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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 51v, page id 00068196:0102
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+
ponapur Roganthinica de scuibi per puncta
sia infinita seu Aesumploto tra sumere du
punctis utennque H et (_), obique applicatis oru
Rectis uta inaequalibas quibus cunque  HK et
hoeui inte ponatur madia proportionales quoteua
pero similiter applicatae medis intervallis
e pt per earum extremitates descripta curvasent
loquuitumica. sit R(H)=
 dipaitire
 et XKf et (X) (K) g. Hinc applicata
inforo loto seu in  eril
59.
utosepeus talom
modiis
rursus media inter hanc et HK sou ferit 1Z (sBsad seu
e
(3
d
48
fg seu
12
i 
s
nles
a
nota si AM sumatur a _ versus (IF)  affici sogno
n vel (11) M a (1) versus H affici signo L. sin contra pro
si
gressu haberi et affici signo minus. Inde unde erit
 ea
A)M)
2
 F. 9 =
C: 9 Jam H()
M. versus (X) sumta voletur n urgo contra sumta dicetur.m
A)M versus A sumta rogatur erib b-m. hinc si m contra sumatur
e
mod.
(N)
e
mob
etm.
= minimae  = p + inm - 2pm +
a
C
b42m, ib l.
e
porro a puncto dalo in esus mplotu
et TC(M) = - m siet M) N seu X =
m. B)
p(X) sit
et fret
btrm ib imib
ce
0 seutd(...)
ducta langente (N) B. scimus B(M Cesse constantem quae vocetur
ideo
qo
2
 vocntur
e
erit (H) M = p+inEt tieq generaliter bu Mhsn R- L.
M,5
ad logarithnicam ducenda sit mcinima seu perpendicularis 
e
et =2M - 2P + d
d
8
n g. Hinc si H(m) sit = n(H) seu F
It L
M) (M) = 2 H(H) fiet (M) C
et
n et generatiter siculo in asum
toto puncto quocunque M, si ibind unde ad Laganermicam
Et
epplicata supponatur MN,  erit MN=
(N
A
MN seu X= FB
e
erit (n) () media poportionalis inter, P(M) et B(M) constante
 p- m=
+2M, : b
 e eC
C
imile
l
m: b
e
2 3
+2M,.0
1
de dnn
g.
e
et fie
a Elob. hyp. de 
seu l0g. Hyp
ergus
dto
EbEmil
p
cu
0
n
imob
Hoc absolvendum et d (.) admealiter quaerenda:
M
i
yC
Cd
mib -(n: b)
te
a
e
seu log. Hyp. (M (V) = n) D
2
(1)
E
haestabit initroi
portionales, ut svicetr
F
it
be
22
uet
p
sed ali
tertias non maldes sut
apoderedibent hy