# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068196:0091
# Permalink to this reading: https://leibnizlegible.com/page/00068196:0091?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 46r, page id 00068196:0091
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 47v); this page is its right half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068196&page=91
# Source image: https://digitale-sammlungen.gwlb.de/content/00068196/jpgs/default/00000091.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 99 lines, status machine
# Lines: 99 recognised, mean confidence 0.79
# 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.

venit, novum leu tentamentum in nculem pro resolutione
differentialium. Constentus it dus fassiosue
prirui puncti X, coincidere
es
dua Xdr gdq ydx
V. g. si esset proea aaequatio
fieret en casu du dy. + axdx = dyc Axdys posito Ad, X get 
Dinter se X et dx.
curvam exprimi, continue variando axest, et cujusque axis initialia tantum
puncta consiterando. sit cuva AB ACQ, sit axis AB Apis AH, et alius FH,
et ex puncto curvae Q duae agantur normales una i Zp in AH
altera Eto in FH. sit AH, a; AP, X; QBy. FId, Z
7t, v ex jam ex Z ectae  HF, L) se secent in G
erit AP: pG: AG = LW: WG: Gq C Ergo Hp: PG= Z_: WG
AP: HH= Z: G et TG: GH = 1oG: GZ sed AG + GWF
=G1o + eo et HG = AP= p GV somitamus aequ. 5
quin sequitur ex etr. _HW + WVF= HF, omittuim
initio HF et HA, sex et AP et FWD
10
sit Ap: (A P + pG)= ZW:
(GW + 3W) qu= HH -Hp Z GE et  eX aequ. 1
Hp. pG GH il in ex ag. 2. per
fint, 1 P: pG qU: H, W0, = SHp + pG2, et ex aeque
10 fint Hp: (H p2 F pG2) = L2:, HW + HP + p G2 2Morni
restat pG. tolcenda per aequ. (2 et 13.
lemne 
ex aequ. 12. Ht = BG (ae: HP) + H1 = VHp + pest. seu
Ap G2. (9W0: Hp) + HW  2HW. pG (ZW: HP) = H p. 7 p G.
 4 + pG: H
Ex aequ. 13 = Hp. eu tep G2 Qqu +HW. Hp + Ap +PG. HP - 2H1 is
seu HI. Zu- PGr. quo AH1S. Hp+ Ap L p G. Ap = 2 HV PG QVO H 
+ 2HW. ApV jam ope 14 et 15 tollatur PG
ex i est pGt = H p4 - Hp. H + Z H Wo. ZWo. HP. pG.:, elo- HpE
ex i5 est pGr = e p4 + HW. Hp = Hp. qu + 2 HI qW. Hp. PG, :, QW -  p
et fet 2Hp. H2 = H p e absurdum est erior in caleu  M. Ar
 p0 - F9W + HW + HP E PG - ZHW.  p + p GrA Ho
il
 Ap. HC - pG. Cto :AB. seu H C exp p (Z1G Hp = AP. Hl eS. Q
.tu
pG = VE2. HP P eW HP + H p + HW. Hp 6 3: 2H (B;, P8 - HW. qW. (Ex 3)P i p - H _ : eW - H sol
 fi p p E q- 2 p p B. pG. = ZW. HP + HI. M B + A pd ( BG. H Ph (3AW.) Ap, - 2Hlo Zud PG
Ex, fit AP. HUS - HP SHNL pGr = BG. ∞W. sen AP +P4
Eet h
y vel y
Wd F = HF, A = AH- AP CAPG YGZ = )eZ. sene
jam Gq
HP: pG  = ZW:, HW - Hp + pGi
(e
2+ Ap= H  HG2. ego ex Y  et 8. fit fHW:, F, HP. PQ H1o. 210 - 1, AP. H13: Cd. A
deu A4 sed  axissen iL: LA et fiot PE 6 t 9 et 0  l: Y = HW:, Ap. Pg- H1. quo
seu p9 = oW + Hp + H13, :, 3 AP. PQ = H H a
superest
Ex ) et H est Ap. p Q = (Y. I) MO + H S H t:
1046. l: r = s. Hp - x 1,:, ZW - Hp seu 1H. N = U ZW= H. AP = YrHp- rr HIS. Ergo
seo HP: BG
ut ope 5gg. 8, 9, I1 tollamus HP et PZ,
H p2 ILW= rr HIO,: (l- 1 = (per 8) HW + HS YN
G =(I ZWrrHWD + HWO l HWrD (= 1HI r: U- 1r Cixdevend.
 fit (UNo rNIo= HuUNu et  si Hol 
Wg. v sit Hp: pG = r: l tit X = Z - rV: NFI y - Z+lIV)B. SAM
que est aequ quae aequalio deberet esse identum est erior in calculo
l- 1
in XFIErrLr et  = X se  y Sitr - b: DV. et fit
Y
YrF)  seu v = (y - X) r: Sit rr
H(yrr =Xrr f. Vitrr) seu q = X(F XVD + yir Xrr,: sitrr
seu Pyt = HW = A = qW
paucis res huc redit
H8, Z.
yFitr  ((9-X): SIF Er) seu Z = (+ yer  y, + X: sit
(y-X)Sitrr
AP X. P2By. B
sitem nyllans vides efficiendi ut res lampatium hac modo redueatur ad
Et Z X +
v = (X y) t
Quadraturqs nam duo raeter duas infinile parvas dus, dx duae
Csidendum
coaneseat.
1B373 3βaB, elc reddueret ad 1
ubi pro arcum circuli componendo
ippsas
et Z = X SItEr +y
seu
naneu, Ende lerninalee 2
3 et t
itaque nul juvat, essi velimus
et alla curva obtinea posset, sed tunc opus A pariari, seu A(+) esse focu,
quid sia s , summando componant aliquid
trajectionem, si
scilicet si 11) 2, contipuaretur in 2825 Maut,  2 aequillam et 435 in 39 2A quoritur valo-
3)4)
2γ 3
ipsius E
Malim ergo
tentari a Iaquiri: a
copretus
Ae si feculum de ar ingentim
ex
1. 1