Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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titudo trianguli C B F ad altitudinem trianguli H E G, ſed horum triangu-
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lorum altitudines eædem ſunt, ac altitudines portionum A B C, H E I, cum
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puncta B, E ſint earundem portionum vertices; </
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<
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xml:space
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">quare vt baſis H G ad ba-
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ſim C F, vel ſumptis duplis, vt H I baſis portionis H E I, ad A C baſim
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portionis A B C, ita reciprocè altitudo portionis A B C ad altitudinem por-
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tionis H E I, ſuntque huiuſmodi portiones Acuminata regularia, & </
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portionalia, & </
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<
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">eorum baſes altitudinibus reciprocantur, quare ipſa Acumi-
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nata, ſeu portiones H E I, A B C inter ſe ſunt æquales. </
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<
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propoſitum fuit, quodque de ſola Parabola demonſtrauit Geometrarum
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Princeps in 4. </
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rabolę quadratura.</
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<
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<
s
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">HInc eſt, quod applicatæ ex terminis æqualium diametrorum in Para-
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bola, vel ex punctis, in reliquis ſectionibus, proportionaliter diuidẽ-
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tibus ſemi-diametros ad angulum conſtitutas, omnino ſe mutuò ſecant; </
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quod rectæ lineę, tùm harum applicatarum puncta media, tùm extrema iun-
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gentes, rectæ ſemi-diametrorum terminos iungenti æquidiſtant. </
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ſtratum eſt enim H I, A C ſecare ſe mutuò in M, & </
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ipſi E B eſſe parallelas.</
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dem Ellipſis, vel circuli, quarum baſes tranſeant per puncta earum ſe-
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mi-diametros proportionaliter ſecantia, etiam ſi ipſæ ſemi-diametri ſint in
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directum poſitæ, hoc eſt applicatæ inter ſe æquidiſtent, eſſe quoque inter ſe
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æquales. </
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riori propoſitione) ei portioni, cuius baſis ſit applicata per punctum propor-
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tionaliter ſecans aliam ſemi-diametrum, quæ cum prædictis angulum con-
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ſtituat.</
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circulo integras diametros proportionaliter ſecent, abſciſſæ portiones
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viciſſim æquales erunt, hoc eſt minor minori, & </
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">Si enim in prædictis figuris ſint duæ diametri B R E L, ita ſectæ in F, G;
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dentium ſubduplis D B ad B F, vt D E ad E G; </
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<
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H G I erunt portiones A B C, H E I inter ſe æquales, & </
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A R C reliquæ portioni H R I æqualis erit.</
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