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# Title: [Ps. 1] (shelfmarks Leibn. Marg. 178, Stück 1; Leibn. Marg. 178)
# Folio 425, page id 175905688X:0447
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=175905688X&page=447
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 51 lines, status machine
# Lines: 51 recognised, mean confidence 0.78
# 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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# After the first blank line: the recognised lines in reading order, one per line.

c
locte
Met
lede
lel
ec
D E RE DUCFTONF A, OUAZLONUH. 425
sen instar incognicae consideratae, per iltam aquationem inveniri
negueat. 2d0 li reperiantur, num ucramque aequationem divi-
danc. quemadmodum in hoc exemplo, ubi reperitur d - e ∞0,
cujus ope urraque ae quatio dividitur, quod, lubrosando a in lo-
cum d, unoincuicu ridere eAt. Acreio sialirer crenisset, conclu-
Lilsem, non dari, _c.
inum adhuc exemplum adjungam.
Proponamus inreniendum esse maximum communem dirisorem
Haru auarUM XGUIAEIONUIM SIVC quanEItatI
TIA A9.
da A.4.
X2a2 = AaXX L X  - =a~3- 20 A3 ∞∞O. _  AaXX  3a∞3 + = + 41 - 16 43 v L X + 20.
Ouoniam aucem lxe non dirisibiles sunt per aliquam literam nec
pernumerum, considero literam aliguam; ad libitum sumendam.
tanquam incognitam quancitacem, puta x, aeque operationem
porro instituo, ur lequitur
Der rmam inreniturNt ∞ AaX =-Z TAANKX L 2OAX --+2a+
add. = 3aX3 = TZAAXN - 26a2X L 24+
FC prO Zd ReqUatIONC ax3- L a AN X + 4 a 3 X L 22 a+ ∞0
dir. PCt a.
X3∞- aXX 4aaX T243.
Substituatur jam hic valor ipsus x3 in ejus locum in alterUEra X
quatione, upore primâ (quamris aurem in hoc exemplo parum
incerlit, pocest camen in multis calibus magnum esse discrimen,
tunc enim oportet, brericatis causi, eligere eam, per quam ope-
ratio tacillime procedit; quemadmodum rulgo, cum dux lune,
dimentionibus differentes, ea, qua pauciores habet, eligenda re-
nit), obtinebieurque X X ∞ A X  6 a a.
Substicuatur rurlus hic raloriplius xx ubique in ejuslocum in
ana praecedentium aequationum, lumendo, breritatis causd, prae-
cedentem 3 dimensionum, invenietur
2da A9.
X3 ∞ aX X = 6 A A X CCI
L A X X 2
aad
a t X
L+aaX F. T2a
DC
 a a X  6 a3
L 4 a a X L L2 a3 ∞
In qua ridemus terminos omnes se invicem tollere, quod ax-
li Lao astateoe Glaaceo MrBHCo eHC
1
per