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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186FED. COMMANDINI fruſtum pyramidis ſit abſciſſum. erit ex iis quæ proxime
tradidimus, fruſti pyramidis a d centrum grauitatis l.
Quo
niam igitur portiones ſpacio o minores ſunt;
habebit cir
culus, uel ellipſis a b ad
137[Figure 137] portiones dictas maiorẽ
proportionem, quàm n l
ad lm.
ſed ut circulus, uel
ellipſis a b ad portiones,
ita a p b conus, uel coni
portio ad ſolidas portio-
nes, id quod ſupra demon
ſtratum eſt:
& ut circulus
uel ellipſis c d ad portio-
1122. huius nes, quæ ipſi inſunt, ita co
nus, uel coni portio c p d
ad ſolidas ipſius portio-
nes.
Quòd cum figuræ in
circulis, uel ellipſibus a b
c d deſcriptæ ſimiles ſint,
erit proportio circuli, uel
ellipſis a b ad ſuas portio
nes, eadẽ, quæ circuli uel
ellipſis c d ad ſuas.
ergo
conus, uel coni portio a p
b ad portiones ſolidas eã-
dem habet proportionẽ,
quam conus, uel coni por
tio c p d ad ſolidas ipſius
portiones.
reliquum igi-
2219. quinti tur coni, uel coni portionis fruſtũ, ſcilicet a d ad reliquas
portiones ſolidas in ipſo contentas eandem proportionẽ
habet, quam conus, uel coni portio a p b ad ſolidas portio
nes:
hoc eſt eandem, quam circulus, uel ellipſis a b ad por
tiones planas.
quare fruſtum coni, uel coni portionis a

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