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# Title: [Ps. 1] (shelfmarks Leibn. Marg. 178, Stück 1; Leibn. Marg. 178)
# Folio 284, page id 175905688X:0306
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=175905688X&page=306
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 41 lines, status machine
# Lines: 41 recognised, mean confidence 0.87
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# After the first blank line: the recognised lines in reading order, one per line.

C
284
E R A N CFSCF a SCHOOT E N
pare quoque detectum alicujus quanticaris, urpore d, hoc est.
xxequari - d) producetur Aquatio
X + =- a X 3 -  a b X X = - 4 bc X - a b5 d ∞0. Oux dividi porest
Lbc + ab d
 aC
a d
 bcd
acd
DeFX = a DO, DEFX = b ∞ O, PeFX = C∞ O, _ Per X - L d ∞ 0, de
non perx plus rel minus ullâ alià quantitate.
Cujus divisionis ope dimensiones ejus in tantum diminuun.
sur.) Sic diridendo aequationem pracedentem, quatuor dimen-
sioneshabentem, Per x + d ∞0, orietur A:quatio
X 3  a X N- + a b X = a b6 ∞ O. IN Qud INCOBHITA GUANEIEaSEreS
m C
L bc
ac
duncaxat dimentiones habet. Oua rursus dirisa per X- C3O, PFO.
dibiexx; x. F ab ∞0, aquatio duarum dimentionum. (ux denuo
perx = b ∞0 dirila exhibet x - a ∞0, aequationem simplicem.
Ende perspicere licet, qua ratione, in qualibet Aquatione,
pluresradices habence, quantitas cognita secundi termini, xqua-
lis sic summae omnium radicum; de quantitas cognita tertii ter-
mini, aequalis summa productorum ex lingulis binis; e quantitas
coenita quartitermini, aequalis summae productorum ex lingulis
TerNIS, AEQUCITA POTTO; ac vero quancitas cognita ultimi termini
sire iple ulcimus terminus, aequalis producto ex omnibus.
Sic cum in aequatione x 3 =9 X X L 26 X = 2 4 ∞ O Eres (I
eadices 2, 3, _ 4, quae delignantur per a, b, ec: erit earum lum-
ma 9, quae denoratur per - a - b - c, aqualis --9, quantitaci
cognitae secunditermini = 9 x x. Summa aurem productorum
ex lingulis binis 26, qua denotatur per L a b F bc L a6, Xqua
lis- F 26, quantitari cognica certiitermini f 26 x. Ec productum
ex iplis tribus, 24, quod denoratur per - ab0, aegnalis - 24,
quanticati cogniex ultimi termini, sire ipsi ultimo termino.
Fodemmodo, Stuerit AEquatio caliS: X = = 4 X 3 = FOXX +
106∞ = +20 ∞0, Cujus radices (IIHE 2, 3, 4, e = 5, atque
delienantur per - L a, + b, F c, d - d: disponatur ipsa, uE termI