Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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rectæ D H F æquidiſtabit, cum & </
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tim ducta.</
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<
s
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xml:space
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">Iam in ſingulis figuris erit portio L E M æqualis portioni A B C,
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eſt quoque portio D E F eidem portioni A B C æqualis, ex hypotheſi,
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quare duæ portiones L E M, D E F inter ſe æquales erunt, ſed vtraque eſt
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de eadem ſectione, & </
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<
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<
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parallelas, ergo baſis L I M tota congruet cum baſi D H F, vnde & </
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<
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ctum I cum puncto H; </
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<
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xml:space
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">quare ſegmenta E I, E H inter ſe æqualia erunt,
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ac propterea erit, in prima, ſegmentum quoque E H æquale B G, & </
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<
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liquis erit H E ad E O, vt G B ad B O. </
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batur.</
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<
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<
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">Sint iam in tertia figura duæ portiones æquales A N C, D P F ſemi- El-
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lipſi maiores, quarum ſegmenta diametrorum ſint G N, H P, & </
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centrum O. </
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<
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">Et cum portiones A N C, D P F ſint æquales, & </
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erunt quoque reliquæ A B C, D E F de eadem Ellipſi inter ſe æquales,
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ſed ſemi- Ellipſi minores; </
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">quare erit, vt ſupra oſtendimus, G B ad B O,
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vt H E ad E O, & </
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H E, & </
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">eſt G B ad B O, vel ad O N, vt H E ad E O, vel ad O P, ergo,
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ex æquali G O ad O N, vt H O ad O P, & </
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vt H P ad P O. </
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