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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 1
# Folio 131v, page id 00068194:0262
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25 4
ita enim terminus continue decrescit in
an ita decrescat, ut nihilominus produ
ctum fiat infinitum, quod aliquando
fit, ut supra exemplo ostendimus, an
ita, ut evanescat in nihilum, sed
per
minus quolibet dato; an aequetur alicui
finitoqu quod rationibus nostris usibusque
commodissimum foret, investigabimus ita:
15 etc
14,. 3g1 5 321  1541.
vel 12 +
vel
,
etc
2 15 1, 17, ec
etc.
Est ergo minus productum quolibet dato, scilicet
Unitas divisa per infinitum. Idem brevius ontendipoterat ex ipsa Rationis hajritatis in Rationem
Sed ut ad postram illam praegressio-
nem f, gometricam securidariam, in
qua aqua etiamnum haeret, redeamus
investiganda est ratio harum duarum progressionum
Termini differentiae
Majoritalis transformave
Omnes Termino seriei cujoscunque
in infinitum decrescentis
videntur esse aut in summit an
differentiae, aut termini, aut pote
tes temi radicesve et hocum
fursus aut suminae aut diffe–
rentiae, horumoe variae mixturae
31 Cic
2 12. etc
in infinitum
infinitum. Sed investigandum est,
con
ete.
summahujus
quaeritur
Ivestigemus rationes aliquot terminorum, ut lux nobis
aperiatur
Addantur termini tam
Nominatoris quam
4
uina hu
Setetholum progressionis
aliiujus Geometricae aut buamo–
invenca est 1.
numeratoris da se
inticem
Erit numeratonis haec reductio
10
Hoq
2- 896+ 112 - 1004
1024
= 64
1024
Et Nominatoris haec erit reductio
LX8 et 2 104
6 64 1024
1024
Abjiciatur ervisor communis c024. et
a nominatore et a numeratore, producta
ratio erit: 1008) 5 e
22
Sed exhis
mullus ad problematis socutionem adistus.
aperitur
(eut tattionice)