Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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">MINIMA linearum ad vniuerſam Ellipſis peripheriam du-
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cibilium, à puncto maioris axis, quod diſtet à vertice per in-
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teruallum non maius dimidio recti lateris, eſt idem axis ſegmen-
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tum, inter datum punctum, & </
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">Aliarum autem eductarum in minori portione Ellipſis, cuius
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baſis, ſit applicata per datum punctum; </
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">quæ cum MINIMA
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minorem angulum conſtituit, minor eſt.</
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">ESto Ellipſis A B C D, cuius axis maior A C, minor B D, centrum E,
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& </
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">latus rectum maioris axis C A ſit C F, & </
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verò C G, ſit non mains
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dimidio C F. </
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ducibilium ex G ad vniuerſam Ellipſis peripheriam A B C D.</
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æqualis dimidio recti C E, ſit mi-
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nor reliquo axis ſegmento G A, pa-
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tet: </
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">quoniam C A ad B D, eſt vt B D
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ad C F, & </
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ad E B, vt E B ad C G, eſtque C E
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maior E B, quare E B quoque maior
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eſt C G, & </
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G maior G C.</
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<
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regulæ occurrens in I. </
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ad A C, vt E L ad C F, ſed eſt A E
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dimidia A C, quare E L recti C F
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dimidia erit; </
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<
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">eſtque G I maior E L,
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ergo G I maior eſt dimidio recti C F,
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& </
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recti; </
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G I, ſiue quadratum G C minus re-
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ctangulo C G I, ſiue quadrato G H, hoc eſt linea G C minor ipſa G
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primę pri
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mi huius.</
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ſed G H eſt _MINIMA_ ducibilium ex G ad peripheriam H A S, ergo GC eò ampliùs _MINIMA_ erit ad eandem maioris portionis peripheriam H A S.
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G M, & </
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oſtenſa ſit C G minor quàm dimidium C A, ſed poſita ſit non maior di-
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midio C F, & </
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C F, erit N O maior aggregato C G cum G N, per primam partem 7. </
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ius; </
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primę pri
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mi huius.</
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quadratum M N maius rectangulo ſub C G cum G N in N C: </
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vnicum quadratum G M, maius rectangulo ſub C G cum G N in N C, </
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