Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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">Si à puncto, quod eſt intra Hyperbolen, ductæ ſint duæ re-
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ctæ lineæ aſymptotis æquidiſtantes, & </
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">Hyperbolæ in duobus
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punctis occurrentes, è quorum altero ducta ſit recta linea vtran-
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que aſymptoton ſecans, à qua, producta in angulo, qui aſym-
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ptotalis eſt ad verticem, à puncto alteram aſymptoton ſecans
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dematur æqualis ei, quę inter eductæ occurſum cum alia aſym-
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ptoto intercipitur: </
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<
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">recta linea hoc idem occurſum iungens cum
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dato puncto, æquidiſtabit rectæ, ſumptæ terminum iungenti, & </
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ſectionis punctum, in quo conuenit recta alteri aſymptoto ęqui-
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diſtanter ducta.</
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C E vltra centrum productæ, ſumptum quodcunque punctum F, à
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quo ductæ ſint F A D, F B E aſymptotis æquidiſtantes, quæ Hyperbolen
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ſecent in punctis A, B, è quorum altero, vt ex B, ducta ſit quæcunque
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B I aſymptoton C E ſecans in G, & </
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& </
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">in directum ipſi B G, iungantur rectæ I A, G F. </
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parallelas.</
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<
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">Nam cum recta G H ſecet vtranque linearum C G, C H continentium
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angulum H C G, qui deinceps eſt angulo D C E Hyperbolen A B conti-
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nenti, ſitque ea (per conſtructionem) hinc inde æqualiter producta in.
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oppoſitam ſectionem. </
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