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# Title: Leibniz-Handschriften zur Mathematik LH 35, 6, 24
# Folio 5r, page id 00068069:0009
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seriess est + L + 
seresit est
se Xt
Ergo  2
det
+ Zsdx  est = Z, , Y 2 + h + 4 + = + etc.
-1
lx
2) XtI
esex
4 +
2. X X -  -  - = - etc. Ergo
ee+
X erit = 2,  + Z X X X X = 3
dx
itagtande 3
=
summationem, 4
x 15 54 n
Cjam olim cum Quadratura Arithmetica edere memini. Similique
ode es methode aeterae summationes sericum rationalium realiter resolubilium
realiter resolubilium
determinati gradus Inveniuntur, aut ad harmonicas, earumque potentias
rediguntur. De imaginaria resolutione, quae et ipsa prodest, mox dicetur. Eademque method sui subinte
Ede Quodsi X vel  essent non recta non termini discreti, sed
continui, id est non series numerim intervallo assignabili differente,
sed lineae rectae abscissae continue  sive elementariter
hoc est per  inassignabilia intervalla crescentes, quarum series
figuram ita ut series terminorum figuram constituat; patet
eodem modo omnes fractionum rationalium determiali gradis constantis
suman
summas, hoc est omnes quad raturas Figurarum rationalium Algebraicarum,
supponendo Radices formulae denominatorem constituentis esse reales,  posse
vel absolute inveniri; vel ad quadraturam Hyperbolae reduci posse
Nam quia praeter integros summandos ut sdx, sedx, sexde etc.
res reducitur ad summationes simplices posito y = xte; quales,
Sdy; Sdy: (dy etc. in quadraturis, autem semper habentur
(au sdque  etc. Hinc patet solam superesse  id est
Hyperbolae quadraturam. Verum enim vero tenacior est
yy1
vanietatis suae pulcherrimae, Natura rerum, aeternarum veritatum parens, vel potius
parens, qua ut id est dicina Mens quam ut
es
etiam ad serie pro seriebus
rationalibus indeterminati
gradus servire posunt
graria sub unum genus