Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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">EX his patet, ſimilium Hyperbolarum per diuerſos vertices ſimul adſcri-
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ptarum, & </
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las, & </
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<
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">Si in quocunque triangulo ABC ducta ſit quæpiam linea DE
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baſi BC parallela, rectangulum ABC ſuperabit ADE rectangu-
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lo ſub DB, differentia altitudinum, & </
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<
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BC, DE.</
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</
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<
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">PRoducta enim BC, ac ſumpta CF æ-
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0105-01
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quali ipſi DE, & </
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<
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A B C parallelogrammis AE, AC, DF.
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">Conſtat parallelogrammum AC ſuperare
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parallelogrammum AE gnomone DCG,
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ſed gnomon DCG æquatur parallelogrã-
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mis B E, GC, & </
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">GC æquatur DC, ſiue
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EF, quare AC ſuperat AE parallelogram-
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mo DF, hoc eſt rectangulum ABC ſupe-
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rat rectangulum ADE, rectangulo DBF; </
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& </
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adſcriptæ, ſunt inter ſe nunquam coeuntes, ac ſemper propiùs
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accedentes, & </
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interuallo.</
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<
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">SInt duæ ſimiles Hyperbolæ ABC, DEF per diuerſos vertices B, E ſimul
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adſcriptæ, quarum commune centrum ſit G, ſitque Hyperbolæ ABC
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tranſuerſum latus BH, rectum BI, Hyperbolæ autem DEF ſit tranſuerſum
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EL, rectum EM. </
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ſe conuenire.</
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<
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">Producta enim contingente ME, donec vtrinque ſectioni ABC occurrat,
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ipſa erit ordinata in ſectione ABC (cum ſint ſectiones ſimul adſcriptæ) ac
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ſectio DEF cadet tota infra contingentem KEM; </
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bet puncto D, applicataque per D recta ADN, quæ iunctis regulis HI, </
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