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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">Ducatur enim per N linea RNS parallela ad BC, eſt autem & </
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æquidiſtans, quare angulus RNM æqualis erit angulo BGD, nempe
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dec Elem.</
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& </
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<
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">planum tranſiens per MN, RS æquidiſtabit plano per BCDE, hoc
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dec. Elem.</
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baſi coni; </
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<
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">ſi igitur planum per MNRS producatur ſectio circulus erit,
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conic.</
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diameter RNS, atque eſt ad ipſam perpendicularis MN, ergo rectangulum
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RNS æquale eſt quadrato MN, vti rectangulum BGC æquale eſt quadra-
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to DG.</
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<
s
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">Iam cum ſit NX parallela ad GV, & </
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ad NX, vt GC ad NS, ob æqualitatem; </
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<
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xml:space
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">in reliquis verò erit GV ad NX, vt
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GH ad HN, vel GC ad NS, ob triangulorum ſimilitudinem; </
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<
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tando in omnibus, GV ad GC, erit vt NX ad NS.</
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<
s
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">Amplius cum in prima figura factum ſit vt quadratum FG ad rectãgulum
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BGC, ſiue ad quadratum GD, ita recta HF ad FL, vel ad GV ei æqualis, ob
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parallelogrammum FV, erit FG ad GV, vt GV ad GD; </
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<
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">quare rectangulum
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FGV æquatur quadrato DG, ſiue rectangulo BGC. </
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<
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cum factum ſit vt rectangulum HGF, ad rectangulum BGC, ita recta HF ad
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FL, vel HG ad GV, & </
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<
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eadem HG ad GV, erit rectangulum BGC æquale rectangulo FGV: </
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ergo in ſingulis figuris rectangulum BGC æquale ſit rectangulo FGV, erit
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BG ad GF, ſiue RN ad NF, vt VG ad GC, ſiue vt XN ad NS: </
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<
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ergo RNS, ſiue quadratum MN æquatur rectangulo XNF. </
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poteſt rectangulum ſub O
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N, & </
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habens FN, in prima figura, ſed in ſecunda ipſum rectangulum excedit, & </
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in tertia & </
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quod ſub HF, & </
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">Sectio DFE, cuius diameter FG in prima figura æquidiſtat AC vni laterum
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trianguli per axem, vocatur PARABOLE.</
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">Et cuius diameter in ſecunda figura occrrrit vtrique lateri trianguli per axẽ,
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dicitur HYPERBOLE.</
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verticem trianguli per axem, ELLIPSIS nuncupatur.</
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<
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terceptum, in ſecunda, tertia, & </
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<
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SVM Hyperbolæ, vel Ellipſis, quod in ſequentibus intelligatur ſemper
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extra Hyperbolen ex ipſius vertice in directum poſitum cum diametro,
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licet in conſtructionibus expreſsè non dicatur.</
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RECTVM ſectionis, quod deinceps concipiatur ſemper contingenter
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applicari ex ſectionis vertice, ſiue ordinatim ductis æquidiſtans.</
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