Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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[11.] PROPOSITIO IIII.
[12.] PROPOSITIO V.
[13.] PROPOSITIO VI.
[14.] PROPOSITIO VII.
[15.] POSITIO II.
[16.] COMMENTARIVS.
[17.] PROPOSITIO VIII.
[18.] COMMENTARIVS.
[19.] PROPOSITIO IX.
[20.] COMMENTARIVS.
[21.] ARCHIMEDIS DE IIS QVAE VEHVNTVR IN AQVA LIBER SECVNDVS. CVM COMMENTARIIS FEDERICI COMMANDINI VRBINATIS. PROPOSITIO I.
[22.] PROPOSITIO II.
[23.] COMMENTARIVS.
[24.] PROPOSITIO III.
[25.] PROPOSITIO IIII.
[26.] COMMENTARIVS.
[27.] PROPOSITIO V.
[28.] COMMENTARIVS.
[29.] PROPOSITIO VI.
[30.] COMMENTARIVS.
[31.] LEMMAI.
[32.] LEMMA II.
[33.] LEMMA III.
[34.] LEMMA IIII.
[35.] PROPOSITIO VII.
[36.] PROPOSITIO VIII.
[37.] COMMENTARIVS.
[38.] PROPOSITIO IX.
[39.] COMMENTARIVS.
[40.] PROPOSITIO X.
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124FED. COMMANDINI in linea e b punctũ g, it aut ſit g e æqualis e f. erit g por-
tionis a b c centrum.
nam ſi hæ portiones, quæ æquales
&
ſimiles ſunt, inter ſe ſe aptentur, ita ut b e cadat in d e,
&
punctum b in d cadet, & g in f: figuris autem æquali-
bus, &
ſimilibus inter ſe aptatis, centra quoque grauitatis
ipſarum inter ſe aptata erunt, ex quinta petitione Archi-
medis in libro de centro grauitatis planorum.
Quare cum
portionis a d c centrum grauitatis ſit ſ:
& portionis
a b c centrum g:
magnitudinis; quæ ex utriſque efficitur:
hoc eſt circuli uel ellipſis grauitatis centrum in medio li-
neæ f g, quod eſt e, conſiſtet, ex quarta propoſitione eiuſ-
dem libri Archimedis.
ergo circuli, uel ellipſis centrum
grauitatis eſt idem, quod figuræ centrum.
atque illud eſt,
quod demonſtrare oportebat.
Ex quibus ſequitur portionis circuli, uel ellip-
ſis, quæ dimidia maior ſit, centrum grauitatis in
diametro quoque ipſius conſiſtere.
81[Figure 81]
Sit enim maior portio a b c, cu_i_us diameter b d, & com-
pleatur circulus, uel ellipſis, ut portio reliqua ſit a e c,

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