Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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<
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">Si per punctum quodlibet ſumptum in angulo à rectis lineis
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comprehenſo, quarum altera ſit datæ Parabolæ, vel Hyperbo-
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læ diameter, aut ipſi æquidiſtans, altera verò ſit quęlibet ſectio-
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ni ordinatim ducta, vel huic parallela, deſcripta ſit ſectio Hy-
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perbole, cuius aſymptoti ſint prædicti anguli latera; </
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<
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Hyperbole datam ſectionem in vno tantùm puncto neceſſariò
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ſecabit.</
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<
s
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">ESto Parabole, vel Hyperbole A B, cuius diameter, vel diametro æ-
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quidiſtans ſit B C, quàm ad quemcunque angulum D E C ſecet D
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E, quæ vel ſit vna applicatarum in ſectione, vel ipſis æquidiſtans, & </
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<
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angulo D E C, per datum in eo punctum F, deſcribatur Hyperbole G
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conic.</
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H, cuius aſymptoti ſint D E, E C. </
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">Dico hancvltrò, citroque productam,
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in vno tantùm puncto ſectionem ſecare.</
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<
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<
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">Ductis enim, in prima figura, per punctum F, quod eſt in ſectione
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A B, rectis L F M, I F K aſymptotis D E, E C æquidiſtantibus, eiſque
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occurrentibus in M, K. </
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">Patet rectam M F L etiam ſi in infinitum produ-
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ctam ad partes L, in ipſo tantùm puncto F ſectioni A B occurrere, cum
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ſit vna applicatarum in data ſectione; </
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<
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xml:space
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">& </
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<
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xml:space
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">rectam I F K in eodem tantùm
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mi conic.</
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puncto F cum ſectione A B conuenire cum ipſa rectæ B C, vel diame- tro datæ ſectionis æquidiſtet: </
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tes G, tota incedit in angulo K F L, & </
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">inter æquidiſtantes F L, K D; </
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à puncto F ad partes H, tota incedit in angulo M F I, ac inter paralle-
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las F I, M C. </
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">quare ipſa Hyperbole G F H in nullo alio puncto quàm F
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ſectioni A B occurret.</
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<
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xml:space
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">In ſecunda verò, ac tertia figura, ductis ex dato puncto F (quod ibi
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extra cadit, hic verò intra ſectionem) rectis F L, F I alteri </
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