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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1110. quinti
_Eſt autem & s b ſeſquialtera ipſius b r. ]_ Ponitur enim
33H d b ſeſquialtera ipſius b k;
itémq; d ſ ſeſquialtera k r. quare ut to
ta
d b ad totam b K, ita pars d s ad partem K r.
ergo & reliqua
4419. quinti s b ad reliquim b r, ut d b ad b k.
_Quæ ſimiles ſint portioni a b l. ]_ Similes portiones coni ſe-
55K ctionum Apollonius it.
i diffiniuit in ſexto libro conicorum, ut ſcri-
bit
Eutocius, εν οἱς α χ θεισωνἐν ἑηάστω παραλλήλων τῆ βάσει, ἵσωι
τὸ
πλῆθος, ὰι παρὰλληλοι, καὶ αἱ βάσ{ει}ς πρὸς τὰςἀποτεμνομένας
ἀπὸ
τῶν διαμέ τρων ταῖς νορυφαῖς ἐν τοῖς αὐτοῖ ς λὄγοιςεἰσἰ, καὶἁι
ἀποτεμνόμεναι
πρὸς τάς ἀποτεμνομένας;
hoc est. in quibus ſi du-
cantnr
lineæ æquidistantes baſi numero æquales:
æquidiſtantes atq;
baſes ad partes diametrorum, quæ ab ipſis ad uerticem abſcindũtur,
eandem
proportionem babent:
it émq; partes abſciſſæ ad abſciſſas.
ducuntur
autem lineæ baſi æquidistantes:
ut opinor, deſcripta in ſin
gulis
plane rectilinea figura, quæ lateribus numero æqualibus conti
66γνωρίμως neatur.
Itaq; portiones ſimiles à ſimilibus coni ſectionibus abſcindũ
tur
:
& earum diametri ſiue ad baſes rectæ, ſiue cum baſibus æ qua-
les
angulos facientes, ad ipſas baſes eandem habent proportionem.

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