Benedetti, Giovanni Battista de
,
Io. Baptistae Benedicti ... Diversarvm specvlationvm mathematicarum, et physicarum liber : quarum seriem sequens pagina indicabit ; [annotated and critiqued by Guidobaldo Del Monte]
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IO. BAPT. BENED.
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<
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<
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style
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">Euclidis uero tertiadecima propoſitio.</
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<
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aliqua proportio plurium proportionum inuicem æqua-
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lium, tertia aliqua proportione, maior aut minor fuerit, quælibet prædictarum æqua
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lium inter ſe, tertia illa proportione maior aut minor pariter erit.</
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<
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xml:space
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<
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fuerint ex vna parte plurestermini (ſiue coniuncti ſiue di-
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ſiuncti ſint) æquales ſinguli vni tertio termino; </
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<
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">ex altera verò parte totidem fuerint
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alteri tertio termino æquales, proportio aggregati priorum terminorum ad
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ter-
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tium, æqualis erit proportioni aggregati reliquorum terminorum ad ſuum tertium,
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& è conuerſo, ita ſe habebit primus tertius terminus ad ſuos multos terminos, ſicut
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ſe habet ſecundus tertius terminus ad ſuos ſimul ſumptos.</
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">Aggregatum ex partibus proportiona litatis continuæ, quod inter maximum, &
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minimum terminum omnium terminorum proportionalium compræhenditur, ſem
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per multiplex eſt ad ſingulas partiales proportiones, ex quibus ipſum componitur.</
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</
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<
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s
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">Quæuis proportio quocunque modo diuiſa fuerit, ex iis partibus componitur, in
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quas diuiditur.</
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dubio inter obie
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ct a ipſius intellectus connumerari poſſint, nullus ſanæ mentis eas negabit.</
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">PRimum, ſecundum, & tertium theorema quinti Euclidis ab ipſo ſatis exactè de
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monſtratur, ſtudioſus itaque autorem conſulat.</
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fig-0212-01
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fig-0212-01a
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0212-01
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0212-01
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clidis ego ſic
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.
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<
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poſtulato præmiſſo, eandem futuram
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proportionem
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ſuppoſito verò
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compo
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nitur ex eis quæ ſunt
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