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# Title: Phoronomia, Sive De Viribus Et Motibus Corporum Solidorum Et Fluidorum Libri Duo (shelfmark Leibn. Marg. 182)
# Folio 15, page id 1066518432:0043
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DE VERTBUS ET MOTTBUS COREORUM. LIB. I. 15
B. Bb + C. nC F D. dd = MI. ce, ergo A. Aa F B. BB + C. CC + D. Dd
GOR OLL A R FUM TI.
46. Si omnia corpora A, B, C, D _C. sine aequalia, omnes eorum FiB. 5.
distantiae a plano ald, erunt multiplum distantia communis eorum
centri graritatis F. ab eodem plano secundum ponderum numerum.
Exceltusque quo distantix illorum à plano PO secundi casus, quae
ad partes centri omnium graritatis posita lunt, excedune distan-
tias illorum, qua lunt in parte oppolita, est distantix centri om-
nium graritatis F ab eodem plano PO multiplum, secundum cor-
Porum A, B, C, D _C. numerum.
S C HF O L T O N I.
17. F X Ie Huse tam Facile deduci potest regula Guldini jam
a Pappo diserte indicata, ut haud abs re Futurum existimem, s cam
hoc loco demonstratam darem, quanquam ca a pluribus jam de-
monstrata SIF. Guldini Regula ita habet: Lieuram ex conversione
cujustibet maenitudinis circa aliquam rectam positione datam oriundam,
aequari facto ex Maenitudine genitrice in viam centri ejus gravitatis.
Figura genitrix dicatur F, dictantia centri ejus graritatis ab azc
rotationis D, Ordinata tigurx y ad axem rotationis, du elementum
axis, Colidum ex conrertione figurx Fcirca axem x dicatur S, ejus
elementum aS; quibus positis per praesentem propositionem erit
D. F = Cummxe momentorum elementorum magnicudinis F =s: Vydx,
nam elementum iplius F est rdu, et hujus momentum 2γ)dx. SIE
pcircumterentia circuli cujus radius est I, e ducatur antecedens
aequario in p, UE Aat pD. F = s: prid. Jam pD est circumferentia
radii D, e py circumterentia radii y, atque adco : pus area circuli
ejusdem radii r, et per consequens: pryda cylindrulus solido S in-
Scriptus, seu ejus elementum dS; ergo pD. F = 545 =S. Ouod
erat ostendendum pro solidis rocundis; eadem est demonstratio in
aliis.
dC H OL I O N 11.
 L12. L0
buS A, B, C, D eadem seu uniformis sumta sIc, ita ut pondera co-
rum absoluta massis proportionalia sine, quoniam tamen graritas
1
48. Ouanquam in hac propositione graritas in singulis corpori-