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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 434r, page id 00068196:0863
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de seriebus Replicate cognitis
Quando ex duobus quibusvis serrei terminis  vicinis datur
eorua
qit
datis terminis duobus; sed proppintas seriri non est determinatu
et potest determinari adhuc magis: Exempli causo haec est
proprietas replicata progressionis Geometrica. l. m n, P etc
ut sit
mm., sed haec replica locum habet in progressione
dupea
hipta
 setemuneoo quacunque vcipit ergo
estrictionem aliquam , v.q sil 2l-m et 2m = n. fit
 In = adeoque n = +l fiet In = 4U et myetiam = 4U
putet etiam hoc modo quandem constatt constantem
en persaot parametrum hoc loco dari ut et semper
in alis seriebus omnibus quendoe  praeter Geomelruam
quando datur relatio inter duas quantitates  opus
test intervenire perametrum, alioqui relatio illa abit in
rationem constantem, hoc est in progressidnem Geometricam
data autem paraenetroin teric coudergente terpiinabili, semper datur terminat
series polygonum inscriptolum tircuto, per subsectionem 
angulorum prodeuntium in circulo est ABB:CC = A: B +
seu bi bis B = ACC + BCC. on C = B A2B: A+B
vee videamus an assumere aliquam liceat relationem
communem inter duos quos vis terminos, quae proinde speciu
polygoni determinet. Nam relatio posita abus inculi
polygonis subsecandis est communis. Sit
2
et C = BE. Ergo C e jam priora C= A. VZA:
ec
Ergo A = Y2A: A+ A seu A
Es
c
Ergo C = AC jam C = A V2A: Ae, Ae Ergo
2euE
20Ce = LAC. es. 20 1 + A e seu A
seu qoere
ed ec reti = 2
seu ec cs
cujus aequationis
reperiri sine A ut certe res succedit in casu quo C = 1. sed ille casus
non jurat.
sit B= f Af ota ut f sit  constans
et C = Be f. fiet C = Aee (2h ce A L2. it AC  seu
AO = ae
ch
2: 14 1: p- a ch  = AC
seu Ae hL pcetie
28: 1
e-h
2 AVe e g P2: 14 e  h
seu Aced re fih grec 3e1  = 2. ponendo es e = 1 seu e-1
si et pro s suib endo  9. fiet
99 + g = 2 et b = A9 et C - B9
cisterron
alibi
detemi
nar
esse
ACCF BBC
B+BC