# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068199:0180
# Permalink to this reading: https://leibnizlegible.com/page/00068199:0180?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2c
# Folio 90v, page id 00068199:0180
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 91r); this page is its left half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068199&page=180
# Source image: https://digitale-sammlungen.gwlb.de/content/00068199/jpgs/default/00000180.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 63 lines, status machine
# Lines: 63 recognised, mean confidence 0.76
# 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.

sit dy + m 1. + nydus  + pyy dx + rdx Z0. fiat
(2d0) y = tv. unde habebimns ex aequ. 1 habebimue
Btro) tdo + Oat V + n Et vav +ntdt vD + rdx L0
+MaxF.
a pet dx.
multiplicetur aeq. 3 per h: t fiet
(4to)
hdo + ht: BV thnt vdo +hnat vo + r dx = 0
+mhaz..
+hPta
2
Habet igitur aequatio A tres partes unam.. do +.. V, alteram
.vdo +.. vo, teritr tertiam  absolutam ab v. Ex his
tertia est per se quadraturabilis; duae priores videndae summabiles
per arbitrarias h et E, nempe ut d+. fiat summabilis
oportet esse hat: t) + mhax = dh et fiet fat. t + max = sah.h
Rursus ut. dv +. vv sit summabilis, fiet hndt+ hptax= dhnt
seu  (2n haC + 2pdx h+ = nt dh+ (nhdt) + ht du
e
nhuc ta d(t)  C
n (hat - tdh) = (dn - 2pdx) ht
et fiet
dc - dh = dn = 2p dx
t
seu  A = at = 2
h
pax
n
du
n
apdx
n
an
2
e
sed supra dh- at = mdx. Ergo indx =
Unde patet nem hac via non posse haberi absolate
+
sed posita hac relatione inter M, 1n, P.
Videndum ergo an non res melius obtineatur ponendo
1 +v + V.
incipdamus he absnitio, et servenus
sit
u Tamysdx tanu dy + pyydxt aat dx =0
legem homogeneorum
sit y= +(. a) + Y fiet dus = tav: a) + dt (p: a + dr. Hinc
e
fobs
(Ato) aatdo taavdt +var+ mtraxtanrax
+ n +D+ (dv: a) + et dvBa) + ntv dy + ret do + ravdb, anrar) =0
 dx H(vD: aa) + 2p X V: a) + pdx YY + aadX
multi plicari intelligatur haec aequatio perade inde insti-
a
adrunt
tuantur aegnationes qua paulo ante.
et pro  dv +.. V, fiet aut patnr a
aa +nr) hav + (aah(at: C) + Mhax + nalnnhar+2h a) cx) V
et debet esse aadB + prdh + h dnr) = aa Hat t) + mtax + nhar + 2p rh: a) aX
pro 2vdv +.. vo, siet (LnHh: a) + Ln: C)h) 2vdo +(h: a) dt + p: aa)hdx) vV
 nta atia) tr.C) relt itE)) = netri. as at F pst. au) tax
ergo fiit (7 mo) Lut: ad a  Isutd  e: (+: a)  +(r: C)) atan + ndt)
l
seu dh: h aa t aa(dt: F) + mdx + ndr + 2pr: 4) aX, : aatnr