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# Title: Leibniz-Handschriften zur Mathematik LH 35, 5, 17
# Folio 3v, page id 00068035:0006
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 4r); this page is its left half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068035&page=6
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 98 lines, status machine
# Lines: 98 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.

b7
Edtod
etb7
Nimirum annes formae, in quibus yX, redibunt ad:
y4.
213
ben 7.
esi
X3 oTt 
seu  TA T. constans
X+ 3
V,H 3E
seu a t
2
X13X73~T+ Y ∞ 2723
13H=
15c 1
27E
Sit aequatio y p X, constat esse +B YX. Nam. X Y  
eu et si 4 +n 3∞, fici te 3y.
Sit jem aequatio Y HX. sumatur alia curva y + b p X unde uno in alterius locum
substituto, fiet, X - y - b p0 iujus aequationis tantum maxima opus est quaedudum
nota.
sit X alia X_ sumatur y p X + c. fiet: X ++C. Ubi
cum C possit pro assu sumi pro artitio, utique sic sumi potest, ut dividi possit per XX
et hac methodo facile perveniri potest ad tangentes singulari via,
Tentemus et hoc: Ad curram datae naturae et verticis,  earum quas simplices voco
ducenda ex puncto in axe dato F. maxinia TC quaeritur ipsa AB, vel BC.
sit ABAX. BCHV et NAB. TB⊓  TAp, B. AB X
TB1 X+ b.
BCp y. TCB X + 2BX + B ( + y  TC12
erit Z omnium possibitium maxiima
ehniteo
Si SC tangit curvamus idem est ac si secet ilauerat ipsa C(C) s EB (B) mor quan ttate
qualibet assignabili. Nam Hinc facili demonstratur tangere: nam si sec ponatuo in duibus
punctis assignabilis intervulli, ostenderem statum intervallam horum duorum punctorum revera
assiguato esse majus. Adeoque hypothesis foret absurda, adeoque non secaret, sed langeret
Hoc ite a non tanget, secabit in duobus punctis assignabilis intervalli contra hypothesin
unde Metrodum Fermatii de Magimis et Minimis, possumus habere pro
demonstrata, quanquam et ab aliis dudum veterum more rigrrose demonstrata sit, unde non
est cur actum agam, praesertim cum nihil hac propositione dicturu simi quod nnon inter Geometrus
constet.
V X7S
a +42b +6 ab + b3 ( + 6 p 8+ 3Cd + 3cdh, d3
a27 3.
Ergo a ch
4abH3Cd
3cd ergo a p +Cb, e a Y
46
1d
quem valorem inserendo vulori ipsius a fiet:
a + 2ab +B  c +d.
 a pC.
64 313
81 d3 B
 ap81 d
64b+
2abrj.
1+
30d
4b
an L. _ C ap . ergo (ap 2b).  ap. 20. 8.
a +3ab + 3ab +B∞ 1+d aC. 3ab p d: erit a
ergo (a p 3bC) et aep 9bc
d. erit (C7  d.
d H 3b
2763.)
sed si quaramus si aBC. et 4ab p d. + erit (ap Hbc
et ita porro ergo generoliter, a f 2) bc. et c
posito a2
c
jam altius: 257
jam ex 1. erit 1 2.. (4)
(8)
a
a
oZ. a2; b, d
et
(27
1
C. seu 92
t
et erit lP 256b
CoH . nisus ex 2, eris a (6) od Za  ()
et quia praeterea: a2 +Z, a b + 22 a2 
V a
co-
13 d2
d. Unde  () co co 
c-1
lons B Z ergo fier.
45co CAZb
ergo CB Zba, et ccol) Zba co  unde juncta 1. fiet: Zb c a2
cod
exprimendum in characteribus esse Z majorem quam co
cod
1,2, 3
ABHX.