regulam C ardani inveniri non poste.
Nocandum autem porro est, Problema propolicum solidum
eAe, Ceria lacera data AB, B C, X C D inter le inx qualia statuan-
tur, cum ad aequationem cubicam reducatur, quae diritione ad
quadratam reduci nequit. Cum rero duo qualibet ex dictis late.
ribus sunc aequalia, tunc quidem ae quatio reducieur ad quadra-
Eam. EE G b ee c aequalia tuerine, derenietur ad aequarionem:
ae
 aa
=- b6 = = abb ∞0, quae dividi poterie per X L a ∞ O, qud
ratione ipla reducetur ad quadratam : X X - a X - = bb 200, qua
ulcerius dividi nequic.
Sin autem eria latera aequalia ponantur, tunc quidem aequatio
hanc accipiet Forma: x 3 - 3 a a X - = a3 ∞ 0, eaque diridi po-
TETIIPeI XaVD, Orietur namque XquatiO: X X L a X + a d ∞O,
duas admittens Fallas radices, quae sibiinvicem lunt aequales. IIn-
de sequitur rerum ralorem radicisx eo calutore? a, ee duostal.
Tosralores esse =a _ = a. Ihoc enim manifestum est, quoniam,
sieria latera AB, BC, ee CD aequalia incer se extiterine, tigura
ABC D tc semi hexasonum regulare, in quo lacus quodtibet
Semidiametro est ae quale.
Porro Si relimus idem Problema per numeros resolvere, esto
AB CCu a ∞ 24, BC (Cub ∞ 20, CD PCU C∞ 25, EE quAratuIE
A D ∞ N. TIINC, CUM aa -L b b - L CCINVENIAEUE ∞ F2OY, QE = a bC∞
14400 exurset eju(modi xquatiO: X 3 ∞ TZOF X -L 14400, seu
X38 O~ N = 22OLN = 14400∞00. Oux dividi potest per v L
25 ∞ 0, Oritur namque a guatio a x - - 25 X -- 576∞ O, TCUXN~
25X -= 576, cujus radix x duos admictie ralores, uE, Y25 F V732
_ 12= =V 7322. Tea uc radix praedicta aquationis x 3 ∞ L2OLN
14400 seu diameter qualica AD eres recipiat diversos valo.
res, unum rerum seu -f Quain O, uE 12 = -L V 7324; aeque duos
Fallos seu - quam 0, uF = 25 8 123 =V 7327. Oui quidem si-
mul sumpei iph vero sunt aequales.
Ouod si vero aequatio supra dicta x 3 B OXX = T2OI V -
24400 ∞0diridi non poruiset per quanticatem incognitam x. +
vel - aliquo numero ultimum terminum 24400 diridente, ar-
suisset id ipsum ex neque ullam ex radicibus tam reram quam fal-
Ca1