Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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dratum D C ad quadratum B G, quare quadratum B F maius eſt quadra-
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to B G; </
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<
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aliud punctum rectæ A C F, præter C. </
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contingens in in C. </
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ſtrata, facilè tamen ad affirmatiuam reducitur, ſi ex ip-
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ſa in principio demantur ea verba. </
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<
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_teſt, ſecet vt E C F_, ad finem verò. </
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_poteſt_; </
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<
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">nam ibi linea H G oſtenditur minor G F, vnde punctum F
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cadet extra ſectionem, & </
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præter C, quare ipſa E C H ſectionem continget in C: </
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idem pateat, en afferemus noſtram directè concluſam demonſtrationem,
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de qua in præcedenti Monito, præmiſſo tantùm (vice propoſitionis 169.
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">ſeptimi Pappi, qua indiget Apolloniana propoſitio) ſequenti Lemmate, in
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quo interim duæ ſimul circuli proprietates detegentur haud iniucundæ.</
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rem partem C B producatur, ita vt ſit A D ad D B, vt A C ad
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C B, & </
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applicetur ipſi D E æquidiſtans, productam diametri partem
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ſecans in F, aut infra D, aut ſupra, & </
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G. </
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rectangulum A F B.</
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">Iam cum ſit A D ad D B, vt A C ad C B, erit componendo A D
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cum D B ad D B, vt A B ad B C, & </
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ſubduplis, erit H D ad D B, vt H B ad B C, & </
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D H ad H B, vt B H ad H C, vel vt D H ad H E (ipſi H B æqualis) ita
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H E ad H C: </
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">quare triangula D H E, E H C, cum habeant circa com-
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munem angulnm H latera proportionalia, ſimilia erunt, vnde angulus
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D E H æquabitur angulo E C H, ſiue rectus erit, ideoque D E circulum
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continget, hoc eſt quadratum D E æquabitur rectangulo A D B. </
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primò, &</
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