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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 22
# Folio 15v, page id 00068235:0030
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Hinc jam habeatur appropiaquatio. Numalibi ostendi residua
valde remota omitti posse, et haberi alternis appropinquationem nunc
justo majorem, nunc justo minorem. in infinitum vero erit: Et ponendo
residuos utcunque remotos fiet:
 aequ ab
18
abcd:
af.
abc5.
abeF.
adef.
Cdef
abcdet.
a
abEd
abe.
ade.
abcde:
div, per
1.85
53
bc d
bc fa
De fg
des
bc def g
et ponendo E. 9. 8. 3 aequales nnhilo atque inter se, utique omitti
poterunt. Volandum tamen residno quo libet omisso ut
etam sequentes quoticites esse omittendos udt f. g. in infinitum
eundo nulli omitti debent
ponendos qu.0.
Puto hac ratione etiam an finitis
posse componi quotientam rationem ex solis quotientibus neglectis residuis
si fumantur residuia
qua sunt o. Eodem modo et potierit quantitas componi exsolis residuis,
sit jam investigandus modus red ucendi rationem compositam ad simplicem
atib
actis qui
ut si X equ.  in  ponendo  aequ  1 + = et B aequ. s+ =
V
m +1
n +
++L
n+1
veu
qua e 5 aequ a +  quaeritur a. b. c. d. Verror ut res sncredat, generaliter
b+
c+-
et
quia etsi constat
nisi multa meditatione. Est tamen determi
nata
His habitis haberemus facile potentiae fractionem replicatam. Similiter investigaas
asset modus addendi plures fractione replicatas in unam: his habitis possemus
data quavis quantitate per fractionem replicatam expressa invenore ancipisa
sit radio alicujus aequationis, et cujusnam. Quod si est transcendens forte
inveniri Tausitus poterit
si mulliplicebur in
m + 7
1 sine reductione fractionis fiet: l5 + L
m 11
ne
15
+s
sit 1
+ 1∞
L+ etC mt ere mere terc
m+ + Ha) quaeritur summa n, v
+
mn +() tv. (a)
fiet n +v + n(a))+ no vmn +. v (∞)
mn +V + mnssa 4 +B (a () ( y
Ad ista problema solvenda opus solummodo perfici artem calculandi analysice
in integrist.
forte suffecerit, nos posse explicare desideratum saltem per tatum
fractionum replicatarum consunctiones additione  mulliplicatione erc. faciendas
imo non sufficit, quia duae rameri irrationales additi cesse vel in se
si in integrum sit progressus, vel in minimis terminis, si  exhauitur
prou fractio replicata, resolvamus, quemadmodum praescribit in partes
quales praescribit O et Y
invicem ducti possunt facere rationalem. Illud tamen certum irrationalem
rationali additum vel per eum multiplicatum non posse facere rationalem