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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 3 (shelfmark LH 13, 3)
# Folio 212v, page id 00068200:0426
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Inveniemus et centrum gravitatis ipsius seuu segmenti
CFE, vel quod eodem redit ADE. modo fieri potest, ADE.
semiscymenti. Nam semosegmenti CFE momentum ex BC
est ut dixi Er +9. 35y Ergo eodem modo semisegne
momentum semisegmensi ADE, ex AB, erit 2Y + X (3r X. nam
pro F succedit DE BF. FE. succedit Bd. DE. seu FE. BF itaque 
substituitur in locum ipsius y.
Et momentum
ejusdem ADE ex BC est semizonae FBAE ex BC est
37y - 2y a quo si auferatur momentum rectanguli
3Fy.39
BE seu DBFE ex BC. quod est ut supra dixi Xy seu YD=Z t6
momentum rectang semisegmenti ADE ex BC. fiet.
3ry - 293 - 3r y +3y, id est 1. sive u momentum
moncntus semisegmenti ex basi est sexta pars cubi a sinu complementi
itaque si in recta DE sumatur punctum N. ita ut sit
le
Nd ad _DB ut momentum semisegmenti ADE, ex axe AB
quod est 2X+x- 3YX ad sem momentum eiusdem ex
basi BC, sive ut 2Y + X - 3YX ad Y, sposito X
sim complementi, et y sinu recto) juncta BN ac producta
transibit per centrum gravitatis p. semisegmenti ADE.
Ex his jam investigemus nomenta sectoris ABE tam ex axe quam ex
basi, ut rectam quaeramus per centrum gravitatis jectoris transcuntem.
haec enim cum jam aliunde nota sit hinc calculi comproba
Ad  y momentum semisegmento AdE
tionem habebimus.
ex basi BC. addatur momentum trianguli BdE ex eadem basi B
tromentum autem BdE ex BC est mom. DBFE - mom. BFE.
Estautem mom AE BFE ex BC, H BF, EF p  ryy et
6n0
mom. DBFE ex BCaequ. est ut supro dipi pu Ergo mom. BdE ex _ est X)
seu nom. BdE ex BC est 3Xy - yXt. 2
6
ABE, ex basi BC. vel pro _ X ponendo r- y. fiet
Y+ 2Vy-21329 , 2Y9. 3 quod est Mom. sectoris exbasi BC
unde ut obiter dicam, posito ADE integio segmento duplo
semisegmenti ADE. eut mome quadrilinei huius.
EBdZ AE. momentum ex basi XY)
sectoris ex axe _ AB est mom. AdE ex AB, + mom DEB ex AB.
_x +X 3rX BDDE XYH rX-X.
Ergo mom. sect. ex axe AB est 2Y3 = 2YX  V- rX
Ergo si _ sumto in DE puncto R. sit Rd ad DB ut mom. sectoris
ex AB axe ad mom. sectoris ex BC basi, id est ut 2r- 2rX ad iry-y
eris jncta BR prod in incidet producta in centrum gravitatis
sectoris ac proinde etiam bisecabit angulum ABE. jam
ob Triangula Ed A, BdR similia erit BD: DR:: Ed: DA:: y: r.X
seu
es
5N
Ergo y + 2y  erit mom. sectoris
Rursus momentum
6
x
Ergo Ery- y: 2r= 2rX debet esse::  y: _Y. X.
r. Y p2r  seu 22y et 2ry-y-x B 2Y. X Chg any 2 X17
ubi necessaniontenor in calculo, quem alias  corrigemus
B
a X
laex
1
a X a3
7 AB. BC