Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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[51.] V.
Page: 84
[52.] DEMONSTRATIO SECVNDAE PARTIS.
Page: 85 (37)
[53.] COMMENTARIVS.
Page: 87 (38)
[54.] DEMONSTRATIO TERTIAE PARTIS.
Page: 90
[55.] COMMENTARIVS.
Page: 93 (41)
[56.] DEMONSTRATIO QVARTAE PARTIS.
Page: 97 (43)
[57.] DEMONSTRATIO QVINT AE PARTIS.
Page: 99 (44)
[58.] FINIS LIBRORVM ARCHIMEDIS DE IIS, QVAE IN AQVA VEHVNTVR.
Page: 102
[59.] FEDERICI COMMANDINI VRBINATIS LIBER DE CENTRO GRAVITATIS SOLIDORV M.
Page: 105
[60.] CVM PRIVILEGIO IN ANNOS X. BONONIAE, Ex Officina Alexandri Benacii. M D LXV.
Page: 105
[61.] ALEXANDRO FARNESIO CARDINALI AMPLISSIMO ET OPTIMO.
Page: 107
[62.] FEDERICI COMMANDINI VRBINATIS LIBER DE CENTRO GRAVITATIS SOLIDORVM. DIFFINITIONES.
Page: 113 (1)
[63.] PETITIONES.
Page: 114
[64.] THEOREMA I. PROPOSITIO I.
Page: 114
[65.] THEOREMA II. PROPOSITIO II.
Page: 118
[66.] THE OREMA III. PROPOSITIO III.
Page: 121 (5)
[67.] THE OREMA IIII. PROPOSITIO IIII.
Page: 122
[68.] ALITER.
Page: 123 (6)
[69.] THEOREMA V. PROPOSITIO V.
Page: 125 (7)
[70.] COROLLARIVM.
Page: 127 (8)
[71.] THEOREMA VI. PROPOSITIO VI.
Page: 127 (8)
[72.] THE OREMA VII. PROPOSITIO VII.
Page: 129 (9)
[73.] THE OREMA VIII. PROPOSITIO VIII.
Page: 131 (10)
[74.] THE OREMA IX. PROPOSITIO IX.
Page: 143 (15)
[75.] PROBLEMA I. PROPOSITIO X.
Page: 145 (17)
[76.] PROBLEMA II. PROPOSITIO XI.
Page: 146
[77.] PROBLEMA III. PROPOSITIO XII.
Page: 147 (18)
[78.] PROBLEMA IIII. PROPOSITIO XIII.
Page: 148
[79.] THEOREMA X. PROPOSITIO XIIII.
Page: 149 (19)
[80.] THE OREMA XI. PROPOSITIO XV.
Page: 153 (21)
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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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