Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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[Figure 271]
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[Figure 272]
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congruit cum maiori axe Sphæroidis) æquales ſecentur, atque ex interſe-
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ctionum punctis plana ducantur portionum baſibus æquidiſtantia, abſcin-
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dentur portiones ſolidæ æqualium axium, & </
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<
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xml:space
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">vnaquæque erit maior quali-
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bet æqualium (totum enim ſua parte maius eſt) ac ideò maior ea portione,
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cuius axi, vel cui portioni nihil additum fuit, quæ quidem eſt ea, cuius axis
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congruit cum maiori axe Sphæroidis. </
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<
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xml:space
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">Itaque ſi omnes planæ portiones
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æqualium axium ſunt hac portione maiores, erit è contra hæc ipſa portio,
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cuius axis conuenit cum maiori axe Sphæroidis, _MINIMA_ earundem om-
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nium portionum æqualium axium, in caſibus tamen poſſibilibus. </
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<
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xml:space
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timò demonſtrandum erat.</
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">MAXIMA portionum de codem Cono recto, vel de quocun-
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que Conoide, aut Sphæroide, & </
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<
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xml:space
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">quarum baſes ſint æquales, ea eſt,
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cuius axis ſit ſegmentum maioris ſemi- axis genitricis ſectionis dati
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ſolidi, reſpectiuè ad Sphæroides.</
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<
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xml:space
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">In Sphæroide autem, MINIMA, cuius axis ſit ſegmentum mi-
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noris ſemi- axis Ellipſis, quæ ſolidum procreat.</
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<
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">QVando enim portiones eiuſdem Coni recti, vel cuiuslibet Conoidis,
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aut Sphæroidis ſunt æquales, & </
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">recti earum Canones ſunt
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& </
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<
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">cum recti Canones, vel portiones de eodem angulo, vel de
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eadem coni- ſectione, quæ ſolidum genuit æquales ſunt, inter ipſorum ba-
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poſt 5 1. h.
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ad nu. 2.</
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ſes, _MINIMA_ eſt ea illius portionis, cuius diameter ſit ſegmentum maio- ris axis reſpectiuè ad Ellipſim, & </
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">_MAXIMA_ eius, cuius diameter ſit ſegmen-
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tum minoris, atque vt ſunt baſes æqualium planarum portionum de eodem
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angulo, vel coni-ſectione, ita ſunt baſes ſolidarum portionum,
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roll. 78. h.</
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ipſæ planæ portiones ſint recti Canones, ergo & </
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tionum de eodem Cono recto, vel Conoide, aut Sphæroide quocunque,
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_MINIMA_ erit ea illius portionis, cuius axis (qui idem eſt cum
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">3. Schol.
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69. h.</
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recti Canonis) congruat cum maiori axe genitricis ſectionis ſolidi, cuius
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eſt portio, & </
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<
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">_MAXIMA_, in Sphæroide, erit baſis illius portionis, cuius axis
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ſit ſegmentum minoris axis Ellipſis genitricis eiuſdem Sphæroidis; </
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<
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">quare ſi
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primò intra has æquales portiones, dempta ea ſuper _MINIMA_ baſi, ducan-
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tur plana baſibus æquidiſtantia, quorum vnumquodque efficiat in portione
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ſectionem prædictæ _MINIMAE_ baſi æqualem (hoc autem ſieri poſſe, & </
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quomodò infra docebimus) per huiuſmodi plana abſcindentur portiones
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ſolidæ æqualium baſium, ſed harum quælibet minor erit quacunque æqua-
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lium portionum (cum ſit pars minor ſuo toto) ideoque minor ea, à qua ni-
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hil ablatum fuit, ſiue minor ea, cuius axis conuenit cum maiori axe dati ſo-
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lidi. </
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<
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">Si ergo omnes aliæ portiones æqualium baſium hac portione ſunt mi-
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nores, erit è contra hæc ipſa portio, cuius axis eſt ſegmentum maioris ſemi-
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axis ſectionis genitricis dati ſolidi earundem portionum æqualium baſium,
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ac de eodem ſolido _MAXIMA_, &</
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