Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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<
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xml:space
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">Nam, ad finem propoſitionis oſtenſum fuit, planum contingens portio-
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nem ſolidam E F G, & </
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<
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">baſi E H G I parallelum, eam contingere ad pun-
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ctum F, quod eſt vertex diametri N F Canonis recti E F G, atque inſuper
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idem punctum contactus F, iuxta Archim. </
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<
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de Conoid. </
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<
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<
s
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xml:space
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">iam notum eſt verticem vocari axis portionis ſolidæ E F G.</
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<
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">EX his itaque notandum eſt, axim ſolidæ portionis eundem eſſe cum dia-
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metro prædicti Canonis recti, & </
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<
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<
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0283-01
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quæ ex conſtructione diame-
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ter eſt planæ portionis E F
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G, eſt quoque axis ſolidæ,
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cum ab F eius vertice, ad N
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centrum baſis E H G I ince-
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dat. </
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<
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">Præterea ducta ex ha-
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rum portionum cómuni ver-
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tice F recta F P ad baſim E
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G planæ portionis, ſeu recti
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Canonis E F G perpendicu-
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lari. </
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<
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">Patet hanc eſſe Canonis
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altitudinem, ſed Canon E F
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G rectus ponitur ad baſim E H G I; </
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<
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">quare F P, quæ ad communem horum
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planorum ſectionem E G eſt perpendicularis, recta erit ad planum baſis
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E H G I, ac propterea ipſa erit quoque altitudo portionis ſolidæ E F G,
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cum perpendiculariter cadat ex eius vertice F ſuper baſim E H G I, &</
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<
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<
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axim ſolidi, cuius eſt portio, eſſe in vno eodemque plano, quod per
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axem eiuſdem ſolidi ad baſim portionis rectum ducitur, ſiue eſſe in plano
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Canonis recti.</
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in plano E B C ducto per axem B D, ſed erecto ſuper baſim E I G H por-
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tionis ſolidę E F G, quod planum E B C idem eſt, ac planum recti Canonis
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E F G intra ſolidam portionem intercepti.</
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<
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tio ducatur planum, hoc erit ad planum baſis portionis erectum, atque in
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ſolida portione rectum Canonem exhibebit.</
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