# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068072:0016
# Permalink to this reading: https://leibnizlegible.com/page/00068072:0016?run=73
# Title: Leibniz-Handschriften zur Mathematik LH 35, 6, 27
# Folio 8v, page id 00068072:0016
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 9r); this page is its left half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068072&page=16
# Source image: https://digitale-sammlungen.gwlb.de/content/00068072/jpgs/default/00000016.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 99 lines, status machine
# Lines: 99 recognised, mean confidence 0.77
# 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.

Generaliter video nihiatus inc determinatiorem fre
quaerimus postremo aequationem qua ratura resolvendamus,  ubi due: adque habetur per do: dz, unde dco: d2
Qvia ergo nimia determinatio est E5
ob aqui 12 et 16 habebitur deo idzue per dv: dz. sed ita ob aec. C et 6 etiam X: a, et dy: dx habebuntur per du: dz
quo posito habebuntur x: a et dy. dx ex se invicem citra interventum quadraturarum quod est absurdum
ita Nam ita in aequdata 7. tollendo dyidx substituto valere per x. a; haberentur semper ordinarie ex seinvicem
ipsurum rationum
Videamus  ergo an alia ratio excogitari possit, ubi initio deo non ingrediatur in valores X. a e
X:a et y:a, nec veniretur ad transcendentes.
X: a et yra assumendos, unde et ejus explicatio nit nocebit. quod fiet adhiberda duplices summas, et postea
cavendo ne descendatur infra in iis tollendis descendatur infra ad, dum nempe ado idioqu multiplicata per aliqua
diffeentialem plimigundus aequatur differentiali primi gradus constanti. Sit ergo X: a =1) (ddZ: d et
y: a = (2) SddZ: dx fit du: dx = Bto) dv: dZ sit jam in data aequatione dy: dx = (4) Xxtyy: aa
fiet dv: dz = (5t0) qu 5a1Z: do + qu. 5 dd Z: dZ et differentiando fiet dZ ddv - d vddZ, :, d2 dz = (610)
(daz: d0) (sddz: dv) + (adZ: dZ) 5 (ddz. dZ) adeoque dZ ddv: ddz = dv, : 2d2 dZ = ()(ddz: dv): dv) H((et 4Z. d Z) : d2)
gaq = dodo ad seu sddz: du dx Cctav. 412 (. 242) = (dvdv. 2424Z) = (d∞: d2) sdlaz: dz =) dudque (dav: ddZ) - dvdv - 2dv dq (a 2. 
dx ua siazite) B3: 2 d Z 1Z adeoque quo  qu. Sdaz: du 2 dud bdqu dZ (d Avd : ddZ ddZ) = 2 d vEd Z (ddv. dd Z) = 4 dodvilndque (dv. 19) (dl r. d.
dot F q doidqe sddZ. dzue + 4 dvdo dZdZ. qu sadz: d Z = (quo per 5 (9no per 5) (dv: d2) = qu s ad Z: dq  a3 4
 item aliter ex sto erit sa Z: d= (dv. 4Z) - qu fddxed Z) Quo minus in calculo labamur
per agamus eum ad huc aliter  (ddz: dx = (10mo) Y ((dv: dz) - qus daz: az) et et differentiando fiet
aldz: do = (11 m0) (d Z ddv - dvddz: d2 4Z) = 2 (d d Z: dz) 5 ddz: dz 3: 2 (d v: dZ) - qu sdaz: d2)
et dar ddZ: dvdv = d Z dZ ddvsp 2 dz dvado daz + de dv ddz adz - 4 dZ d Z dd Zdaz q u sa d z: dZ - (+ d 2 az la, silv tsedvaq. 1, d1)d
3: a (4, dv: dy) = 4 qu )dd Z: dZ) du + seu (dr: AZ - qu (aaZ: d Z) 4 d2 = il X dz el Adr (clilvdav: da q dt az) : 2d 2 dv e dv: at 2)
F dB = + 4dZ dz dodo qu fulz: a2 = 4 d 2aZ do dv dd v.: dd z) Sad Z. dq + 4 dx haZ sdd : aZ. ed Fies igitur
e
(daZ 34 d du - aet- dz z aodi e rax + 22q v a
l2 (d dv: dd3) + do
4dZ (aZ (d2dZ + dodv) dZ
qu fdaz tr  d
inde fiet pidaqu dt proitad
4 dZdZ (dZdZ + dodv)
d Edo- 4 de du a de duuo ve u ala see
compendio faliamus jam constantem aliquam quantitatem, qualis dze ddo: dd  do
4 dZdZ (d E d 3 + dv dv)
per compendium quomodo vocabimus ita enim eam voculimau
et ex aequ. 14 e
fiet ( aaq (15) 2 2dco dodp = 2 dv + dZ 1 (16 d 3 d - 4 dv - 4 deo du dvdlv + 8 deo dv3 + 16 dz d v)
4d2 (dX Z + dx d0)
seu sa is ita an. Iu a Z S (16 d do Clj A ravar) -  ( a - a1
4dZ (dzdz + dv dv
C = deodlodlps
deo (deo) d 2
pBavagibnr 
+diavadq Y (4 dodip aesde
a 1 a ddo + dip avdd-de d da 
deo dipdi
+ qldaze Hdod +l. serdodds
=dz dd p N. d945
d pall - ae d (( dv al - d9des)
4 dvad  + 4 d p v - 249 dde
dcoulp 2 Y (4 dv dep - d9 dis
ddo per aequ. 15 et 19
add (20
+dipq ub dav
docex.  o
+arll Et
Hosteq ( a dv do)
et compendiu faciendistico du) d aco
fiet squr 11 extio ) dvelc (+ av daetu d y - dco uo d9. des)
Uinde differentrando:
de avddips
du dide
dis  (4 dudip - d9 d
deodcsta vaex -agag) = 16 du tv + 16d2 dv - q avavdco a  d d ud  -4d v vidiamus an hanc quantitatem
et 4 4 dv d - d 9t)
liceat reddere extrahibilem sit dz = dv d8: deo et fiet derdr, P 16 +3 d
3 4dvav: deo
Ergo () d E F (5 d edeo deo duax-(2deo  + xdcodvdo dco: s quari debet quadrato daor
seuddo dco d +de
et Bde =
= do + o s C) (dco  aleod E dco  t a 
2) (4d83d
(2) (4 de - deo)
2deo deo de dcod5)- d d cot et deo radiols hrtode di pulestimim
413- deo
B(152 de)
4 d33- dco
Lndm = icst an d = 4 dco de3, . du dy - deo
XX: 9a = sd : dv
gy: da = 5 dar A2
xdur udd
2 xax
vuniar ause
13. pancta super
ignis posita
adicant colla-
tionem calculi
aequationis u
cum calculo
une cao iptur
issem ale
quo dndrirgusade
An+ M =am
nntenterran
n tantir- r
un +2bn _ m
in + 2b n +bb
et n- Snetbb.
Tetat tale vime