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# Title: Leibniz-Handschriften zur Mathematik LH 35, 15, 2
# Folio 2v, page id 00068204:0004
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Sive - 1. -  2 = 1
e
Sive. + 16, 16
 L
a
3
e, d sie in infinitum. Unde cognovi, desideratam
aream segmenti circularis esse. X2~  t X
 162 3
128 C. et eadem ratione prodierunt etiam interserenda
areae reliquarum curvarum, ut et area hyperbolae. et caeterarum
alternarum in hac Serre. 1  ∞ 8. 1. + Xe X. 1 2 1 + Xxt, Z.
1 =  KC. Et eadem est ratio intercalandi alius
Serres idq). per intervalla duorum plurcumve terminorum
simul deficientrum. Dic fuit primus meus ingressus un tras
Meditationes; qui e memorra Sane exciderat, nisi oculos
in adversaria quaedam ante paucas septimanas cetulissem.
bi vero haec didiceram, mon considerabam termines
1 = ∞e∞ Z. 1= X ∞ 13. 1= X (2. 1- X 2. ke. oc est 1. 1- Xa.
1= (2XX + 3. s - 3XX 73XX H. Eodem modo interpotare
posse ae areas ab ipsis generatas: et ad hoc nihil alud ccequiri,
quam omissionem denominatorum 1, (3, 5, 7 deC. interminis
exprimentibus arcas; hoc est coeffiientes, terminorum uus seroie
quantitatis intercalandae 1 =  X (Z, vel 1 ex vel
2
generaliter 1 = XX , prodire per continuam multiplucationem
terminorum Bujus Seriei M X - 1 Y M- 2 M B
(3s
 die.
adeo ut e. 8. 1  2 valeret ) -t X2= 2 ∞ 4 - 16X h
et   Valeret 1 =  x + 3  + 16 X  et 1 - XX
valeret 1 - 3XX -  9 ∞+ -  X RC. sic itaq innotuit
Mitri generalis neductio nadicalium un infinitas series per
regulam illam quam posiu anitio expistolae prioris antequam
Surem extractionem raduum. Sed hac cognita, non potuit
altera me duu latere: nam ut probarem has operationes
Multipacaris 1 - 2 X- 3 - 15X C in se, defactum
est 1 - x; terminis relguis in infinitum evanescentibus
percontinuationem serzei. Alque ita 1 -  9
 he bis in se ductum produxit etiam 1= X. Guos
ut certa fuit harum conclusionum Demonstratio; sic me
manu duxit ad tentandum e converso, num hoe series
quas sre constitit esse cadices quantitatio 1 , non poslent
inde extrahi, more arithmetico. Et tees bene Suec essit
XX
orma
Operationit1X
in quadraticis  duibus aeco=Xx
erat
Dis perspectio negecaei penitur xx +  
interpolatianem Serierum, de has
operationes tanguam fundamenta
magis genuina solummodo adtribui
nec latuit reductio per divitionem,
 et
et
farina
a1 + GX + 5 a
0 = 2∞= 6 .
xeo utigs facilior. Sed et resolationem opectarum aequatonum