# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068166:0025
# Permalink to this reading: https://leibnizlegible.com/page/00068166:0025?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 10, 13
# Folio 13r, page id 00068166:0025
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 6v); this page is its right half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068166&page=25
# Source image: https://digitale-sammlungen.gwlb.de/content/00068166/jpgs/default/00000025.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 65 lines, status machine
# Lines: 65 recognised, mean confidence 0.89
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
# Licence: CC BY 4.0, Leibniz Legible. Machine output: do not ingest it as verified text; keep this provenance with the text.
# Wording rule: say "the machine reads it as …", never "Leibniz wrote".
# After the first blank line: the recognised lines in reading order, one per line.

em quia non valde difficilis est
exequi placet, e primum quide
si omnia sint in rodem plano
ND sit Ap et _N) sit du erit
ND sit du et D(V) augnentu
DN m incrementum ipsius FN seu descenseus ponderis vocetur du
et D(N) delinatio in latus seu crementum ipsius AF, voletur df
ANL ef adeoque FN sit n, et AFFKF, fietque proinde
+ FN _ et d. AN = AF DNY) L FN. DN: _AN. Eodem
equ d ANV
modo d. BN ~ - BF. D(N) L FN. DN,: BN et d. CN = - YF. DNV) L FN. DN,: DCN
possibilium minimum, id est debet esse nullum, seu fi
oBF, D(G + FN. DN
BN.
= cF. 1) + Fv DX (5)
. CN
Patet enim si nulla sit ista quantitas ulto minorem fore quam alias
sit ergo EAF. BN DCN + BF. AN. _CN + H. CF N. ABN (6) DN
FN. B DBNHCN +GPA N ACN + H _ AN ABN
seu sit: -E.AF:  +GBF: BN+  CF: CN
EIC FN EANA G. BN AH: 
(7) DN
XN)
D()
si esst si E, G, H, forent aequales
res redipet ad theorema a mesilulam
de invenienda tangente curve
Cujus in qua summae AN+BN+ C
debent esse aequales
quod si velum rem etiam exprimere per curvam, st concipi summu in rectangulis
ub,  rectis ei AN, BN, CN, in datas respondentes E, G, H factis
am jungendo aequationem 2 et _7 reperietur d. AV: DX nam
debere esse aqualem
per 59. 7. tollatur De) ex aeq. 2. fiet:
 L. AN:  FN. C.AN + G: DI + H: N
DN
Ergo L. AN - dBN
1
=E. AF: AN + G. BF: BN + H. CF: N
En
FN FN = FN. BN-AX Quod est theorema elegans
BY
AN. BX
Nempe differentia  quibus trahuntur duae quaevis chordae est ad AN, BV
AN
DN
conatuum
conatum
a pondere N (nempe d. AN  d. BN) est ad oimponderis trahentis X
(nempe ad DN)  _ e in ratione composita radisd secantem (B)
anguli majoris et differentiae secantium ad secantem anguli minoris (FNA
Et differenli duorum cha conatuum quibus trahuntur paria aordarum sunt (d AN- dBN
binae chorda
sunt in ratione composita directa differentiarum inter chordas, et raciproca rectanus
(BN - AN) et reciproca rectangulorum sub chordis. ponendo clavos chordarum
Quod m Theorema etiam verum est, si pondus
N per pendiculariter desceidere conetur seu regatur a crena perpendiculari
in eodem horizonte.
AX- Nq C: um:: EN. XB- AV 4: X B. AA ex aminandum an hoc verum
a
A N = s, A H
AN= si
et pro inde resistenti intit
AF. D (V) + F N. DN 
.AN