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# Title: LBr. 396 · Hermann
# Folio 34v, page id DE-611-HS-973581:0068
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 33r); this page is its left half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=DE-611-HS-973581&page=68
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 312, 2026-09-10T21:55:22Z — 56 lines, status machine
# Lines: 56 recognised, mean confidence 0.87
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
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# After the first blank line: the recognised lines in reading order, one per line.

pervenit ric progrediendo ad uique 70 aquationem, quis omnes non nisi 34 ad
summum diversas curvas defignare ostendit, Rarumque curvarum asgniptotas
aves, puncta flexus contraru aut reverrionis aliaque simblia diligenter assiynat.
Duantum ad methodum Bernoullianam de ducenda-
minima linea in quibusdam supersiciebus ut in conoiditus
rectis, illa non diversa multum est ab ea qua lineam
celerrimi descensus anter inquisiverat, et si recte memin
itc circiter habet. Esto Curva qua cunque ABC rotata circu
AB, qua gignat conoides ABC FD A, in ujus superficie dur
cenda sit linea BkH inter eosdem terminos travisrima
Sint eF arcus aquatoris, ABC, Ases, AHF tres meridiane
BN, XL arculi descrixti a punclis B et X; et Sunto, CD = 12 = 5D = a, BG = NG = f;
XP = _LP = g; et = m, 35 = n; BK = S, XH = u. et tan dem NC = AeL = p. Euibus positis
CD. Ct :: BG. BN ) 1D. 17:: kP. KC )VBN2 = NK = BH (VXC + LH2 = XH)
a. m:: f. Em
a
a. n:: g. gn
hypothesi Vmt + go = V unqu
as
a
ea
aa
L+ pp = Min. unde: Hmom + Agndn
aas
punita B,  fexa sunt, erit am = - dn; adeoque m=sgn
aas
aau
is
etam ex
aau =0, et quie
hoc ett Am
aas
conitanti
Sint jam BG = f = X, ee = y, Cs = m = dy; tangens in se velk C = t erit KN = Fd x. p
adeoque Bk = s= Vmms
ac
un de elicitur dy-
actar
aa
x
ax des
= const. = nc
Vx dy2+ aat a
V Longitudo Curva erit = Sfdx. Hanc
Vx -CC
Methodum Universaliorem reddidi ut in omnibus plane superficiebus lonoidics
et non conoidiui aqualiter succederet; sed ne longiore mea exiitola Ampl.
Tua tadio sim in aliam occasionem eam reservo. Clarisoimi Viri Ballierius
et Bernoullius me rogarunt ut Cultum suum Tuci Ampl. et officia viusrin
deferrem, hicus insignis vir sperat ultimam suum esirtolam rite Titi teaditam
esse. Hiice Vale, Vis Consultissime et benevolentia Tua Complectere
C
asilea 177 Julii 1706
elebersimi Nomines Sui
ultorem indefestum
Hermancrem.