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# Title: [Ps. 1] (shelfmarks Leibn. Marg. 178, Stück 1; Leibn. Marg. 178)
# Folio 511, page id 175905688X:0533
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=175905688X&page=533
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 54 lines, status machine
# Lines: 54 recognised, mean confidence 0.75
# 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.

toce
ac relu
de mod
.
mimum
eentine
reme
enie
ea no
 im
3
D E ENI A ZT XITS E F NITN TM. TS.
SIF
quantitates non ejusdem denominationis fuerine, iplas sub eun-
dem denominatorem reduco. Quo peracto, considero hujusfra-
ctionis incerrum Numeratorem cum unoquoque Membro Peu
parte leparata Denominatoris (li ex direrlis partibus constet)
cariquam unam quancitarem, Maximum aue Minimum delignan
cem, ac unum quodque membrum seu partem separatam Nume-
ratoris mulciplico per dimentionum numerum quancitatis inco-
onitae iltius Nembri, postquam ab eodem numero establatus di-
mensionum numerus incoenita quancitacis, qui in hoc Membro
Denominatoris reperitur; productoque per hoc Membrum DC-
nominatoris mulciplicato, erunt omnia ejulmodi produera Cimul
∞0, ut ex sequencibus exemplis clariuspatebit.
I Exemplum.
F(FO Fa a b3 + 5 a3 X f ∞5
a 3
= a X F bx - F a b ∞ alicui maximo.
Deletâ quantieate cognita ab, reliquisque terminis sub com
nuni Denominatore reductis, obtinebitur
44 a b3. F5 a3X L X5- a x + ] bx 4
NuIE. nuI. Per - 3, - 2, + 2, +. 1, + T:
Ht = T2aab3 - TOA3X L 2~5 =ax F L b x + UIE. PeF N∞O.
_, diridendo per ∞3,
=- T2a a b3 - TOA3 X F 2 ∞ 5- a X E. L bX + ∞O.
suxta generalem Methodum
et
44 a b3 +- 5 a3 X -  X5
X3
 a X F bX L a b ∞0;
d eAt, 4a ab3 + 5 a3 X F X5-- a x  + b x + F a b ∞ 3 ∞ d;
Deu, ordinata aequatione, x5 - a x + + ab X3X + 5 a3 X. F 4a ab3 ∞0.
Lb-
= 23- FF, O,  13 =- 23
3
2XE- a x X X- 1O43 X- 1244b3 ∞O.
Fb
2 Exemplum.
a d v - b 43 - X4
t
A  
A a + X3
nma.F N 3 alicui maximo.