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# Title: Leibniz-Handschriften zur Mathematik LH 35, 2, 1
# Folio 182v, page id 00067993:0366
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18 60
88 36 106 eu erc erc et erc
5. 24 120
ubi patet terminos 2. 6. 24. 120 esse productos continuorum, nempe:
2 et 23. et 2. 9. 4 et 2. 3.4. 5.
sed 2. 8. 36. 186. ita pracedunt.
set  8 est 2.3 + 2 et 3b est 84 +2.2 seu 2.3. 4 + 2. 4 + 2. 2.
et 186 est 36.5 +2. 3 fiet: 2. 3. 4. 5+ 2. 4. 5 + 2. 2.5 +2. 3.5
Methodo autem supra reperta haberi potest communis relatio inter
.
36. et 8. 36. 186 cujus ope inquiri potest aliqua
24
6
24 120
communis relatio inter  duas quaslibet et constantem seu inter
2
2
6.
constrntem a.  24
6
24
eandem constantem. a Et reperta ipsa a. hatebitur ultimus seriei
terminus quem aliunde fermu esse, 7
Ingens autem hic nascitur compendium, quod miori usus
esse arbitror ad quadraturas. Scilicet quandoeunque series summanda
terminorum a. b. cud revocari potest ad relationem communem trium
terminorum, quae constante quantitatem constantem includat, tunc
aequatio  et hinc deducta proprietas seriei onu summatricis
inter w.xy includat eandem constantem; eaque constans non evanescat, si
singulos terminos ponamus aequi seriei summatricis, W. X. y
ponamus aequales inter se; tunc habebitur terminatio seriep
summatricis. Ex. g. si sit series, in qua positis terminis
tribus continuis appellatis. V. X. y. sit V aequ e4
a
y ux
in ultimo fiet  aequ a. seu terminatio erit + erit aequ. a. posito
ei sit series: L.  2. +. 23 1 seriem esse talem, ut terminique
sibi vicinorum, dijiserentia, tandem est
suit infiniti semper
t
gne
utes
in isto casu si sumamus
X. , 1. 1 6 L. L, 6. L . 1. 6, et C.
tedieam interpolando infinitis interjectis interpolare etiam
quam
possumus sed non prodiret talis series. in qua ipsi termini certo intero
distantes tandem coincidant.
didendum quomodo terminos seriei possimus hoc modo
interll terminorum seu subscissam. Nempe exemplicansus.
Caequ
mago 9q43 Zh Arhili
3t eh
N aegu.
ex ra
Aecrica
referre si non ad constantem, saltem ad termi numer–
sit a aequ i. baequ
lago viti
ati
3
it series L = 5
Ejus summatis decrescens
ii infinitum est
Nam horum differentiae sunt
sed seriessummatrix
2
etc etc erc
2 2 etc etc et
erc, erete
crescens in infinitum
19 16
0
erit