Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of contents

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[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.
[61.] ALEXANDRO FARNESIO CARDINALI AMPLISSIMO ET OPTIMO.
[62.] FEDERICI COMMANDINI VRBINATIS LIBER DE CENTRO GRAVITATIS SOLIDORVM. DIFFINITIONES.
[63.] PETITIONES.
[64.] THEOREMA I. PROPOSITIO I.
[65.] THEOREMA II. PROPOSITIO II.
[66.] THE OREMA III. PROPOSITIO III.
[67.] THE OREMA IIII. PROPOSITIO IIII.
[68.] ALITER.
[69.] THEOREMA V. PROPOSITIO V.
[70.] COROLLARIVM.
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130FED. COMMANDINI
SIT cylindrus, uel cylindri po rtio a c: & plano per a-
xem ducto ſecetur;
cuius ſectio ſit parallelogrammum a b
c d:
& bifariam diuiſis a d, b c parallelogrammi lateribus,
per diuiſionum puncta e f planum baſi æquidiſtans duca-
tur;
quod faciet ſectionem, in cy lindro quidem circulum
æqualem iis, qui ſunt in baſibus, ut demonſtrauit Serenus
in libro cylindricorum, propoſitione quinta:
in cylindri
uero portione ellipſim æqualem, &
ſimilem eis, quæ ſunt
in oppoſitis planis, quod nos
86[Figure 86] demonſtrauimus in commen
tariis in librum Archimedis
de conoidibus, &
ſphæroidi-
bus.
Dico centrum grauita-
tis cylindri, uel cylindri por-
tionis eſſe in plano e f.
Si enĩ
fieri poteſt, fit centrum g:
&
ducatur g h ipſi a d æquidi-
ſtans, uſque ad e f planum.
Itaque linea a e continenter
diuiſa bifariam, erit tandem
pars aliqua ipſius k e, minor
g h.
Diuidantur ergo lineæ
a e, e d in partes æquales ipſi
k e:
& per diuiſiones plana ba
ſibus æquidiſtantia ducãtur.

erunt iam ſectiones, figuræ æ-
quales, &
ſimiles eis, quæ ſunt
in baſibus:
atque erit cylindrus in cylindros diuiſus: & cy
lindri portio in portiones æquales, &
ſimiles ipſi k f. reli-
qua ſimiliter, ut ſuperius in priſmate concludentur.

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