Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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">Si Conus rectus plano per axem ſecetur, per in quo verticem du-
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cta ſit quędam linea, quę non in directum ſit poſita cum aliquo late-
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rum trianguli per axem perque ipſam agatur planum, quod rectum
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ſit ad idem planum, per axem ductum: </
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<
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tantùm vertice coni ſuperficiem continget, quæ tota cadet ad alte-
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ram partem ducti plani.</
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<
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">SIt conus rectus A B C plano per axem B D ſectus efficiente triangulum
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A B C, in cuius plano, & </
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">per verticem B ſit quælibet linea E B F, non
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tamen cum aliquo laterum B A, B C ſit in directũ poſita, per quam tranſeat
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planum G H I K, quod ad planum per axem A B C ſit rectum. </
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<
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planum G I in nullo alio puncto, quàm in vertice B conicam ſuperficiem
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contingere, &</
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<
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ipſi A C baſi trianguli per axem, an-
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guli interiores E B D, A D B duobus
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rectis æquales erunt, ſed A D B re-
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ctus eſt, cum ſit axis B D plano baſis
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A C perpendicularis, quare, & </
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gulus E B D rectus erit, ſed planum
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A B C ponitur rectum ad planum G
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I, & </
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<
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">in eo ad communem horum ſe-
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ctionem E B F ducta eſt perpendi-
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cularis D B, ergo ipſa D B erit
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vndec. E-
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lem.</
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cta ad planum G I, eſtque eadem B
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D recta ad planum baſis A C, quare
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duo plana G I, A C inter ſe æquidiſtant, atque eſt punctum B in vno
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Elem.</
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no G I, & </
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">circuli peripheria A C in altero A C, ergo recta B A, quæ ma-
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nente puncto B circa peripheriam C A circumducitur conicam ſuperficiem
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deſcribens, hoc eſt ipſa conica ſuperficies tota cadet inter plana ęquidiſtan-
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tia (vbicunque enim ducatur planum per axem, habentur communes æqui-
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diſtantium planorum fectiones inter ſe parallelę, inter quas cadit communis
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ſectio ſecantis plani cum ſuperficie) ac ideò planum G I in ipſo tantùm ver-
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tice B, coni ſuperficiem continget.</
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<
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<
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B E D circa axim B D conuerti concipitur, rectam B E coni B E L ſuperfi-
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ciem deſcribere, cuius triangulum per axem eſt B E L idem cum plano A B
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C, cui rectum eſt planum G I ductum per latus B E, quare idem planum G
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I continget conicam B E L in ipſo tantùm latere B E, ſed latus B E
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tingit conicam B C in vnico tantùm vertice B, ergo planum G I conicam
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A B C in ipſo tantùm vertice B contingit, ac propterea ipſa coni ſuperficies
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cadit tota infra planum G I. </
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