# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068198:0380
# Permalink to this reading: https://leibnizlegible.com/page/00068198:0380?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2b
# Folio 190v, page id 00068198:0380
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068198&page=380
# Source image: https://digitale-sammlungen.gwlb.de/content/00068198/jpgs/default/00000380.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 97 lines, status machine
# Lines: 97 recognised, mean confidence 0.80
# 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.

Assumatur h dq + gddz = 0 fiat Z = t. b fiot 12 = d t. b + + dys b
unde fiet
ddze - adt by + de sy b7 + dt dy b + . t dydus b + + days b7, Unde, collectisue
Ed prodet t omnibus et divisis per bi, prodit:
proinde
hdt + t+ dy + gt dydy + 9+ ddy = o quaeaequatio solvi potest
 dd+ +29dF dy
videamus an datam aliquam huc reducere possimus
Sit lD + mdo +n ddv = 0, fiat V = W. b7 dv = du b ado = dd1s b + W dydy b + W ddus b7
Unde colligendo in unum, et dividendo per b7, prodibit
Wdy b 2dlodys b
Lu + Budus + nudydus + nioddus = 0 aequem coincidentiamus aeqq0 et 
m du pndudu
enwat. F
ft  (nW = ot, seu g = nwet, ob dy fiet ht +  = m W + 2n du
ob dy dy et dy fet:
A ob y, fiet lio emdu tnddio ( hdt = lu + mdio + nddeo - nu dat: fi = demw: t + 2ndtaa: t - n d itut: H
n dau
seu fiet h = atm 10: F + 2ngduo: t - 2n W dt: Et
vide ams an lice Destmere W, faciendo et m n at d. t = n ddt, seu m - 2nat = n dat
se quod procedit felicter fit enim (m2fat 
quae a quatio videndum an possit divelli in duas
quaeaequat
quid si Z= t. 97 f 4= d 87F sie quaeretur log 83 = y logg 
de
Ergo d (7) = et y d + logesidus 87 Ergo si Z= +G erit dz = G at + +G’y f+ t loges dy 93
Ergo  eZ + fdz -0 dabit et + fdt + ft de y + f+ log8 dy abog9,
lo
ddZ = ddF 87 + d+ 8’ y dlogg + dt loges dy G7 H tdy 97 +y dF G7 + A y yy d hog 5. + Ly loge dys 9)
ddelog 5, ty, gr . iloges
ty ddloges g)
+log Gddus P + t dys dlog e est + loges dy dt 9) + tlog5s ys ydlopge 19 cst + + logg dy dy loge. 8
loge vocetur V, et fiet
eZ+ faZ + g ddZ -0:
 fdt + fti a + f + ipdus + tdgd pysus + tdp V ydus
et
e
gdat gdt  py tgdt 2 du +gt dudy9 + gt dv Vy dy
9at 
9depstus +9det dy
g ddi ty
otus cotdidus
si ponamus e = 0 erit aequatio haec solubilis
Quat dy
oteptis ydus +gt  ddys Gt  lydus
si tam sit e constans, evanescent y, yy, ydy, et fiet fdl + ft ydu + gt p ddus + gt q. P dydy = 0
gddt 29dtre dius
ubn divisis omnibis per G, fit f: g = K, fiet Hi dt + K L qpdus + A 1B ddy tirs Ays dy = 0
ddt +2 Y at dy
ddv- ddy + ddu sit data aequatio 10 + 11 d + 12 del b + 13 dd x, assumatur B =  Y + cet, fiet dv = Wodus + ydu + deo
et +dD = Wddus + yddt +2 duodus  et dudv = con dycus + gy duodio + a nydydio
104
1Ideo + 11 dy
+daco
13ddco + I 13ddy
12 deoduo tr2 rcuodus + 12ddus
  = p  p+: 13 = 4t: 12 fit 2 = 13: 12 n = t. 13: 12. 12
F (id (1 +  2. 1dco) = K H132)+ 2(13) dt
1.
L. 13 (10 + 11 ded + 13deodeo + 13 ddco) = H dt + ddt
fit H+ at = = H La + = Fdtdo = 2 dt d + = 3 + t + 1. 13 Hdco B Hdcodio + 13. 13+ tddco - tdd F
se
P. 12
2. 12
.dB Et + GBB dy. + ) C, ddys + V B Clydy
12. 12
infirdum hinc egitus
ubi 1, (3, conpaates, e, 9,) datae  . a 2) a Bdus
81B
si possemus fdt + ftidus + 9 + Y daus + 9+ 1 B du =0 coincidentiare ipsi  et
penendo e constantem
gddt 29d y ay
huc Vb in constrnti ratione ad ot, su b = 9t efici 9BX gt + 2) BA gdt +, tg. 21 (3AfdG = YFF + Ygdt,
et En ot + es t gat + G2 + dq + V a gdat + V A F ddus +.) A dgdt = fat + gddt
et Bnostanti rabe ad I
s fit 5(A YB V F t at = gB1, Fat + 2YBA, Et  F 27 B) tgdus - rEsg atat
ex t e AVgtC + gL Y gtat + es 2 Wp H dg +7 ) V gtddt +VAW Hdlus t3) deptytat
8gt ddt
Fd ftat =  e,  L + Csp  +) da B - gF dat = 8β0at + 2γ Bdt dD. 2 ap g dtat
+ ftius tgta + A
= Cha((rZ + SdZ) = rdZ dr Z + t + sddZ, Ergo in s fit igat pty ti e
f
dsdz
giat
 (hZ + g dZ) cer
facimus e= dr, d, et 5- 4s tdg soliu etiam potest aequatio
multipticemus aequatione O per m, habebimus ubique em, fm, om loco e, f, 9; et manet in artiham
E debet esse em = dr gm = 5, et fm = r + ds, fit r = df fm = ds = f m = gdm - m dg = Y
et sit fdm + mdf - odam -ram dg - m adque d A gt = em = dr
 = v - y +Cd
lco
audv= dgitus tedaetco
hdiodus
e
Lloga
d loydus
alogus