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# Title: [Ps. 1] (shelfmarks Leibn. Marg. 178, Stück 1; Leibn. Marg. 178)
# Folio 364, page id 175905688X:0386
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36.4
A P P F H D LZ DE CUBTC A R AN.
adinitiere veros ralores sibi invicem aguales, qui singuli per
unamquam que ex illis inlcripeis delignantur; ac praetereatallum,
alcerurrius illius duplum.
Caeterum si delideremus propolitum Problema per numeros
xelolrere, elto A B ∞ a ∞ 24, B C ∞b∞ 20, CD ∞C∞ 25, de
quaeratur AD ∞ x. Flinc cum a a L b b - L CClIE X2OF, _ 2 ab5 ∞
F4400, inrenietur aequatiocalis: X 3 ∞ T2OY X - 24400, seu
X. 3 8 ON N = TZOT X f 24400000. Oua diridi pocelt per
X = 25 ∞O, OFIEUI nAI quC _ quacIO ~ X L 25 X - 576∞O,
(et X X ∞ = 25 X- L 576. Cujus porro veraradix ct V 732+
222, _ Fal(2 - V 732= = 123. Ica ut diameter quae lICa AD,
hoc est, xradix praedicta aequationis x3 D +2OT~ = 2440O, tres
ferat differentes ralores, duos scilicer veros leu L quam 0, ni
mirum L 25 majorem, ec V7322 - 12= minorem, e unum
Fallum Peu - quam 0, nimirum - V 732 = = F27, qui veris istis
Sinul Cumpris es aequalis. Quocirca cum eres superioris aequario.
HIS X 3∞ F2OT ∞ ] 24. 400 radices inVeHEX (INE - 25, 12:-
V 7322, _C F2, - V 732 Patec eastantum ex o esse anterendas,
Leu earum signa esse immutanda, ad habendas eres radices hujus
posterioris aequationis.
Ouod sirero hec ip(a aequatioxZ B OXK - (2OLN F Y + 400∞0
diridinon poruissec per quanticarem incognicam x L vel aliquo
numero ulcimum terminum r4400 diridente, aroumentum fuil.
set quod e nulla radicum cam rera quam fallaullo numero fuil.
Pet explicabilis, sed eam tunc delignandam esse per rectam darum
angulum relarcum in cres xquales partes diridentem, rel alio de
nique modo, ut intra ostendetur.
CIC si in exenplum proponatur x quario x3 ∞, 2700 N -- 32400,
Peu ∞ 3 8 OX X = 270OX = 32400∞O, gua cum praecedenti
modo diridi nequeac, poterit quoque ralor radicis x, sire is verus
sire Fallus fuerie, nullis numeris exprimi, nec per latera quorur
dam cuborum, quorum contentum cognolcitur, ut docent CAr-
dani regulae. Ouippe illum ad has non revocare licet, cum iplxe
exieane ut cubus trieneis numeri radicum a quadraco Femiltis nu
meri ab soluri auteratur, qui quidem cubus hic major datur. Adeo
uc radices ejus per rectas subcendentes erientem anguli vel arcus
dari sint denorandae, ut vult D. des Cartes, at que ut eciam AIber-
us Girardusinnuir. Scilicer describendo circulum cujus radius