Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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">Si fuerit quodcunque quadrilaterum rectilineum A B C D, cu-
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ius oppoſita latera A D, B C bifariam ſecta ſint in punctis F,
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E, iunctaque ſit recta F E, in qua ſumptum ſit quodlibet pun-
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ctum G, vel intra, vel extra quadrilaterum à quo ad terminos
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alterius ęquidiſtantium veluti ad A, D, ductæ ſint G A, G D,
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ac in triangulo A G D, ſit quædam H I ipſis A D, B C æquidi-
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ſtans, & </
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gula A B H, D C I inter ſe æqualia eſſe.</
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<
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">NAm totum quadrilaterum A B E F, æquale eſt integro quadrilatero
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D C E F (vtrunque enim diuiditur per diagonales A E, D E, in
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duo triangula alterum alteri æquale, eò quod ſint ſuper æqualibus baſi-
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bus, ac inter eaſdem parallelas) eadem ratione quadrilaterum A H L F
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æquale eſt quadrilatero D I L F, & </
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">quadrilaterum B E L H æquale qua-
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drilatero C E L I, ergo, & </
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">reliquum triangulum A B H reliquo triangulo
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D C I eſt æquale. </
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">His itaque præoſtenſis, ad inueſtigationem MAXIMARVM, MI-
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NIMARV MQVE portionum per idem datum punctum ex qualibet coni-
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ſectione abſciſſarum accedamus, præmiſſo tamen, ſuper figurastertij Sche-
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matiſmi, ſequenti Theoremate, vniuerſalem, ſimulque facilem methodum
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exhibente, qua æquales portiones de eadem coni-ſectione abſcindi poſſunt.</
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