Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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inter ſe ſolida Acuminata proportionalia, & </
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cantur, vnde Coni portiones inſcriptæ inter ſe æquales erunt; </
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ſolida portio ad portionem æqualem de eodem ſolido, vt inſcripta Coni
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portio ad inſcriptam Coni portionem (ob æqualitatem) & </
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ſolida portio ad ſibi inſcriptam Coni portionem, vt altera æqualis portio ad
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ſibi inſcriptam Coni portionem, & </
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<
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mand. in
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lib. de Co
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noid. &
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Sphęroid.
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Archim.</
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portio ad circumſcriptum Cylindricum, vt reliqua portio ad ſibi circum-
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ſcriptum Cylindricum, &</
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">MAXIMA portionum eiuſdem Coni recti, aut Conoidis Hy-
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perbolici, ſiue Sphæroidis oblongi, vel prolati, & </
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ſint æquales, ea eſt, cuius axis congruat cum axe ſectionis, quæ
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ſolidum genuit; </
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">& </
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lipſis genitricis.</
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Ellipſis.</
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">ETenim quando portiones eiuſdem Conirecti, aut Conoidis Hyperboli-
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ci, ſiue Sphæroidis cuiuslibet ſunt æquales, & </
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ſunt æquales, & </
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">quando recti Canones ſiue portiones de eodem
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vel Hyperbola, aut Ellipſi æquales ſunt, inter ipſorum diametros _MINIMA_
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eſt ea, quæ ſimul ſit axis anguli, vel Hyperbolæ, & </
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poſt 5 1. h.
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ad nu. 1.</
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minor, & </
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Coni recti, aut Conoidis Hyperbolici, vel Sphæroidis fuerint æquales, in-
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ter ipſorum axes (qui ijſdem ſunt, ac diametri rectorum Canonum)
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69. h.</
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_NIMVS_ erit is, qui congruet cum axe Coni, vel Conoidis Hyperbolici,
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aut cum minori axe Ellipſis Sphæroidis, & </
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maiori: </
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">quare ſi primùm axes harum omnium equalium portionum, dempta
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ea circa _MINIMV M_ axem, huic _MINIMO_ axi æquales ſecentur, atque ex
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interſectionibus ducantur plana baſibus portionum æquidiſtantia, auferen-
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tur ab ipſis portiones ſolidæ æqualium axium, ſed vnaquæque erit minor
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quacunque æqualium portionum, (cum ſit pars ſuo toto minor) ac propte-
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rea minor ea, è cuius, axe, ſiue à qua portione nihil ablatũ ſuit, quę quidem
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ea eſt, cuius axis congruit cum axe Coni recti, vel Conoidis Hyperbolici,
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& </
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tiones æqualium axium ſunt hac portione minores, erit è contra hæc ipſa
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portio, cuius axis congruit cum axe dati Coni, vel Conoidis Hyperbolici,
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& </
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">pro Sphæroide, cum minori axe genitricis Ellipſis, earundem omnium
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portionum, æqualium axium, _MAXIMA_. </
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ducantur, ac prædicto _MAXIMO_ axi (qui iam, vt ſuperiùs </
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