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# Title: [Ps. 1] (shelfmarks Leibn. Marg. 178, Stück 1; Leibn. Marg. 178)
# Folio 359, page id 175905688X:0381
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=175905688X&page=381
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 43 lines, status machine
# Lines: 43 recognised, mean confidence 0.87
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due
SE OU A ZTOHAM RESOLATIORE.
355
DC F. Elinc, qualium partium angulus A est L, calium angulus
CD A eric 23 d D C F 3, hoc est, criplus erit angulusDC L an-
Suli A. Duemadmodum tuic propolitum.
Denique quoniam omnes limiles aequationes ad aequationem
praecedentis Problematis rerocari queune, pocerimus quoque ra-
dicem x aequationis propolitxe x 3 ∞ 243 x F 12F5 SiC incerpreta-
ri: dicentes eam esse diametrum semicirculi, supra quam delcri-
Peo quadrilatero inaqualium lacerum, eria superiora in se invicem
ducta Faciane 607= cu =q; at vero lumma quadeatorum ex ipsis
Faciat 243 Ceu p.
Ubi praeterea nocandum, aequationem numericaM F (3, ∞ Y3 1)
 12, a Csirardo allatam, non indigere ue radix ejus hoc modo
exprimatur, cum in illa L (D raleat. F 43 = 3, & - 2; ac ipla X-
quatio F(3) 80(2, = 13(D) = 12∞O PeF F (1) = 4 ∞O, & Per
L(I + 3 ∞ 0, aEque etiam per 1(1) - + 5∞ 0 diridi queat. IFaUF
tantum radices earum aequarionum secundae formulae juxca ali-
quem praecedencium modorum opus sic exprimere, in quibus
constaciplas necnumero, nec C aidani resula exprimi posse.
Sed jam tempus est ut ad certiam aequacionum Cubicarum For-
ulam accedamus, ubi Z3 aqguatur + L pZ - 4.
Haec aurem xe quatio eres diversos radicis ralores admittit, duos
nempereros dc unum falsum, aqualem veris illis Cunul sumpris,
Ticut ex ejusdem aequationis constiturione agnoscere licet. Nam
si ponamus x ∞ b seu x --b ∞ 0, ec x ∞6leu N =C∞ O, atque etiam
X ∞ -d seux -f d ∞ 0, _ multipliceimus X -- b ∞ O PCF N - 6∞O,
aC denuo quod inde hc per X. F d ∞ o, proveniet aequatio:
∞3 - - d X X - b ab X -f- bc e ∞ 0, VCl ∞ 3 ∞ --- d X N - ( - b d X - bc d.
L b
6
C a
 b6
In qua siponatur d, valortallus radicisx, regualis b -f - c, duo-
bus reris raloribus ipbus a lunul sumpris, tunc quidem b Lc de-
Sruet =d, terque oxx, hoc elt, eranescet adfectio (ub X N, nec
amplius sele deltruent. Nam cum ex hypochesib- L cX quatur d,
mulciplicando urrinque per d, tiet quoque b cb- f c d 2qua lc d d.
ACvero de majus est quam bc, quandoquidem cancundem raler
ac bb. = 2 bc-c0, quadratum videlicet a b - L c. Ouare e b d-]
sd ajus eric quam bs, manebitque adfectio sub x cum (181o-.
I