Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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ſunt æquales, quando verò recti Canones, ſiue portiones de eodem
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lo, vel de eadem coni-ſectione, quæ ſolidum procreat æquales ſunt, inter
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ipſarum altitudines _MAXIM A_ eſt ea illius portionis, cuius diameter
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poſt 51. h.
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ad nu. 3.</
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ſegmentum maioris axis, & </
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noris; </
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portionum eædem ſunt, ac altitudines, & </
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69. h.</
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portiones eiuſdem Coni recti, vel Conoidis, aut Sphæroidis ſunt æquales,
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inter earum altitudines _MAXIM A_ erit ea illius portionis, cuius axis ſit ſe-
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gmentum maioris axis genitricis ſolidi, cuius eſt portio, & </
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">_MINIM A_ eius,
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cuius axis ſit ſegmentum minoris. </
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">Itaque ſi primò altitudines omnium ha-
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rum æqualium portionum, (dempta ea circa _MAXIM AM_ altitudinem)
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producantur, & </
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">huic _MINIM AE_ altitudini æquales fiant, atque ex interſe-
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ctionum punctis ducantur plana portionum baſibus æquidiſtantia, abſcin-
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dentur ab ipſis portiones ſolidæ æqualium altitudinum, & </
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ior erit quacunque æqualium portionum (nam totum ſua parte maius eſt)
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vnde, & </
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">maior ea portione, cuius altitudini, vel cui portioni nihil additum
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fuit, quæ ea eſt, cuius axis conuenit cum maiori axe genitricis ſectionis dati
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ſolidi. </
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">Si ergo omnes aliæ portiones æqualium altitudinum hane portio-
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nem excedunt, erit è contra hæc ipſa portio, cuius axis congruit cum maio-
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ri axe genitricis ſectionis dati ſolidi aliarum portionum æqualium altitudi-
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num _MINIM A_.</
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<
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">PRo Sphæroide autem, ſi altitudines omnium prædictarum æqualium
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portionum (dempta ea circa _MINIM AM_ altitudinem, quæ iam ea eſt
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circa minorem axem Ellipſis Sphæroidis genitricis) ę quales ſecentur eidem
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_MINIM AE_ altitudini, atque per puncta ſectionum, plana ſolidarum por-
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tionum baſibus æquidiſtantia ducantur, hæc à portionibus auferent portio-
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nes ſolidas æqualium altitudinum, ſed vnaquæque ipſarum minor erit
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quacunque æqualium portionum (eò quod pars ſuo toto ſit minor) quapro-
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pter & </
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">minor ea portione a cuius altitudine, vel à qua portione nihil dem-
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ptum fuit, quæ quidem eſt ea, cuius axis congruit cum minori axe Ellipſis
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datum Sphæroides procreantis: </
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dinum hac portione ſunt minores, erit ex aduerſo hæc eadem portio, cuius
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axis conuenit cum minori axe genitricis Ellipſis dati Sphæroidis earundem
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omnium portionum, æqualium altitudinum, _MAXIMA_. </
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pererat demonſtrandum.</
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animaduertenda. </
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">I Nter axes æqualium portionum eiuſdem Coni recti, vel Conoidis Hy-
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perbolici, aut cuiuſcunque Sphæroidis, _MINIMV S_ eſt is eius portionis,
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cuius axis congruat cum axe, & </
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ſectionis dati ſolidi, & </
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congruat cum maiori axe eiuſdem genitricis ſectionis.</
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