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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 3 (shelfmark LH 13, 3)
# Folio 212r, page id 00068200:0425
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dediasma
pro Quadratura
sidetur subfine
secundi demonstrat
invenire duas sectores portiones impossibilitas quadi
circulares, ex diversis circulis eccenticis tmae onfecialis
centrum gravitatis commune habentes
Quoniam inveni ratio nem generalem
semisona portione
data
portione circulari, save sit sector, sive segmentum
sive alia qualiber inveniendi axem  aliquem
o ostian e conae
cijocus
uifb
fig. 1. duo Hin si dua reperiri possint, portiones circulares, centrum
asp
verb. pat peltores ABC. DEF) (licet ex diversa circulis) centrum gravitatis com
mune ohabentes, ita tamen ut duorum circiloram
centra gravitatis et du centrum gravitatis
commune portionum non cadat in eaudem rectam
tunc inter sectione ductum axium aequilibuii per
51
Ebicperiri posse hoc
 oe
circulorum centra transeuntium
centrum gravitatis commune, etG) adeoque habebitur circu
hujus portionis circulais area
Haec inquisitio quia elegans est, tametsi non per omnia succederet
perse tentari meretur sed rem ab quo iohoem initio repetamus
sit fig. 2. sit quadranseinsta CD d in ducto simu DE sit segum
et AB, 1
eant
semiseumentum ADE sit AD CBd AX. DE, y. et  A
q
VH ar - X et Sy ax psrax - X dx  rx  ex 3r  X
sec
semigon  o BBECE posita X sedmomentum
quod est momentum eusmtati ADE ex axe AB. (qui momentum
a co
rectae pujusque
iphius y ex uxe  ad qbem
est constat esse y posito
Rursus momentum hujus
semitonae semisegmenti quaeramus ex basi BC. ex Edemittatur
in basin perpendi cularis EF. quod si ergo habeamus momentum
ipsius ABFE ex basi IC. habebimus et momentum ipsius
Momentum quadrilinei A BFE ex basi BC. ita invenieaus
X2 r. y.  crescunt autem ipsae X a parte B
versus A.
Eid Ejusdem semitonae momentum
ex basi habetur hoc modo: quaeratur prius
momentum semisegmenti CEF. ex basi, quod ita fer:
sit CF ,  v. Et  EF X, erit X 2YD- v
et (X do  (2rvao - v do  _, 1 V - V, orv - Ov
Cs
mc fX do 3Y + 317 - 6ry = Yy + 3r y_3r5 2149 - 3ry
quod est semisegment  momentum ex basi e posita y esse
simu rectum. Huic addatum aromentum rectanguli
BE ex basi BC. quod est Xy, X seu Xy fietc
momentum semitonae ex basi e ius t a est autem
jam X, r. y. erit (OXY p ry - Y. et
momentum semifonae ex basiocerit. Er+y- rys + 3ry -3
seu erit: 21 - 293
r3. yd Momentum autem
ejusdem semitonae ex BC ejusdem autem momentum
ex AB erat 3r2X - 2X. Itaque si in recta F
CG
sumatur , quae sit ad BF ut momentum exBC sive recta
GL posito Gese dentrum gravitatis semitonae ad momentum
exaxe sive rectam BLaesid est ut , id est si fiat ut FH ad
et BF, ut 2r- 293 ad 35X - 2 X3, juncta BH
erit axis aequiliomi seu transiber elr Gcentrum gravitotis
sesu
N. elegans
thectema