# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068199:0202
# Permalink to this reading: https://leibnizlegible.com/page/00068199:0202?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2c
# Folio 101v, page id 00068199:0202
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068199&page=202
# Source image: https://digitale-sammlungen.gwlb.de/content/00068199/jpgs/default/00000202.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 83 lines, status machine
# Lines: 83 recognised, mean confidence 0.81
# 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.

Hac methodo videamus an non per Maximus liceat exhibere
lineam ex tungentium proprietate datam
AB, ∞ BC, y AP, p ita dx: du = y:,   e B p- X 47
quod si ergo datur dxodus e da = dy: dx = Z: a. posito Z dari ex X et y.
fiet a  ex dat ex natura lineae per tangentes data, fiet
Z: a = p - X : y. seu y ap - _X,: Z
fiet
 BC BCquadr + Bp quadr = max. pC quadr. seu max.. Ergo fi
gy + Pp - 2p ∞ + XX = mm et per y substituendo valorem,
fiet; aa pp - 2aa pX + aa XX = ppZZ - 2pX 3Z + XX XZ : ZZ = mM
Hinc si Z detur ex sola X id est si linea qua cC sit quadratiix sid summatiix
et ad eam ex puncto in axe dorto p incenda sit max perpenduaaris
dabitur coordia distantia puncti curvae quaesiti a condirectrice, seu
ex X et Y sed sit
in exemplo, fiet per 4
a= X= (aa =ap 9x. Ergo gy + aa =mm: sed hinc nihil
(S
ex 4 
fet
4 (1
X. sed hoc
sit 7 gu. sit ze = y A Z sit Z = a: 9 qu (10)
aa a a2L py - X y uide tollendo p- X ex 8g. 6.
yy + Wa: gy = nim seu fiet 2y 8-24: y3. = 0 seu y = a
sed nihil hinae quod videtur absurdum, neque enim quaevis p habebit
unde videtur colligimus non posse to
ex aeg. 6. sit Ergo ZCa = X Z= Xy: a. et fier
uinam eandemque conprantem y.
debere tolli p
curjus ope toltamus  X Ergo ex aeq. 6 per 9
fit aap - aax + PPX = X + X, : X = mm et differentiando fie
ex 6g. 4 f, et ryy D aapH = aa X c10
-aap  = ep + 2X = 0 seu PH = 2X3, 2 pXxt aa nvs 17 e
eitipve hu
e
fit aap=aax e ppX= hpXX + B3: X= m nim et differentranto, fiet:
sirus anigracur nor perincie nns fvis, non
ex aeq, a erat fit X aap.: aa +gy
b _ et XX = a pP:, a +24ayy+yt. Et ex 4g.6 to lendo X fet gy+ op- Eppaa: aatgus t app: a tuig +) n
et differentiando ex fiet: 2y + 4 ppaay  a pp4ay + app4
e
C
Faciamus e ergo 2 a ayy Z  a: gy. fiet
0)
hos har onmor, nogor on
J
jam si quaecamque ducere
maximam vel minimam ex puncto P dato, ad curvam CC
dabitur abscissa quaesita
ercimus.
videtur absurdum
Laa p: XX 1
61)
O
seu firet
er qat appa (4 aatgus + Da apP ) aatyue - 2a pp aa +gu = 0 seu fiet
(20
4Jaatgy
raap p= (3l aatgus: (ad F yy =aa seu  p = aa tgu saatgu : ay Y2 L2X: 2Nx +9a
modes
Ilaatyus
sed ita liceret invenire lineam, seu relationem inter X et y, quod non ausom, s sperare
dg  seu dgid = px: y. seu fiet
dane si differentiemus aeg. C fit codu- e pax) + X dx 
Ergo per a9u 2. fi) pax, ly = 7. l a id est redit a4. 3 V) 2doB
C
ond teati drodu Rsuere valorum
esters dovinc u
q
Za
et deinde rem
seu cur pro Z substituto valore in aeq. 4 4 tollere demies  X vel y (pe pag oribere jam proprie
applicare ad maximas. Nam nobis in vatore quo quaeritur matima, non la  mi rB = +xx. sit t:
+
a
axrit t = fiet dx: dus = adz. Sin
sid
Iit X+F: y = a:L
Et sed video jam cur methodus ista
sit sed non list disterentiare socundu t  geminas, et p, vi Zu unne lu
tatem maximae aliunde notam
+
doloes