Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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LIBER I.
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<
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xml:space
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">Tres autem proximæ Propoſitiones etiam in meo Speculo Vſtorio de-
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ſcriptæ fuerunt, cum & </
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<
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">ibi ijſdem indigerem, has verò hic repetere
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volui, vt qui meum illud Speculum non viderunt, etiam ijſdem potiri
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poſſint: </
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<
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<
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Commentatoribus ſumemus, vt iam oſtenſa, ne has demonſtrationes, quæ
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apud præfatos Auctores videri poſſunt, fruſtra repetamus.</
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">SI ſphęra, vel ſphęroides, conoides parabolicum, vel hy-
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perbolicum planis ſecentur ad axem rectis, communes
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ſectiones erunt circuli diametros in eadem figura ducta per
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axem (quæ eſt illa, quę per reuolutionem creat dictum ſoli-
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dum) ſitas habentes.</
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<
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">Patet hæc Propoſitio, nam ſupradicta ſunt ſolida rotunda, na-
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34. huius.</
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ſcuntur .</
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<
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<
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">SI conoides parabolicum plano ſecetur non quidem per a-
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xem, neque æquidiſtanter axi, neque ad rectos angulos
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cum axe, communis ſectio erit ellipſis, diameter verò ipſius
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maior erit linea concepta in conoide ab interſectione facta
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planorum, eius ſcilicet, quod ſecat figuram, & </
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<
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">eius, quod
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ducitur recto per axem ad planum ſecans, minor verò diame-
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ter æqualis erit diſtantiæ linearum ductarum æquidiſtanter
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axi ab extremis diametri maioris.</
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<
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">de Conoidibus, & </
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bus p. </
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<
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<
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">SI conoides hyperbolicum plano ſecetur coincidente in
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omnia conilatera conoides compræhendentis non recto
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ad axem; </
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<
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xml:space
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concepta in conoide à ſectione facta planorum, alterius </
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