Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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genti parallela, erit hæc vna ordinatim ad diametrum ſemi - applicatarum,
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datumq; </
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">Parabolæ inæqualium laterum per eundem verticem ſimul adſcri-
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ptæ, ſunt inter ſe nunquam alibi coeuntes, & </
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ctum latus minus eſt, ſuntque, in infinitum productæ, iuxta intercepta
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applicatarum ſegmenta ſemper magis recedentes, & </
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perueniunt maius quolibet dato interuallo.</
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rum communis diameter B H, & </
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verò ſit minor B G. </
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inſcriptam eſſe. </
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eſſe inter ſe magis recedentes.</
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cunque duabus ADH, IL M; </
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regulas in P, O, N, R; </
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dratum I M ad M L, ita recta R M ad M N, vel vt
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H ad H P, vel vt quadratum A H ad H D, erit etiam
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recta IM ad ML, vt AH ad H D, & </
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rationis, & </
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ſed eſt IM maior AH, quare, & </
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omnes huiuſmodi applicatas proportionaliter diuidi à Parabola B D L) ita datũ
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interuallum N O ad aliud O P, & </
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B R æqualis P N, & </
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conic.</
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ſtans, quæ Parabolæ ABC occurrat in I, & </
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ſtructione, quare IL ipſi N O ęqualis erit, ſed applicatę infra I L inter Parabolas
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excedunt ipſam IL, vti nuper oſtendimus: </
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uallum perueniunt maius dato iuteruallo N O. </
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<
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nos, qui de aſymptoticis lineis mutuam acceſsionem, vel receſsionem
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perpendendam ſuſcepimus, æquidiſtantium linearum ſegmentis, inter
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conuergentes, ac diuergentes aſymptotos interceptis vſos fuiſſe, veluti
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in præcedenti, vbi iuxta lineas, ſiue portiones A D, I L ex ordinatim
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app licatis ad communem diametrum, datarum ſectionum diſtantias commetimur;
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