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# Title: Leibniz-Handschriften zur Mathematik LH 35, 11, 18C
# Folio 48r, page id 00068193:0097
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Sect. 1. Cp. 3. De Durtibus
sus scilicet ut CQ sectio ipsius gravis per planum fundo paralle 31.
lum ductan suam gravitatem, et praeterea in CZ particulam al-
titudinis gravis, ipu sex in ductu solido anumti proportione e
spondentim, componit cum reliquis similiter tractatis integrum
gravrs pondus; id tantum observando, quod altitudines ez vel
.
L
XN evanescunt cumo nulla est assignabilis portio gravis ut Zez
qua eandem ubiqe habent gravitatem, peuficam.
Haec solida primus consideravit Gregorius à S. dimcentio.
Prop. 9.
Duitus est factum ea ordinatim ducendis in elementa
cupientes, proportionale figurae isogoniae, cujus abscissarum
elementa sunt ut elementa reupientis, ondinarim vero appli-
cata sunt proponnonales ordinarim n reupientis elementa du
cendis.
Gravitates specificae majores versus fundum, ducendre sint
in a
qnective in CD sectiones liquoris, per plana fundo horizontali
parallela. Sumatur (Fig. 11.) recta L M et m ex puncta N
quotlibet sic amignentur, ut sit LN ad LM, ut, spatium liquous
C
vel extensio ACD ad totam eus extensionem seu volumen; et
tunc portiones rectre LM, inter duo X distantiam evanes centem
habentia interceptae, seu rectre LM partes elementares, quales sunt
N2N, 2 N3N, erunt propontionales iptis elementis spatio-
rum liquoris inter respondentes sectiones intorceptis, quales
sunt 161D2D2C, 2. C2D3D3C; quod si crassities spatiorum
LC2C, 2C3C, anumantur aequales, ita ut ipsae AC crescant uni
formiter, erunt spatia inter cepta ut ipsae sectiones, et erit
o
JN2N ad 2N3N, ut 1CYD ad 2C2D. Itaque sectiones CD sunt
ut abseisarum LN, elementa 1 N2 N, 2N3N. Sijam ad ab-
scitsas ordinatim applicentur NG gravitatibus specificis se-
etionum C proportionales, patet duetum LNG vel LMP, esse
ut