Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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cioppoſitas, ſit infinitæ extenſionis, ſecaret omnino Parabolen AGC, vt
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per ſe patet: </
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<
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ſita. </
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<
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ctionum, circuli, & </
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<
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">anguli reciproca inſcriptione, ac circumſcri-
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ptione, per punctum in ipſis, vel intra, vel extra datum, iuxta
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ſæpius memoratam definitionem, hactenus pertractaſſe ſuffi-
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iat, quæ ſi grata vobis fuiſſe perceperimus, multa his ſimilia, & </
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<
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quàm plurima ad aliud tempus proferemus. </
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<
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xml:space
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">Cæterum, in proximè ſequenti-
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bus, quæ ad vberiorem doctrinam, & </
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xime conducunt, hac omiſſa definitione, inſcriptio, & </
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<
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prout in ipſis propoſitionibus exponetur.</
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">Si recta AB ſecta fuerit in C, & </
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">in D, ita vt AB ad BC, ſit vt
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AD ad DC: </
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">Dico ſi BD bifariam ſecetur in E, punctum E cadere
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inter B, & </
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tando BA ad AD, vt BC ad CD, ſed eſt BA ma-
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ior AD, quare BC erit maior CD: </
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bifariam ſecans BD cadit inter B, & </
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AD.</
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<
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xml:space
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">Iam cum demonſtratum ſit eſſe BA ad AD, vt BC ad
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CD, erit BA ad AF, vt BC ad CD; </
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ad FA, vt BD ad DC; </
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dijs, EA ad AF, ſiue ad AD, vt ED ad DC, & </
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uerſionem rationis, AE ad ED, vt DE ad EC, vnde re-
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ctãgulum AEC ęquabitur quadrato ED. </
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