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# Title: [Ps. 1] (shelfmarks Leibn. Marg. 178, Stück 1; Leibn. Marg. 178)
# Folio 309, page id 175905688X:0331
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=175905688X&page=331
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 61 lines, status machine
# Lines: 61 recognised, mean confidence 0.79
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
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3.d.
L Cate
lan su
3.
Di
Oneit
quaelio
incogni
eniantI
minuere
Cae qua
mus diric
caule dirite
busquingu
um binis
2SVC
et
cat
el
610
+3i
6.
opiselle
COMMLEBPAREE TN LEBRAMTII.
309)
Ubicandem nocandum, ad Peligendos dirisores divisione sque
Fuxerfuas eritandus, spectari etiam posse ea, quae Vir Clarisimus
D. de Beaune delimitibus Aquacionis, intra quos ejus radices
cadume, cradidit. Oualia icta in 2d Fractatu continentur, qui und
cum primo de nacura d consticurione A:quationum huic cdicioni
nunc accesE.
Unde coenoscitur, valorem ipsius Z esse = V a a + c cC
 V  = a 4 -L =Cc = Z aV a a F CC, vel Z V a a - L CC
V  =a a  =6C, ] = a V a a - L cC.) utpote qui eliCier
ex priori aquatione ZZ ZV aa L 6c. L = aa = a V aa L cC ∞0.
Oux quidem primi rel terrii casus esse porest aequacionum Oua-
dracarum pas. 6d 7. Primi videlicet, M13 a a est minus quam cC,
quo calu = V a a + 66 f V - 2 a a L =6c, t= a V a a - L cc dC-
Tignabic rerum ralorem radicis Z, _ = a V a a  L CC
V - = aa f 26c. F = a V a a L cC, Falsum ralOrem, juXta CR GuIX
P28, Y6Z aMNOTAVIMUS. AEtertii, (1 = a a majus tueric quam cc, quo
caluueraque radix est vera. Ubi porro notandum, aequationem
Posteriorem Z
Z + ZV aa 1 66 + = aa t = a V a a- L 66∞O.
Postquam = a a. L + cc non fuerie minus quam = a a  2 a
Vaa Lcc, lire, quod idem est, c0non minus quam 8 aa, duas ad-
mittere tallas radices, quemadmodum p. IG5 monuimus, quae Punt
2Y aa + 66 + V = 2 a a  = CC - = a V a a + C6, e
=V aa CC - Y = = a a - f = 6C - = a V a a -  cc. IEA UE
quatuor sine radices binarum praecedentium aequarionum sire x-
quationis
eutltde
7+X  Eaa - 43
 1s a +
 cc acC = adCC 00,
7∞ :V aa + c0 = V +60- = a a = = a V a a. I. CC,
∞ 2Y aa LC0 - 1 = CC = = aa  Z a V a a - L CC,
D- =V aaL CC- V + CC- = aa- = a V a a - L cC
D = - V aa + C6 - V = 66 - = a a = = a V a a L 6C0
Et quandoquidem supra feceramus Z L = a ∞ X, innotescit, e
quan