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# Title: Leibniz-Handschriften zur Mathematik LH 35, 6, 11
# Folio 20r, page id 00068056:0039
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Nihil hac
Filum ACB ita inflestere, inter extrema data A et B, in duas rectas AB AC, BC, ut fial descensus
centri gravitatis G asus horitontem  omnium possibilium maximus, seu recta He
maxima, quaeritur punctum C. Dantur AF, et BF, quaruntur AE CE. patet esse
AE + EC= AC et (EF= seu AF- AE, + FB- EC CB et ACFBC~ L filo dato
Momentum ipsius AC ex AH, est AC in LAE, et momentum ipsius CB ex AH est, CB in AF - L EF
seu CB in ERF + = AE. Ergo debet esse AC in LAE + CB in tAF + L AE = Max siu AC. E AC+ L. AC. L. AF+ AE- map.
AEB A5 - - AF. AE (+ AE) + FB = 2FB. 5C (+EC) = AE (EC) = (CB - AC ) L. (BC- Ae son) L . AC
AE AAE F EC _EC = AC LAC ex 1 - 2AFAAE - 2FBaEC = L. - 2 +AC seu AFdAE + FBd EC = 2 L d AC
 Ge = SAC - AC = AEB LA AF + FB2 - ZAF. AE - L. L-EAC, : 2FB. cujus differentialis, erit:
EACdgC - AEABE  AF dAE + LdAC, : FB seu 2FB. ACdAC - AE dAE = L dAC- AFd AE, AF = rB - 2F A5- L. L. 2AC
ASR-AE Ex ag. 4 fit ZA C  AC. AE + CB. AF + CB. AE = M. seu AE = M - CBAF : fC + C Bteu) :L
Exa seu AE L3 M -  C- A AF. L et dAE = dAC AF: L quem valorem substimendo in aeq. 10. fi
EFBI AC- AE. AF: L  L = AF AF: L, AFLA FN -2AF. A5 - L. L- 2AC
ob 14 in casu Maximi fit AE d AE seu AE AAC. AF: L.  - AC +AC = EC dec seu fit
dec:  Draa = AE. AF = AC. L, : L. EC
ACAEE in aequ. 8, AF + FB - L. L; 2FB vocetur Mf N:FB, et siet:
AC- AE 27) N - 4 N. AF. AE - 4 N. L. AC + 4 AFI AE + BAFAE. L. AC + 4 LL AC,: 4 FB
ubi pro AE substituendo valorem ex aeq. 13. fiet: N - 4N. LAC + 4 LL AC.
AEB AC An = 2M. L-AC. AE  + S - IL. ACFAC NE: V = A AB A PEN PE AC. L. FEbAC~ VI MAT A LACAF. L
... 
i
FE = et Z CQ _eZ CE = W
W = a + bZ+ c2Z + eZ3 etc
et duo = bd 2CZd2 + 303342 + 4 f23 dz et
Q+ dio co = Sdque (1 + b + 2c9+ 3eZ et a + bZ + CZ2 et = max-
 ubi summam actu ipso instituendo fit = l+ mZe nZ etc. (2bi
L, m, et exprimuntur,er a, b, e, ete, ubi in casu totius pro Z
substiluitur ACFV et f = f et sit l+ mf + nf erc = max et sic
m + inf + 3p f  ex = 0 ubi f date, m, n, p, eadeoque a, b, c, ea isitae
an prus  quoque Sed hoc pro toto,  in parta quoque descensus debet esse maximus. Exempli cansu; Assumatur
aliquod punctum curvae C, et suntu FE( pro arbitrio dabitur ex ea CE, er aeq. initio assumtum curvo naam exprimente
dabitur et eodem modo ac ante aequatio M +2DZ Y 3pZ et C = 0, unde cum hoc debeat fieri quaecunc sit Z
necesse est a b C ote assumi tales, ut fint m =o, et n = 0 etc. ipsa maxima seu doscu momentum fieret
=l. quod dlamen ii fator alsurdum, quia l est ostans, sed momentu, hoc non pt esse ostans, hoc ergo
prosundius contideranda