Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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F Q H ſit obtuſus, eò quod alterno Q F B obtuſo ſit æqualis) ſed eſt F Q
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maius F P, quare educta F H eò maior erit educta F P. </
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">Ampliùs ducta
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qualibet alia F R, adhuc maiorem angulum facient
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cum _MAXIMA_ F D,
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agatur per R recta R S axi F E parallela, quæ cadet intra Ellipſim, (cum
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ſit ad minorem axim H I ordinatim ducta) ſecabitque F P in S, ac in
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triangulo F R S obtuſiangulo ad R, erit latus F S maius latere F R, & </
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educta F P eò maior educta F R; </
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">eademque ratione oſtendetur quamli-
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bet eductarum ad peripheriam H A, vtputa F R, maiorem eſſe ſemi-ap-
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plicata F A, ſi ex A ducatur A V parallela ad E F, &</
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<
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">quare eadem
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ſemi-applicata F A omnium eductarum in portione maiori A D C erit
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_MINIMA_. </
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<
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">Aliarum autem, quæ cum _MAXIMA_ F D maiorem angulum
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conſtituit, maior eſt. </
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">Si in triangulo A B C, cuius rectus angulus ſit ad B, fuerit
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latus A B maius altero B C, ſitque de maiori B A abſciſſa pars
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B E, quæ non excedat dimidium ipſius B C, & </
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puncto G ducta ſit G H parallela ad B C. </
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">Dico primùm ipſam
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G H ſemper maiorem eſſe aggregato B E cum E G.</
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">Et quoniam A B ponitur maior ip-
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ſa B C; </
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">B C verò dupla, vel plus quàm dupla ad B E, erit omni-
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no A B plus quàm dupla ad B E, ſiue AE
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plus quàm dimidium ipſius A B, quod
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memento ſed, vt A E ad A B, ita E F
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ad B C; </
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">quare E F eſt maior dimidio
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ipſius B C, hoc eſt maior ipſa B E. </
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igitur E S æquali ipſi B E, ducatur S K
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D parallela ad B E, eritque B S paralle-
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logrammum æquilaterum (cum E B,
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E S ſint æquales) iungatur denique C S
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rectam G H ſecans in T.</
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<
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">Itaque cum E B, ſiue B D poſita ſit
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æqualis, vel minor dimidio ipſius B C,
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erit C D æqualis, vel maior ipſa D B,
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vel D S. </
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">Cumque ſit, vt C D ad D S,
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ita T K ad K S, erit quoque T K ęqua-
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lis, vel maior ipſa K S, ſiue G E, qui-
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bus T K, & </
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">G E additis ęqualibus K G, E B, proueniet tota T G æqua-
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lis, vel maior aggregato G E cum E B, ſed eſt H G maior ipſa T G: </
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<
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re H G erit omnino maior aggregato B E cnm E G. </
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