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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 3 (shelfmark LH 13, 3)
# Folio 183v, page id 00068200:0368
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J2on. 1676
curva Hastariae natura depressio calculi
Maximam curvae latitudinem
seu punctum H quaerens
inveni eadem opera et
minimam.
M N
C P
C L
prodiit aequatio:
Positis enim
e+= a e + - ac  + aC p0.
quam si dividas per e- a f0
posterior
prodibit: e3 - ac 0 quae non nisi
unicam habet radicem possibilem. nempe
Vac. Aequatio ergo radices habet
duas, unam e-apjo. seu eF, a.
alteram C- Yac 0. seu e Yac
quod significat uno quidem aequationis casu
B aequari ipsi hastae a. altero aequari
primae duarum proportione mediarum inter
humerum et hastam
Hoc ubi ad figuram vid retuli statim vidi,
uno quidem casu minimam curvae latitudinem
extiberi, altero maximam. Minimam
cum C aqu id est recta a curvae puncto
ad horizontalem ducta aequalis est ipsi hastae a
curba
ut C D, alt AB. Nam ex punctis A et C.
in rectam AB demissae ordinatae, usque adeo
omnium aliarum minimae sunt, ut infinite sint
parbae. Maximam vero significari apparuit,
cum e est  ac id est CL quaesita
quae producta maximae a excursionis puncto H,
occurrat. Est ergo C L. prior duarum proportione
cuediarum inter CB et CD, quando CD coincidit ip
inter C B. et 1N. M, id est hoc loco CD.  Hic aliquam
e
calculi cnverlactionem animadmento eritque HS ordinatarum
ex curda CHI A in rectam AC demissarum maxima.
Hic aliquam calculi, qualis fieri solet, imperfectionem
adverto. Dicere enim non potuit, utra inventarum maxima
aut minima esset. Ac ne illud quidem duas esse minima
vitata multitudine
radicum
P