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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
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MIIIIIII
PFITLOSODHTE NATURALIS
CONVONOA PROPOSITIO ZXXVIII. THEOREMA XXX.
Globi, in Fluido compresso infinito ex non elastico uniformiter progre-
dientis, resistentia est ad vim qua totus ejus motus, quo tempore
octo tertias partes diametri suae describit, vel tolli possit vel
generari, ut densitas Fluidi ad densitatem Elobi quamproxime.
Nam Clobus est ad Cplindrum circumscripeum uc duo 2d eria;
sE propterca Vis illa, quxe tollere polit motum omnem Cxlindri
incerea dum C. Hlindrus describat lonsitudinem quatuor diametro-
rum, Clobi mocum omnem tollet interca dum Clobus describat
duas ccrtias parres hujus longitudinis, id es, Octo tertias partes
diametri propriae. Resiltentia aurem Cylindri est ad hanc Vim
quamproxime ut densitas Fluidi ad densitatem Cylindri vel Clobi,
DEF PFOD. XRZVEI; _ Resistentia Clobi aequalis est Resistentix Cy-
lindris peF LCM. V, VF, VIT. 9. F. D.
Corol. T. Globorum, in Mediis compressis infiniris, resistentix sunt
in ratione quae componitur ex duplicata rarione velociracis, et du-
plicata ratione diametri, et duplicata ratione densicaris Mediorum.
Corol. 2. Velocitas maxima quacum Glohus, vi ponderis sui com
paratiri, in Auido resistente porest descendere, ca est quam acqui-
rere porest Olobus idem, eodem pondere, ab (que resistentia caden-
d0 ex catu suo describendo spatium quod sit ad quatuor certias
partes diametri sux ut densitas Globi ad densiratem Fluidi. Nam
Olobus tempore casus fui, cum relocitate cadendo acquisita, de
Teribet spatium quod erit ad octo certias diamerri luxe, ut denscas
Globi ad densitatem Fluidi; ex vis ponderis motum hunc generans,
erie ad rim quae motum eundem gencrare possit quo tempore Clo-
bus octo certias diametri sux eadem velscitare delcribit, uc denlitas
Fluidi ad densitatem Globi: ideoque per hanc Propositionem, vis
Donderis aequalis erie vi Resictentia, e proprerea Globum accele
rare non potes.
Corol. 3. Data et densirate Globi e velocitare ejus sub inicio
mOtuS, ut ex densirare Auidi compressi quiescentis in qua Globus
MOveTUT; datur ad omne tempus de relocitas Cilobi et ejus resi-
Aencia ec spacium ab eo detcripEum, per C OrOl. 7. PFOP. XXXV.
Corot.
DE MOTD