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# Title: Leibniz-Handschriften zur Mathematik LH 35, 6, 11
# Folio 22v, page id 00068056:0044
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 23r); this page is its left half.
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 66 lines, status machine
# Lines: 66 recognised, mean confidence 0.84
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sit filum trectum
duo
GE, EF
sit articulas rectolinem GF, suspendeneplibu  catenam
Em
FA. sit cenlius ,  in N et centum cntenae a FBC
sit in P. erit AP = sX san gus: 5 sdx  di AH, X. FH, y
st AM = + AB m. HI et HN = L_ eA X -X, : 2.
et AN = p - X, : 2 +X = N+X,: 2
sit G. rentum grav. totius eFAFC fiet pg. F = Nq. EF
Aq = Ap + PZ et P NP = AN = A B et PZ: Np:
ii EF: EF+ FA sErgo pu = NP. EF: EFAFA = AN- ApDEF: EFAFA
fia AQ minimus, erit seu AG = X Saxtadu + Z r+Y. EF; EF+ FA, ubi sola Efi
varians
Et sbtique noinam, et d Aq = = EF +FA i vix = SX Laptatus B E rt X. EF ubi imior Loanssere EF
Tigum FF cum inde dependente chorda A FAF pendeat ex
artienlis GCF. sint Z EF et FAF ponderosa. Debet
manenles distania  punctis GG et distaum =4 si disponi
lolumut centr. y. mux une descendat
Dideamus an non possit esse uius maximae et
minimae ad determinandam curva parametium investrus ata
am speco in qquam  catena curvasri debet: Et hoc videtur
samino debere lonum alaquem habere
Curvae naturam esse invenimus ut posita A, HE, y  et OHia
af.IY. Scax tx sit  y = as, dZ. (Z2- aa = nc et
sit (Sd q + diu = syn - aa = AF
Ponamus jam dari HF seu y et A AF
Quoritur ergo datis punctis, F et H, et aequatione 1, naturam curvae
exprimente, qualis sit parameter a, seu BA, ut centrum ipsius
AF quam maxime descludat,
A3= Z Saque dus: R=
dz = du = Z4Z: se- aa
Efficeedua este rvantur
vaeritur data suqaa dataque as, dz. _7 aa, ptalia quae nam sit a
et Ay = (ZZZ: X2-aa: ut txna B
ut fqaadus. Sat aa fint omniam possi bilium minima.
33-a4:77-aa fiat omnium possibilium minima
Equidem q non est constans
e
Sit (ZZ- a a = f
et y = C, nempe in casu dati puncti F
et 532.2: 122 aa: f = Min im
Sed difficultus est, quod hic caliulum de maximis et minimis non videtur commode
fiet CL a5, dZ: 122. aa
2 Sq aa.
Si aequatio 1. esset cli absolute calculabilis, seu
relationem confineret inter solas c, Z, a, ejus ope Utique ejus ope daretur relatio
Z per a et C sed ex aequ. 1. datur hy  per a et f
licere applicare.
hos duos valores ipsius Z, dabitur d per c et f datas, itaque
video  admissis aequationibus E, 2, dari aEex c et f, adebqe et sine
nicet cut
ergo jungendo
Et proinde  non dari applicationem calculi
 maximis et Minimis, si utrumque datum ponamus, c et A, sed si datum
intercedente. aeq. 3.
it alterum tantum ponamus ergo dari C, non vero dari f. itaque
et AP AZ = (AP+ Pq =) (AP. ER+ AP. FA + AN. EF (- AP. EF): IE riA
et AP. FA = Tx Sax + du et AN. EF = . V. EF + = X. EF. sot
filu EF
ut S2
E
ly + yd
a
.
pt