Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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portio M F N maior portione H F I (totum ſua parte) ſed portio M F N æ-
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qualis eſt portioni A B C (cum ſit D F ad F L, vt D B ad B E)
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portio A B C erit maior H F I, & </
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<
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">hoc ſemper de qualibet alia portione, cu-
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ius diameter æqualis ſit axi B E: </
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">ergo portio A B C eſt _MAXIMA_ portio-
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num æqualium diametrorum. </
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">æqualium dia-
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metrorum eſt ea, cuius diameter ſit minoris ſemi-axis ſegmentum.
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">MINIMA verò, cuius diameter ſit ſegmentum maioris ſemi-axis.</
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<
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">ESto A B C D Ellipſis, cuius axis maior ſit B D, minor A C, centrum
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E, ſitque ex minori ſemi-axe A E demptum ſegmentum A G, & </
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maiori B E ipſi A G ſit æquale B F perque puncta G, F applicatæ ſint
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axibus rectæ L G M, H F I. </
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">Dico portionem L A M eſſe _MAXIMAM_, & </
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H B I _MINIMAM_ aliarum portionum eiuſdem Ellipſis circa diametros ipſis
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A G, B F æquales.</
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0248-01
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Nam cum ſit E A minor E B, A G verò
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æqualis B F, habebit. </
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norem rationem quàm E B ad B F: </
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ergo E B ad B N, vt E A ad A G, & </
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bebit E B ad B N minorem rationem
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quàm E B ad B F, ſiue B N erit maior
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B F; </
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<
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">quare applicata O N P cadet infra
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H I: </
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">& </
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<
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ad B N, erit portio L A M ęqualis
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">ibidem.</
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tioni O B P, ſed hæc maior eſt portione
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H B I, totum parte, ergo L A M maior
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eſt H B I.</
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<
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">Præterea, ducta inter ſemi-axes qua-
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cunque ſemi-diametro E Q, ex ipſa, quę
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maior eſt E A (eo quod hæc ſit ſemi-dia-
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metrorum _MINIMA_ ) & </
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<
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mi huius.</
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A G, dematur Q R æqualis ipſi A G, vel B F, appliceturque S R T. </
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cum ſit E A minor E Q, & </
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">A G æqualis Q R, habebit E A ad A G mi-
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norem rationem, quàm E Q ad Q R, ac ideò vti ſuperiùs oſtendimus, por-
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tio L A M erit maior portione S Q T. </
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">Eadem ratione, cum ſit E Q minor
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E B, (eò quod hæc ſit ſemi-diametrorum _MAXIMA_) & </
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<
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habebit E Q ad Q R minorem rationem quàm E B ad B F, quapropter
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portio S Q T maior erit portione H B I, & </
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<
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ne, cuius diameter ſit inter ſemi- axes; </
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<
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& </
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<
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<
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ſtrandum.</
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