Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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plicetur NMO fectionem, ac diametrum ſecans in N, O.</
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<
s
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">Quoniam igitur eodem pænitus argumento, quo ſuperius demonſtratum
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eſt rectangulum AHB ad quadratum HI, eſſe vt quadratum CB ad BD, eſt
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quoque rectangulum AOB ad quadratum ON, vt idem quadratum C B ad
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BD, vel vt quadratum BO ad OM, erit permutando, rectangulum AOB ad
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quadratum BO, vt quadratum NO ad OM, ſed rectangulum AOB ſuperat
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quadratum BO, (exceſſus enim eſt rectangulum ABO) ergo & </
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<
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NO, maius eſt quadrato MO; </
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<
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ctum M cadit intra: </
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altera aſymptotos, quæ diuidat angulum ab aſymptotis factum. </
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<
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ſecundò demonſtrandum.</
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rum demonſtremus aliter decimam quartam eiuſdem, abſq;
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diget, præmiſſo tantum ſequenti Lemmate.</
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cunque BE, rectangulum AED maius eſſe quadrato EC.</
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ad BC, vt BC ad BD, & </
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CB ad BD. </
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DE, habebit CD ad DB maiorem
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rationem quam ad DE, & </
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nendo CB ad BD, hoc eſt AC ad CD maiorem habebit rationem
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ti elem.</
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CE ad ED, & </
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DE, & </
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quam EC ad ED, vnde EF erit minor ED, ſed (cum factum ſit AE ad EC,
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vt EC ad EF) rectangulum AEF æquale eſt quadrato EC, quare rectangu-
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lum AED maius erit quadrato EC. </
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ſec. con.</
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dunt, & </
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<
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accedere, & </
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