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# Title: Leibniz-Handschriften zur Mathematik LH 35, 15, 5
# Folio 48r, page id 00068207:0095
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Additio pro totte cus u sectorimeni
tollenda difficultate in casu qu quadeantis, et regela regula pro casu sectors
e
quadrante. majonis
Notandum estt demonstrationem pati difficultalem si
quis eam in solo casu speciali instituere voluisset
respectu solius quadrantis. Nam quia in casu
foret
quadrantis est y aequ. 1. est segmentum
quadrantis AN C A aequal 2f- 4 + 6 - d et
quod subtrahendo a sectore quadrantis, qui est
4 - - 2 + -. Ck. fieret. residuum
1- 1 + 1 = 1 + 1 etc. Id est. o. quod
est absurdum restat enim semiquadratum radii
sien.. Verum quidem est tali ssvisione
etiam polo at inquies 1 - 1+ 1 - 1 + l etc
est etiam  ni seu = nam si
1- 1 + 1 = 1 + I CHc. multiplices per 1 + 1 prodit
dicendum es
ergo etiam erit aequ. 0 quor
absurdum
esi dojnum
2
Responsio est Respondendum
series in finitas
debere quas  ad hibere
licet in tali calculo debere esse decrescentes
ita ut de illis demonstrari possit errorem
prout longius in serie progrederis semper decres
in fra valorem datum
qualis est 1-= + et non vero ter
2+fek+ vel negue 1- 11L1 etl
A
applicatio tamen ad quadrantem fieri potest
reductione ad absurdum; demonstrando valorem
aliu segment
u
cerentiaa aliu alterius
Aus
sectoris cujqus diffeantia a nt excessi
sectin
eliam quamt
lus
e
 seriem 1- = + etc valore minore
quovis dato.