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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 381r, page id 00068196:0757
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fittatiationes curvarum ixpluribus quadrataris pondentuu
AxX =y a AX, x A ICCXEV, etc,
XW, vel X2L vel X3C ct)
svel. CiY vel 2E2Y vel 3E3YL S
vel 1Y. D.
1E3E erit de
et Dierit dys
quaeritur tangens curvae Y) Yy tangens
D sint dy: de seu  eEDEYE: EY =
 9 = (ex Te)(X: a) et sy fit YE: ET sou dyide=
seu dy: de = (dx bg(X: a) _ (C(X: a) = Z: a
Y log(. a)
jam y = ( (1:, et 1) P (X: a) itaque seite patet
data tangente curvae V E. dari summam formulae hujus
Sed Hince non potest duei expressio analytica
tn
y = X eix+B d se dy Hec. e) = de e logx X. SD. :, x +b sed in
summae quaelitae; sed tantum constructio
E +5 mandum.
-
his nit difcimus Rati Sumer
hoc loco  seu haberi
Curva autem construm potest,
in alis quibusdam, ut (dx X: a+X
2
(ex (C((X: a) etsi e sf non integra
sed secus et in inter schndentibus seu non nisis cum
uibi res non procedit, nisi cum C est integer. Unde
c
e a
Non
datur interpolatio nisi per seriem infinitam
adeoque nec descriptio curvae A AV
e, quia b
TaX: etk, utcunque variet 
nnon Pariat et fiel dy = de fax Xb: quo et X
Sed haec datur
Aliter
do
Ergo
y= Cdx a cir etx
e
six
dx 5
ex eft exta sas
f+X
x y= (dx (de
+X
C’Egoy est ad rectam
dy = de fax sax
e
(4) sy- de ((dX Gc)
etXd X
(dx log X log(b1) y (de
Netx
ax. Ergo t
etxs
de y de dy = de 1Y si haberetur Sdx logx loglb +X)
uper hujus curvae langentes
tatium curvarum quaerantur, ex. gro
(dx + X, differentiatio fiet solum secundum X, nam puncta
e
si continui concursus
E, et Y oiunt communis, et fiat y =  + e XC quae foret ad
curvam As2, ex omnibus selectam si indetoleremus e, seu quaereremue curvam
e+x
+x
sed sublata X quaerevum eginam sec y et e, habereum.
sec. X et ) crbor ex unctis concurtem
composit
et in O, et post
e
ec