Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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de applicatis ad puncta arcus A I D, tum de ijs, quæ pertingunt ad puncta
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reliqui arcus D B, hoc eſt prædicta rectangula hinc inde à puncto D, con-
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tinuè decreſcere, quò magis diſtant à _MAXIMO_ rectangulo A E D.</
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">In dato ſemi - circulo, vel ſemi - Ellipſi, hinc inde à MA-
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XIMO rectangulo nuper inuento, bina æqualia rectangula re-
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perire.</
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<
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">SIt datus ſemi- circulus, vel ſemi-Ellipſis, cuius diameter A B, centrum
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C, & </
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">punctum, ad quod peruenit _MAXIMVM_ rectangulum, ſit D,
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(quod habebitur ſi diameter A B ſecetur in L, ita vt A L ſit tripla L
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93. h. &
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ex 94. h.</
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& </
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">applicetur L D,) ſitque exempli gratia è quolibet puncto E arcus A E
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D, applicata E F ad diametrum A B, & </
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ctum G reperire, ita vt ducta G H ipſi E F parallela, rectangula A F E, A
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H G inter ſe ſint æqualia.</
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">Ducatur ex A ſectionem contingens A I, quę ipſis applicatis æquidiſta-
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bit, atque in angulo aſymptotali I A B per punctum E deſcribatur
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Conic.</
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perbole E G. </
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care, vt in G, & </
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">Etenim demiſſa ordinata D L, cum hæc aſymptoto A I æquidiſtet, ipſa
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neceſſariò Hyperbolen E G ſecabit, at
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11. primi
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huius.</
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vno tantùm puncto, veluti in M, & </
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perbolen, erit rectangulum A L M
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Conic.</
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rectangulo A F E, ſed eſt rectangulùm A L
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D maius eodem rectangulo A F E, cum ſit
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_MAXIMVM_, ex hypotheſi, ergo idem rectan-
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gulum A L D maius erit rectangulo A L M,
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atq; </
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re L D maior erit L M. </
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G ſecat omnino D L inter D, & </
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producta neceſſariò ſecabit peripheriam arcus
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D B, cum ſpatium L D B ſit vndique clau-
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ſum, & </
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rectangulum G H A, ob Hyperbolen, ſit æquale rectangulo E F A.</
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<
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bole arcui A D, vel arcui D B occurrat, manifeſtum eſt: </
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curreret, vt in N; </
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æquale rectangulo A F E, quod eſt falſum, quoniam ob circulum, vel El-
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lipſim, quando punctum N eſt inter E, & </
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quàm rectangulum ad E, & </
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