Viviani, Vincenzo, De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei

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          <p>
            <s xml:id="echoid-s8317" xml:space="preserve">
              <pb o="113" file="0299" n="299" rhead=""/>
            nones E A F, C A D (qui, ex conſtructione, ſunt ad plana baſium recti)
              <lb/>
            ſunt æquales, ergo & </s>
            <s xml:id="echoid-s8318" xml:space="preserve">ipſæ ſolidæ portiones æquales erunt. </s>
            <s xml:id="echoid-s8319" xml:space="preserve">Vnde
              <note symbol="a" position="right" xlink:label="note-0299-01" xlink:href="note-0299-01a" xml:space="preserve">45. h.</note>
              <note symbol="b" position="right" xlink:label="note-0299-02" xlink:href="note-0299-02a" xml:space="preserve">78. h.</note>
            nes ſolidæ portiones eiuſdem Coni recti, vel cuiuslibet prædictorum ſolido-
              <lb/>
            rum, quarum baſes contingant eiuſdem ſimilis, & </s>
            <s xml:id="echoid-s8320" xml:space="preserve">concentrici ſolidi ſuper-
              <lb/>
            ficiem inter ſe ſunt æquales, & </s>
            <s xml:id="echoid-s8321" xml:space="preserve">ad centra baſium eandem ſuperficiem con-
              <lb/>
            tingunt. </s>
            <s xml:id="echoid-s8322" xml:space="preserve">Quod oſtendere propoſitum fuerat; </s>
            <s xml:id="echoid-s8323" xml:space="preserve">quodque Cl. </s>
            <s xml:id="echoid-s8324" xml:space="preserve">Tor. </s>
            <s xml:id="echoid-s8325" xml:space="preserve">inter pro-
              <lb/>
            prios pugillares geometricos regerere non eſt dedignatus: </s>
            <s xml:id="echoid-s8326" xml:space="preserve">animo, vt opina-
              <lb/>
            ri libet, huiuſce haud iniucundi Theorematis, a me ipſi tantummodo expo-
              <lb/>
            ſiti demonſtrationem inquirendi, quam poſtea ſolùm de Coni portionibus
              <lb/>
            nactus fuit, vel potiùs circa ipſas tantùm placuit ei meditari: </s>
            <s xml:id="echoid-s8327" xml:space="preserve">eminentiſſimi
              <lb/>
            enim, ac propè diuini ingenij Vir, & </s>
            <s xml:id="echoid-s8328" xml:space="preserve">de aliorum ſolidorum portionibus fe-
              <lb/>
            liciùs quàm à nobis ſuperiùs factum ſit, hoc idem reperiſſet, ſi tantillùm ex-
              <lb/>
            cogitaſſet: </s>
            <s xml:id="echoid-s8329" xml:space="preserve">verùm proprias, ac ideò ſublimiores contem plationes affectans,
              <lb/>
            ab his nugis meis fortaſſe ſe abſtinuit.</s>
            <s xml:id="echoid-s8330" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div865" type="section" level="1" n="346">
          <head xml:id="echoid-head355" xml:space="preserve">SCHOLIVM.</head>
          <p>
            <s xml:id="echoid-s8331" xml:space="preserve">Hlc autem animaduertendum eſt, quod nihil refert vtrùm baſes, huiuſ-
              <lb/>
            modi portionum ſolidarum inſcriptum ſolidum concentricum con-
              <lb/>
            tingant ad puncta eiuſdem ſectionis ſolidum genitricis, vel diuerſarum: </s>
            <s xml:id="echoid-s8332" xml:space="preserve">nam
              <lb/>
            omnes genitrices ſectiones eiuſdem ſolidi concentrici, ſe mutuò ſecant in
              <lb/>
            eodem vertice axis reuolutionis prædicti ſolidi; </s>
            <s xml:id="echoid-s8333" xml:space="preserve">ſed omnes portiones ſolidæ
              <lb/>
            exterioris, quæ quamlibet ſolidi interioris genitricem ſectionem per centra
              <lb/>
            earum baſium contingunt, æquales oſtendi poſſunt per ſuperiorem prop. </s>
            <s xml:id="echoid-s8334" xml:space="preserve">78.
              <lb/>
            </s>
            <s xml:id="echoid-s8335" xml:space="preserve">eidem tertiæ portioni ſolidæ ab ipſo exteriori ſolido abſciſſæ, ei nempe,
              <lb/>
            cuius baſis tranſiens per axis verticem ad eundem axim ſit recta, circulum
              <lb/>
            in ſectione efficiens; </s>
            <s xml:id="echoid-s8336" xml:space="preserve">ergo omnes prædictæ portiones ſolidæ, vbicunque ea-
              <lb/>
            rum baſes contingant ſuperficiem ſimilis, & </s>
            <s xml:id="echoid-s8337" xml:space="preserve">concentrici inſcripti ſolidi, in-
              <lb/>
            ter ſe æquales erunt, cum tertiæ cuidam portioni ſint æquales, &</s>
            <s xml:id="echoid-s8338" xml:space="preserve">c.</s>
            <s xml:id="echoid-s8339" xml:space="preserve"/>
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        <div xml:id="echoid-div866" type="section" level="1" n="347">
          <head xml:id="echoid-head356" xml:space="preserve">THEOR. LII. PROP. LXXXI.</head>
          <p>
            <s xml:id="echoid-s8340" xml:space="preserve">Si planum ductum per axem Coni recti, vel Conoidis Parabo-
              <lb/>
            lici, aut Hyperbolici, Sphæræ, aut Sphæroidis oblongi, vel pro-
              <lb/>
            lati à quadam recta linea ſecetur, per quam ductum ſit planum,
              <lb/>
            quod ad planum per axem rectum ſit: </s>
            <s xml:id="echoid-s8341" xml:space="preserve">ſolidi portio, quæ per hoc
              <lb/>
            planum abſcinditur, MINIMA eſt omnium portionum à quibuſ-
              <lb/>
            libet alijs planis per eandem rectam ductis abſciſſarum.</s>
            <s xml:id="echoid-s8342" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8343" xml:space="preserve">ESto quodlibet prædictorum ſolidorum A B C, cuius axis reuolutionis
              <lb/>
            ſit B D, & </s>
            <s xml:id="echoid-s8344" xml:space="preserve">planum per axem ductum ſit A B C vbicunque ſectum à
              <lb/>
            quadam recta A F, ad vtranque partem ſectioni occurrente, per quam con-
              <lb/>
            cipiatur duci planum A E F ad ipſum A B C rectum, portionem ex </s>
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