# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068194:0150
# Permalink to this reading: https://leibnizlegible.com/page/00068194:0150?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 1
# Folio 75v, page id 00068194:0150
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068194&page=150
# Source image: https://digitale-sammlungen.gwlb.de/content/00068194/jpgs/default/00000150.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 62 lines, status machine
# Lines: 62 recognised, mean confidence 0.75
# 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.

ex AB delapsum
curvam quaerens in qua descendens grave aequabiliter recedit a certo
quodam puuncto, hanc tandem aequationem differentialem inveni:
8 bt AC = X. Bd = v dv: ax = 8
Des
c
()L(C)
fore b V - 2b VX G + Vet  = 0 quae aquatio resolvenda
e2d
+ ax
Quod quia in ordinariis difficile est, tentetur per seriem infinitam:
sit V Lx 1 mX + ux px a qu etC et V l’et retme
v - 1X + 2 X + 3X+ 4x + 5X +6X esc et v = 11 X + (2)1. 2X + () 13X (2) 14X L (2) 15X esc
 = (1). +() 2X + (3)3X + (4) 4 X + (5) 5X + (6) 6 X ds C
Y 2.2 +(2) 23 ()24 ese
3.3 est
492 = (16) 1. 1 + (2))(16) 1. 2X + (2( 1(2) 1. 3 (2, 19(4) 1 4X + (2)(1)5)1. 5. X +(2)16) 16. X =I, 611,B
SuB (1) Cx CeX. )1 X Neges 125 ) ( 1
1(2). 2.2 +(()) (3) 23 +() 4 + (9 (2(5). 2.5 Xe D (2)(6) 1.6.
2.
 jam d = 2 v d 28. Ergo v = d vi
seu V8s = (1)1. 1 X + B) 1. 2 X + (4) 1. 3X3 + () 1. 4 X= +b)1. 5XE esc
+ (2) 2.8R (5)2.3, (6) 24 esc
(3) 3.3 ec
et  m vB () i x +
+ (9(44. 4
bvg1)Xn 1B) ∞X + (4) 1. 5X 2 F(2Y (5) B aX +() (16) B35 Wx 1 = b5 g2
D (1.2) 12. (2) (15) (2. 23 (2) (16) 1. 24
(2) (1.3) 1. 3.3,
+(3.3) 5.5 Y(eD B+) 1. E3. (2∞65) 124 
(2) (3.5) 1. 23 (2) (35) 1. 2.3
dunibus ergo in unum additis, fiet: +(44) 1.5 dC e
(27) (4. 2) 12. 3
arv: - ) CaX - (e C3) i2a X  CxCealisaL entes) it aX -- axves
(4
-(21 (. 2) Cta. =(2) (1.5) 12. 23a Al
=(3.3) 1. 2 a. -(2) (. 4) 5. 2. 3a
1)’ax HAB) I2aX + () B)13 ax
(D Ge Vx IB)LLVX (HCt B X
-() (1) e2 BX- ( 1 2bX (3) ( 1. N X (es e l14B X
1+ b X + (2)1 2b X + (2) 1.36 st F + () 14b X
() 23V
Extermino x fit 11) (2)41) = 0 quod verum. ut allatur a X
tollatur. I x3 fit
=(2) (3. 2) 1. 2 a
+(N I X  = ax g2
+(4) 2.2 a + 6211 (6) 2.3 a.
=(2B) eb
) 21. 7211 () 23b1c
2at
4(2) 1. 5. bX e
(2) 2.4. V.
26(2) = 6(2) +) -0 Ergo
bv
m a  et conesit) set (401 - 9b)+ etrao, ax sesi tubia
4
Et ut tobtabus  s quod
uobse lati
xl
=()10) 1. 5. b X (s = - 26∞1
(2) (5) 24V Al
(2) B) 33V