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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 1
# Folio 24r, page id 00068194:0047
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2B inn. 1676.
De curvarum areis per infinitas series exprimendis regula generalis.
et 2
Inveni de methodum generalem cujus ope obtineri semper poterit sertes rati figura rationalis
datae homologa; adeoque sec expressio curvae propositae, per semem infinitam. Quae ut intelligatur
en
iaccli
sit curva 1C2C3C. Axis A1B2B3B. Ordinata  B, C, EB+C, 3B3 C. habscssae lesint
Suse.
5. Area figurae.
 alia litera, quaelibet, Z eique talis tribuatur 
quod fiert si tum V, tum X, syit rationales ex due
itit
Sul
CVax. sit quantitas rationalis ut exempli causa, ponatur (aZ. eumque
valorem substituendo  in aequatione 1, 4aZ2 4a74
+4a 2  44e
g2+ Z4
i2
9)a+Z
seu y dx p. _ 3Z
a+ 2
1y et 2a(),. a + Z a + a Z + 24 (. V. et reducendo.
a+Z41β+B2) a + 2442+ 74
a + 242 + 24
(3)
uo a+ E A Jam dX ita investigabitur,
 (242+4a 3Z +643 (, (+ 4β a2 + +aβ2 (+ + 6a
et dx Y 4a3
a+34Z+ 3424,767
eritque 457- et 477 +
At)  et ex 9. et 5. ent yax p, pa
t
N aB 1 anZ
aeteraen sicri potest aliquando quae est figura rationalis ad
quam summa sinuum reducitur. 
aeterum saepe idem poterit obtineri compendiotius, si neque y, neque X, adeoque nec dx sint
rationales; sed tamen factum ex iptis ydx sit quantitas rationalis. Quod contingere poteris
si per eam quantitartem irrationeem uno dividitur, per quam altera multiplicatur. Porro quod
diximus de resolutione figurae in parallelogramma per ordinatas, locum habet etiam de ejus resolutus
per convergentes in triangula, aut truncos triangulorum residuos; aliaque id genus
Toti ergo res eo redit, data aequati. Caeterum si vulgari ratione modo ab initio posito.
qutam dX, quam y, sive tamx  quam y rationales, quaerimus, tunc tota
moblema de areis curvarum per series infinitas ex primendis redit ad problema ta