Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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<
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xml:space
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">Æquales portiones de eodem ſolido, quodcunque ſit ex ſæ-
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Prop. 78.
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huius.</
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pius memoratis, habent Canones rectos, in ipſis interceptos,
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inter ſe æquales.</
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<
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<
s
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xml:space
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">ETenim huiuſmodi portiones ſolidæ æquales, habent axes, vel
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ſe æquales, vel proprijs ſemi-diametris proportionales, vel ad idem
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Conoides ſimile concentricum, & </
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axes ſunt quoque diametri prædictorum Canonum, & </
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<
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prop. 69.
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huius.</
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metri habuerint conditiones huiuſmodi, ipſi Canones recti ſunt æqua- les, ergo ſolidæ portiones æquales, habebunt rectos Canones inter ſe
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ex 45. h.</
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æquales. </
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<
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xml:space
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">THEOR. LV. PROP. LXXXV.</
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">Baſes æqualium portionum ex eodem quocunque prædicto-
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rum ſolidorum, ſuperſiciem eiuſdem ſimilis inſcripti ſolidi con-
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Prop. 80.
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huius.</
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centrici ad earum centra contingunt.</
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<
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">POrtiones enim æquales eiuſdem ſolidi habent rectos Canones in ipſis
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interceptos inter ſe æquales, ſed quando huiuſmodi Canones ſunt æquales (ſi concipiantur translati ſuper eandem ſectionem ſolidi geni-
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tricem) ipſorum baſes ad puncta media, eandem concentricam, inſcri-
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ptam, & </
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<
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tranſeunt per has baſes rectorum Canonum, atque ad eos ſunt erectæ, nem-
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pe ad planum per axem dati ſolidi, quare eędem baſes ſolidarum portionum
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contingent ſuperſiciem interioris ſolidi concentrici ab inſcripta concentri-
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ca ſectioni geniti (dum hæc circa axim conuertatur) ad eadem puncta,
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quibus baſes planarum, ſectionem interiorem contingunt, quę puncta ſunt
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centra axium, vel baſium ſolidarum portionum ex Archimede, & </
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nobis animaduerſis.</
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<
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">Solidæ portiones eiuſdem Coni recti, vel Conoidis, ſiue Sphæ-
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ræ, aut Sphæroidis, quarum axes (pro Cono recto) pertingant ad
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idem inſcriptum concentricum Conoides Hyperbolicum (vel pro
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Conoide Parabolico) ſint æquales (ſiue pro reliquis) ad proprias
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ſemi - diametros eandem habeant rationem, habent baſes altitu-
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dinibus reciprocè proportionales.</
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<
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">ETenim cum axibus huiuſmodi ſolidarum portionum inſint prædictæ
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conditiones, ipſæ portiones ſolidæ æquales erunt, pariterque
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huius.</
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