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# Title: Leibniz-Handschriften zur Mathematik LH 35, 8, 3
# Folio 7r, page id 00068098:0013
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pars INta A .d. angentiu m versae et n punctio abqus sunus
Regressus an haberi possit in a Tangentibus, aut aliis functionibus ad oedi tas, quaesti
ringua Exempes gratia 2 ax = Y, unde fie at 27: 2 ax Ergo
data ergo hac aequatione l = 2X multiglicetur utrumque per a, fie al = 2Xa A.
si sit l = X. al = ax Ergo ax= ax a - a.
V = a,  a = YX. Ego yX = yX. Ego yt - y4.
ay = l. Ego ay- xy
Xy
Res pa accuratissime investiganda, per Carones aequationum, ut ippareat quor
modis aliquid produci possit ex aliis aequatimibus, et quaenam postea ex illis eligi debeat
Est quaedam ipsius Analyseos Analysis. Sed in qua profecto consisit Apex scintae dumanae
humanae in hoc quidem genere rerum.
ABG
ad boF adbys
si sit Parabola, ABC D. et spatium Hsperbola Asymphoton AC D abed.
sumantuque in utraque oidinatae duae, CB, FG, et ita ut minima Hypert p
seu prima sarabole sit punctum, seu prima seu maxima Hiperbolae
sit infinita seu Asgyplotos. Ante omnia minimae atque maximae applicatari
investiganda quantitas. Nimirum in Parabola ob aX = y, posita
X = +, fiet  = y, et y = 1
in Hyperbola, ob a = yX posita X H minisua = 1, fiet a = y.
Sumatur abscissa in Purabola AE in Hperbola ae. illa dujus duplam abscissa
pla
indeque ducta applicata EB, vel eb. ad abscissam perpendiculari X ad punctum
B vel b. ducatur tangens B, vel bf quae axi seu directrici assumtae occurrati
in N. f. constat in parabola Ef esse esse = 2AE, et in Hyperbola et
esse = ac. et quoniam semper A ac duplum est AE, erit EF = ef..
pothesi nostra
porro alibi demonstratum est, differentiam inter duas applicatas proximas seu
infinite parvo dissitas intervallo esse, applicatam alterutram, divitam per
suam productam in minimam X. ductam, et. per productam suam divisam.
ideoque in cum utrobique producta sit X. et in applicat Mrabola minima
X sit , in Hyperbola minima X sit 1. hinc ut ab a prima applicatam
differentiarum
ordiamur, series in Parabolae haec evit.
2
itt 1
126
serist
NE
etc. in infi–
ttus
 (2)+
Si si Hrebola prof achibendum. 
suta
il
12
a d
d