# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068207:0041
# Permalink to this reading: https://leibnizlegible.com/page/00068207:0041?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 15, 5
# Folio 22r, page id 00068207:0041
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068207&page=41
# Source image: https://digitale-sammlungen.gwlb.de/content/00068207/jpgs/default/00000041.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 126 lines, status machine
# Lines: 126 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.

AF, a. CF
Ce-CA
AV, v.
KanvVa. 
Ad Epistolam du. Barons Bodeni. 23 jun. 1691
a
puncto, recta et circulo positione datis; invenire minimam interceptam
inter rectam et circulum fa quae producter transeat per punctum
Neuipe dato centro C et radio CB, adeoque circulo, dataque p recta cB
popositione recta GH indefinita cui producta CB occurrat normaliter
in G et dato puncto A, adeoque rectis CF, FA, quaeritur ducenda
AH, secans circulum in  E, sie ut EH sit omnium possibilium minima
quaer sit GHx sit  CB, b, e CG, g. CF, f, AF, a
GH, X
gatur
Ex puncto E deillatur EM  normalis ad cG
et CM sit m et Cm sil C. fiet eet mm = bb
a - e, : M = f :: a -X, : 9 - f
postremo et
ita determinatum est punctum E per intersectionem recta
AH, et circuli BE.
porro HE sit y minima eritque
 ce HE = cG. Cm + CM - GH. seu yy = g9 - 29m + mm + e- rex + XX
55 ag. 1 est cde = = mdm, et ex aey. 2 est - de g. f= dn a -x  = dx m. f
erg. 3 est Rydy = -gam = edx + xdx et quia du =0 ub mimimam
s fit: de 2 gdm + Xle C Xdx - e dx
A
(1
EBBaBa rursus AF = EM ad CM - CF, ut FA - GH ad CG- CF seu
2
2
porro ex aeg. 2
F
fit a porro, g- f. per compendium vocemus p, fietqu e
aeq. 2.,
10
act ap - ep = ma = mx - fa + fx et per compendium
11
sit ap + fa = 99 fietque que = epa mx+sx, et
pe ita compentiosius pro sg+ habebimus +xam + max = p de + fdx quae coincudit cum aeg. 5
xoe  e=  4 94 - fx + xtam,: p =bb - uim ex 12 et 1
porio, jungantur aequationes 4, 12 et 4, ad tollendas differentiales, fiet
de =-mam: e (ex 4)  N- a dm + im dx = f dx 3: p = (ex 8) Xdx cax- gam: X
(19Y
c2
 ex 1b et 17 fit dx = - pmam: C + a = X dm ,:, m- f = (ex 191) et D) - xmam: C + gi i29.
ergo ob eq 20 evanescente am, fit . pm + a = XC X - e L =xm + ge m- f
e per 14 et 15 sit ge ex Ex 3 ope 14, et 15 sit
+ gg 29m. 6+ x C R 2Ab minX ex is est X
+ Y
23
 et ex aeq. 3 sit gg rr - xx- rex  2gm et ex
 sit gg. t bb2
aeq. 14 est pC - qq am, m  quem valorm substituendo
 et quia a= C p: f - in + a = X
e
e
m. mafnt gen
 seu X= a na -pa -e,: n
sit f+ m = n t et ex ag. 22 fiet
(25)
A-nes pn + a epe, al Ha-e Bn p=  ar Bon
= un =na + pa-pe ntf + gen
et a-e faciendo v. fiet
=n + f Pn + V pa B, v. np = un - na + pP ntf L gn a- v
s seu, = pnn = pnf + PaV = pPV, vn-vp=  un exentannatutgann
bbacoco et quia. Ce+ um, sera aa - 2ar + vv + n + fn + f   =bb fiet utr
es
vo + nn = bb - ff - aa - 2fn + 2a0. sit bb - ft = a a = BB et
fiel en+ nn= BB - 2fn + 2 aV et 6g. 27.
=pBB + p fn, -  p avC pns) pav
siel
et quia p - g = - f per aeg. 9.
=pBβ +. (2) p fn = (2) p av (= pr F + paD, vn - xp = nn  gf Vn Fann xso Aan
et problema solvetur ope duarum aequationum, quarum una est aeq. 31 ad
circulum, altera est aeq. 32 ad lineam duobus gradibus conica altiorem
vnp B3F pt. Vnn = pavOn +ppCBVC +ppavv = - fVN- an tEp f Vt par
BPF
c’ et pro vn substituendo valorem ex aeq. 31. fiet:
pes Vn + pp BC V + fvH + an pan= (pan-ppa PB + 2av - nn - 251)
ppa ((3 - 3pp a a V + ppann + 2pn fan + 2paavn ( pan
)(34)
2p af nn + pa βBn
Eergo v a ia eB= riptan
quae est aequatio ad  curvam
lecet per numeros ratianales
3
Lpatn
B(B
PB1
22
rationalem quarti gradus, quam etiam Peuiu puncta invenire
habit solutionem problem abi
Ruoe arqu. 31
at=at (e SBe-2fn. nin
groblemta est impossibile solum et semper sit BB+ ac- 5) sentb. aa, sit minor quam f+n seu minor
qu a fubtco sorocib quam nins  bb dib, es, in rins qeao dibilitas eitandu est  s. d a tiem  ns aalemi, ut 35. abile
n.
ud aet
blaitu
31 un segus
nur das gua
caerie
3 taustrgus negativa
c
c
e
Ec
4
eu v. abb facns fulbio
sed non video,
quid hinc lucremur
Contraretur Magis
calculus si in valore
ipsig. V aeq. 35 siat
numerara et nomi-
nator yndivisibiles
g. f = P pf- 95 t)
BB= bb- aa -
(Ex aeq. 32 si
3B + 244 = bb ta +- g
Pa-2af = ga- fa
BBtpS =
31
seu v = atrbb - 5+R
at sba ta