Archimedes - Archimedis De iis qvae vehvntvr in aqva libri dvo

Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of contents

[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.

[41.] COMMENTARIVS.

[42.] LEMMA I.

[43.] LEMMA II.

[44.] LEMMA III.

[45.] LEMMA IIII.

[46.] LEMMA V.

[47.] LEMMA VI.

[48.] II.

[49.] III.

[50.] IIII.

[51.] V.

[52.] DEMONSTRATIO SECVNDAE PARTIS.

[53.] COMMENTARIVS.

[54.] DEMONSTRATIO TERTIAE PARTIS.

[55.] COMMENTARIVS.

[56.] DEMONSTRATIO QVARTAE PARTIS.

[57.] DEMONSTRATIO QVINT AE PARTIS.

[58.] FINIS LIBRORVM ARCHIMEDIS DE IIS, QVAE IN AQVA VEHVNTVR.

[59.] FEDERICI COMMANDINI VRBINATIS LIBER DE CENTRO GRAVITATIS SOLIDORV M.

[60.] CVM PRIVILEGIO IN ANNOS X. BONONIAE, Ex Officina Alexandri Benacii. M D LXV.

14115DE CENTRO GRAVIT. SOLID. bere proportionem, quam ſpacium g h ad dictã
figuram, hoc modo demonſtrabimus.

Intelligatur circulus, uel ellipſis x æqualis figuræ rectili-
neæ in g h ſpacio deſcriptæ: & ab x conſtituatur conus, uel

95[Figure 95] coni portio, altitudinẽ habens eandẽ, quã cylindrus uel cy
lindri portio c e. Sit deinde rectilinea figura, in quay eade,
quæ in ſpacio g h deſcripta eſt: & ab hac pyramis æquealta
conſtituatur. Dico conũ uel coni portionẽ x pyramidiy æ-
qualẽ eſſe. niſi enim ſit æqualis, uel maior, uel minor erit.

Sit primum maior, et exuperet ſolido z. Itaque in circu
lo, uel ellipſi x deſcribatur figura rectilinea; & in ea pyra-
mis eandem, quam conus, uel coni portio altitudinem ha-
bens, ita ut portiones relictæ minores ſint ſolido z, quem-
admodum docetur in duodecimo libro elementorum pro
poſitione undecima. erit pyramis x adhuc pyramide y ma
ior. & quoniam piramides æque altæ inter ſe ſunt, ſicuti ba
116. duode-
cimi. ſes; pyramis x ad piramidem y eandem proportionem ha-
bet, quàm figura rectilinea x ad figuram y. Sed ſigura

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