Archimedes
,
Archimedis De iis qvae vehvntvr in aqva libri dvo
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quindecim ad quatuor; </
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<
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">& </
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<
s
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">ad eam, quæ uſque ad axem maiorem pro
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portionem habeat: </
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<
s
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">erit quæ uſ que ad axem minor ipſa k c.</
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<
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<
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<
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_quæ in translatione non erant._</
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<
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<
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d b ſeſquialtera ipſius b k; </
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<
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<
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">d ſ ſeſquialtera k r. </
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ta d b ad totam b K, ita pars d s ad partem K r. </
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s b ad reliquim b r, ut d b ad b k.</
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<
s
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<
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">]_ Similes portiones coni ſe-
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ctionum Apollonius it. </
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">i diffiniuit in ſexto libro conicorum, ut ſcri-
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bit Eutocius, εν οἱς α χ θεισω
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νἐν ἑηάστω παραλλήλων τῆ βάσει, ἵσωι
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τὸ πλῆθος, ὰι παρὰλληλοι, καὶ αἱ βάσ{ει}ς πρ
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ὸς τὰςἀποτεμνομένας
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ἀπὸ τῶν διαμέ τρων ταῖς νορυφαῖς ἐν τοῖς αὐτοῖ ς λὄγοιςεἰσἰ, καὶἁι
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ἀποτεμνόμεναι πρ
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ὸς τάς ἀποτεμνομένας; </
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<
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<
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cantnr lineæ æquidistantes baſi numero æquales: </
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">æquidiſtantes atq;
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</
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<
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">baſes ad partes diametrorum, quæ ab ipſis ad uerticem abſcindũtur,
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eandem proportionem babent: </
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">it émq; </
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<
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">partes abſciſſæ ad abſciſſas. </
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ducuntur autem lineæ baſi æquidistantes: </
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">ut opinor, deſcripta in ſin
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gulis plane rectilinea figura, quæ lateribus numero æqualibus conti
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neatur. </
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">Itaq; </
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tur: </
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<
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">earum diametri ſiue ad baſes rectæ, ſiue cum baſibus æ qua-
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les angulos facientes, ad ipſas baſes eandem habent proportionem.</
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<
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xml:space
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">_Tranſibit igitur a e i coni ſectio per k.</
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teſt non tranſeat per k, ſed per aliud punctum lineæ d b, ut per u.
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">Quoniam igitur in rectáguli coni ſectione a e i, cuius diameter e z,
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ducta eſt a e, & </
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<
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">d b diametro æquidistans utraſque
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a e, a i ſecat; </
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proportionem eandem, quam a z, ad z d, ex quarta propoſitione li
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bri. </
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<
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æ. </
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ipſius z d: </
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<
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d b ſeſquialtera eſt ipſius b u. </
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ra. </
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<
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<
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teſt. </
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</
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<
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