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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2b
# Folio 133r, page id 00068198:0265
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ed
11
sedv _ (fdco
lev  nto
et
sunt ut logarithmi, si
sint ut numeri
nam si 9+cZ, lt e = m + fco, fit
ostendit calculus nam (cdZ + sedo
(cdZ + sed v
9+Z, ltev, misco
= feo, quod
Soteqe Itev
saca
= ( edZue tce bdZ + gdv + cqdo mosco
greque diten
9+ cZ, lt ev
d, 9teze, ltev = (9+ cZ. Cdv) + (H ev, cdzF
possestat Ciquid excogitari ut
.
Ha ergo summae sunt progressionis
authmeticae, si termini, sint geometricae.
Sicebitue aliquid ex cogitare, ubi pro authmetica sit Anthmetiia
replicata seu ut differentiae Geome tiica sit aca aC
ubi pro Geometria adhibeatur aliquid replicati, seu ubi quae in vicem ducuntur
non aequalia sed anthmetica v. g.
fint ,
p, pra, Ptra, unde
3V + Va, 2 + 3 + 24 ete Horum quaeramus quasi loga
siit termini  primus He, secundus (1) tertius L
primus V secundus  (2, 3tiue 2). fint (q -q,:  = a, quem
rithimos
valorem substinendo in palore ipsius 3 fiet 23+ C - 313 +2a1- 2a0 =
seu rersus = (17434 (= 3 1p + 2 1 - 24  - 24  (215) seu
fiot i C3Y + 4 a = 2(2 seu (3) = 2 ep. - by . 
seu ex ((2V: 1 = e + (2:2) itaque in progressione Geometrica
communi medias termine divisus per primum dat tertium, sed in
quadratam becundi
replicata madi termini divisus per primum dat dimidium 3tii et
quadratum secundi
secundum et terrium
pim mediam arithmeticam inter tertiam et primum. sin
n
quadratum medii est factum ex primo in mediam arithmebicam
inter secundi et 3tii vel primus fit ex quadrato med secundi
diviso per mediam arithmebicam secundi et primi tertii.
prim Sec.: med. aritam. Sec. et 3.
 ergo sec prim
med. auitrua sec et 3 = med. _C3
sec = F 3tiu: med. nrikm. 3 et 4
mad. ar. 3rt 4
(med. arithm. 3 et  quadr, med. ar. B e mad an (3 et 4)), 3
et et
mod. ar. 2etq
3 +  med. ar et. 4)
E, med arithur 3 etq
Ergo psim
=
A
193
3.
med.arhet 4
med.ar (at 3 et med. ar (3 et 4))
med. ar. 3 et 4 med. ar. (3 et med B et 4)
per medium arithmeticum inter 2dum stiuq
us  . an juter 3t. et a et 
et ex Cubo 3tii diviso per (med. ar. inter 3tium et medaritum. inter 3tilm et contraque