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

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          <pb o="118" file="0304" n="304" rhead=""/>
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        <div xml:id="echoid-div876" type="section" level="1" n="350">
          <head xml:id="echoid-head359" xml:space="preserve">COROLL.</head>
          <p>
            <s xml:id="echoid-s8444" xml:space="preserve">SI datum ſolidum fuerit quodcunque Sphæroides, vel Sphæra; </s>
            <s xml:id="echoid-s8445" xml:space="preserve">patet re-
              <lb/>
            liquam portionem ſolidam, dempta _MINIMA_ nuper inuenta, eſſe
              <lb/>
            _MAXIMAM_ quæſitam.</s>
            <s xml:id="echoid-s8446" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div877" type="section" level="1" n="351">
          <head xml:id="echoid-head360" xml:space="preserve">THEOR. LIII. PROP. LXXXIII.</head>
          <p>
            <s xml:id="echoid-s8447" xml:space="preserve">Æquales portiones ſolidæ eiſdem Conoidis, vel Sphæræ, aut
              <lb/>
            cuiuslibet Sphæroidis, ſi fuerint de eodem Conoide Parabolico
              <lb/>
              <note position="left" xlink:label="note-0304-01" xlink:href="note-0304-01a" xml:space="preserve">Conuer-
                <lb/>
              ſum Pro-
                <lb/>
              p. 79. h.</note>
            habebunt axes æquales. </s>
            <s xml:id="echoid-s8448" xml:space="preserve">Si de eodem Hyperbolico, vel de Sphæ-
              <lb/>
            ra, aut Sphæroide quocunque, erunt axes proprijs ſemi- diametris
              <lb/>
            proportionales. </s>
            <s xml:id="echoid-s8449" xml:space="preserve">At ſi fuerint de eodem Cono recto, extrema ip-
              <lb/>
            ſorum axium pertingent ad idem inſcriptum ſolidum ſimile, & </s>
            <s xml:id="echoid-s8450" xml:space="preserve">
              <lb/>
            concentricum.</s>
            <s xml:id="echoid-s8451" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8452" xml:space="preserve">SInt duæ de eodem quocunque prædictorum ſolidorum portiones æqua-
              <lb/>
            les, quarum recti Canones concipiantur transferri ſuper eadem ſectio-
              <lb/>
            ne A B F per ſolidi axem ducta (hoc enim fieri poſſe manifeſtum eſt, cum
              <lb/>
            ipſi recti Canones intra ſolidas portiones intercepti, ſint portiones eiuſdem
              <lb/>
            ſectionis, quæ in reuolutione circa axim ſolidum genuit) & </s>
            <s xml:id="echoid-s8453" xml:space="preserve">ſint A B C, D
              <lb/>
            E F, quarum baſes ſint A C, D F, & </s>
            <s xml:id="echoid-s8454" xml:space="preserve">diametri B G, E H, quæ ſimul ſunt
              <lb/>
              <figure xlink:label="fig-0304-01" xlink:href="fig-0304-01a" number="246">
                <image file="0304-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0304-01"/>
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            axes ſolidarum portionum. </s>
            <s xml:id="echoid-s8455" xml:space="preserve">Dico, in prima figura exhibente
              <note symbol="a" position="left" xlink:label="note-0304-02" xlink:href="note-0304-02a" xml:space="preserve">3. Schol.
                <lb/>
              69. h.</note>
            Parabolicum, axes B G, E H eſſe inter ſe æquales, & </s>
            <s xml:id="echoid-s8456" xml:space="preserve">in ſecunda exhibente
              <lb/>
            Hyperbolicum, atque in tertia Sphæram, vel Sphæroides, quarum centra
              <lb/>
            ſint O, eſſe axim H E ad ſemi-diametrum E O, vt axis G B ad ſemi-dia-
              <lb/>
            metrum B O.</s>
            <s xml:id="echoid-s8457" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8458" xml:space="preserve">Ex altero axium, videlicet ex E H, ſecetur in prima figura ſegmentum
              <lb/>
            E I ipſi B G æquale; </s>
            <s xml:id="echoid-s8459" xml:space="preserve">& </s>
            <s xml:id="echoid-s8460" xml:space="preserve">in reliquis, fiat O E ad E I, vt O B ad B G, </s>
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