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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2b
# Folio 197r, page id 00068198:0393
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Nit hinc sugulare
certae
sut AB, AB) progressionis Gometricae et rursus AB, A(B) alterius
progressionis Goetira  AB vocentur X; et AB vocentur rX quae
int in data ratiore ad X. patet totidem sumendo YX, quod X; per ipsas
PX longius pertingi, et summatis y, secundum ex majus osse patium
quam si summentur secundum X. N secundum X1 sumana sidx facit
AB CA et secundum rX (, Cytdx facit AB_A. sit aren
y = Hrb) S(at b xns: 1aa+ ExX dve (y) = HCaa Hb rr PXX,:, aat crrux)
quaentur fydx 1 fes) rdx = v
aaa
haberi debet
quaeruntur duae zonae BE, FL, quarum differentia sit data
fitt V et= pt flytrdx rsy) ex - x sydx + sir ( (C Ax - f. e) ((y) dx
e
aa
AdEA
ABCA fRHLA = f AFGAt
Videndum an post differentiationem, quodam possint
i sublationemque fractionum et irrationatium quaedam possint
destrui, quo dende nova summatio melius procedat
Res facilior proratione indaganda Ut si fsydx + 4(y) rx + b = 0
fiet fyax + grydx =0
= aa: xx quia
in Hyperbola primaria dy:dx = y: X (y = a aa : X et fiet
d et di  aa dx ax et frit aa 2XX ~
et dydus + lxdx = 4 y LX, X = aa Y XX, : XX
Ex dx
a ai
a
 a +1
at + 1)
seu L(dydy + dx dX) = dX, 1(
CM sit Sdx ( 1) et CN - Y Sdx Y(_ + 1), debet esse
PF.CM + F CN + b = 0 seu F(dx (a +1) + X sdx 1(   1) + a =d
et differentiando siet dx Y ( 1) +  ax (a + + 1) =0 adeoque frot
f
au
a
aa gua + Wr
sit ftaa = a, seu f= aa
aa sed hoc methodus nen procedi
fiet re aa = rr
IY
elib
aq
C C) = X (C) GC + GR CK HC) + HK = (C)K
besc
R  eG  + GdE FC = HK H(C) = F(C) = GR
Qarit Data curva quaeritur in ea relatio generalis inter c(C), CK, K(C)
fCF = sit AB GC) = AB) - AB + A p - AP)
K = AB- AB + AP - AF
(C) K = ABAB- AB L AX- A(p)
Dantur ad huc tres aliae aequationes inter AB et AP, A(B) et A(P), AB et AF
l
C
literae autem folleu
poqa
ACC+
AP, A(), A(P), AB, AH, itaque ut hae tollantur
setmpatione LR +H(C) L + LK- mux siet
2 +. LK = ax CF + _ faet CL deL L LK d+K. cC). cIdeL + A 
peb
CLk
+resc C
at summa insirplarum sit maxima, sed optimumforet si posset inveniti
determinatio, per quam progressio iuf perimatiorum pot inserplorum
haberetur
m: n = b: L