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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 3 (shelfmark LH 13, 3)
# Folio 213r, page id 00068200:0427
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plediasma 2
pro quadratura
videtur sub finem demonstrat
vera quadlaturae impossi
bilitas
Invenire duas tiportiones lirculare
centrum gravitatis commune habentes.
sint (exigr.) duo sectores ABC. LMN. centrum gravitatis
commune habentes G ita tamen ut rectae puncta LAG,
nn sint in eadem recta manifestum haberi hoc centrum
travitatis commune. Ducta enim LG. bise cante angulum MLN
in quam necessario incidit centium et AG bise cante angulum
BAC. quia centrum gravitatis commune cujusque sectoris est in
recta angulum bisecante, etet hoc loco utrique sectori commune
in
est erit in harum rectarum intersectione G.
ato jam centro gravitatis sectoris, etiam area ejus
habetur itaque tantum opus est, ut quaeramus modum efficiendi
tde scribendi duos fectores hujusmodi centrum gravitatis
Commune habentes.
Area sectoris primum ergo assumamus pro arbitrio duos
huriusmodi sectores inde examinemus an habeant centrum commun
gravitatis, quo facto perveniemus ad aequationem
sit
ergo unus eorum datus ABC. assumamus alterum, cujus centrum
circuli centrum sit L. ey quo perpendicularis occurrat
ipsi cA productae si opus in D. sit et datum punctum N ex qu
N P perpendicularis in CA si opus  productam. loco puncti
H. ponatur dai angulus M ML N. seu area sectoris 
assumi
LinN. sit sector ABC equ.  cor  cuus ejus
area ponatur esse co. Dat quoniam autem dabus est positione
datum erit momentum ejus ex AB. quod scribemus b. item momentum
ejus ex basi AC (quadrantis ACq) sit c. a nam
haec momenta constat esse data, fiet: GR   et
ARB C. His itaque positis quasi datis habebitur et
ae
punctum Gdatur otaque itaque et cum recta LN (it data
data erit et perpendicularis GS ex puncto G. demissa in
LN. Ex puncto N demittatur perpendicularis NT. inrectam
si opus productum LD. datur Ld. datur et DT aequ. PN. datur
ergo et LT. datur et PA item Ad. ergo et NY. Et quin asecet
dari R A habuimus RA, et PA, habetur et R. LA secetsC in V et Gsim s
LT: NT: LN:: NP. pV: NV.: SB: SV: VB:: VB+PY + pR_: GR: G5+5B
Ergo PVR et NP, NT. SA. SBA VB, LF et SBA GR, LN -G5
X
C+
Ergo GS  GR. LN YB, LF . iam VBF GR, L. F - p BR.
NF
fiet G5p GR LN
+
LN
XF
SR, LT2 + PV, LT + PR, LF
ALN, NT
LN
LN
QuiaL LFH NT
rBa
seu G5p GR, LN - GR, LT + PV LT, NT L PR, LF, NF  SR, N7 + PI LFF PR HF
LN, NT
ubi si ponatur  PV + PR 10. seu si intelligantur coincidere
puncta R et V. fiei G5, LN LF x est auter LN LF, aC, fiet G5, GR, NY
N
LN, N7
ergo fier verum video id sicu non posse commode, quia AR est quantitas
involvens aream sectoris ABC. est ergo Gs
A
GSp) GR, NT, + NB, NT, 1 + AR, L7= AP, LT. ubi ponendo
L N
INP, NT= AB LTpO
fiet GSp GR, NTF AR, LT quo casu
similiter, ut quaeracuus 5L erit: LF. N T. L N. : 5(3. ( SV: VB.: LD. (B1 oA. AP W. St 2 et V
fiet. SL A DV, L- SY
v
2 A
Sinr) GRLY. PV NrCAR XE AB NB (
1D, LI
ubi siminty ponantur coicidere et et D. fieret Den Dipo. et Sl p .12 172 a  
N7, 21
coincident
579
figura est ad
fin schediasmalis
praecedentis
pag. ult.
seu AL NE+ PAp
Seu Ne, N7, AR- AP