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

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        <div xml:id="echoid-div895" type="section" level="1" n="356">
          <p>
            <s xml:id="echoid-s8576" xml:space="preserve">
              <pb o="123" file="0309" n="309" rhead=""/>
            inter ſe ſolida Acuminata proportionalia, & </s>
            <s xml:id="echoid-s8577" xml:space="preserve">baſes altitudinibus
              <note symbol="a" position="right" xlink:label="note-0309-01" xlink:href="note-0309-01a" xml:space="preserve">70. h.</note>
            cantur, vnde Coni portiones inſcriptæ inter ſe æquales erunt; </s>
            <s xml:id="echoid-s8578" xml:space="preserve">erit
              <note symbol="b" position="right" xlink:label="note-0309-02" xlink:href="note-0309-02a" xml:space="preserve">74. h.</note>
            ſolida portio ad portionem æqualem de eodem ſolido, vt inſcripta Coni
              <lb/>
            portio ad inſcriptam Coni portionem (ob æqualitatem) & </s>
            <s xml:id="echoid-s8579" xml:space="preserve">permutando
              <lb/>
            ſolida portio ad ſibi inſcriptam Coni portionem, vt altera æqualis portio ad
              <lb/>
            ſibi inſcriptam Coni portionem, & </s>
            <s xml:id="echoid-s8580" xml:space="preserve">ſumptis conſequentium triplis,
              <note symbol="c" position="right" xlink:label="note-0309-03" xlink:href="note-0309-03a" xml:space="preserve">ex Com
                <lb/>
              mand. in
                <lb/>
              lib. de Co
                <lb/>
              noid. &
                <lb/>
              Sphęroid.
                <lb/>
              Archim.</note>
            portio ad circumſcriptum Cylindricum, vt reliqua portio ad ſibi circum-
              <lb/>
            ſcriptum Cylindricum, &</s>
            <s xml:id="echoid-s8581" xml:space="preserve">c. </s>
            <s xml:id="echoid-s8582" xml:space="preserve">Quod erat, &</s>
            <s xml:id="echoid-s8583" xml:space="preserve">c.</s>
            <s xml:id="echoid-s8584" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div897" type="section" level="1" n="357">
          <head xml:id="echoid-head366" xml:space="preserve">THEOR. LIX. PROP. LXXXIX.</head>
          <p>
            <s xml:id="echoid-s8585" xml:space="preserve">MAXIMA portionum eiuſdem Coni recti, aut Conoidis Hy-
              <lb/>
            perbolici, ſiue Sphæroidis oblongi, vel prolati, & </s>
            <s xml:id="echoid-s8586" xml:space="preserve">quarum axes
              <lb/>
            ſint æquales, ea eſt, cuius axis congruat cum axe ſectionis, quæ
              <lb/>
            ſolidum genuit; </s>
            <s xml:id="echoid-s8587" xml:space="preserve">& </s>
            <s xml:id="echoid-s8588" xml:space="preserve">reſpectiue ad Sphæroides, cum minori axe El-
              <lb/>
            lipſis genitricis.</s>
            <s xml:id="echoid-s8589" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8590" xml:space="preserve">MINIMA verò, cuius axis congruat cum maiori axe eiuſdem
              <lb/>
            Ellipſis.</s>
            <s xml:id="echoid-s8591" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8592" xml:space="preserve">ETenim quando portiones eiuſdem Conirecti, aut Conoidis Hyperboli-
              <lb/>
            ci, ſiue Sphæroidis cuiuslibet ſunt æquales, & </s>
            <s xml:id="echoid-s8593" xml:space="preserve">eorum recti Canones
              <lb/>
            ſunt æquales, & </s>
            <s xml:id="echoid-s8594" xml:space="preserve">quando recti Canones ſiue portiones de eodem
              <note symbol="d" position="right" xlink:label="note-0309-04" xlink:href="note-0309-04a" xml:space="preserve">84. h.</note>
            vel Hyperbola, aut Ellipſi æquales ſunt, inter ipſorum diametros _MINIMA_
              <lb/>
            eſt ea, quæ ſimul ſit axis anguli, vel Hyperbolæ, & </s>
            <s xml:id="echoid-s8595" xml:space="preserve">in Ellipſi, quæ ſit
              <note symbol="e" position="right" xlink:label="note-0309-05" xlink:href="note-0309-05a" xml:space="preserve">Schol.
                <lb/>
              poſt 5 1. h.
                <lb/>
              ad nu. 1.</note>
            minor, & </s>
            <s xml:id="echoid-s8596" xml:space="preserve">_MAXIMA_, quæ ſit axis maior, ergo, & </s>
            <s xml:id="echoid-s8597" xml:space="preserve">dum portiones eiuſdem
              <lb/>
            Coni recti, aut Conoidis Hyperbolici, vel Sphæroidis fuerint æquales, in-
              <lb/>
            ter ipſorum axes (qui ijſdem ſunt, ac diametri rectorum Canonum)
              <note symbol="f" position="right" xlink:label="note-0309-06" xlink:href="note-0309-06a" xml:space="preserve">3. Schol.
                <lb/>
              69. h.</note>
            _NIMVS_ erit is, qui congruet cum axe Coni, vel Conoidis Hyperbolici,
              <lb/>
            aut cum minori axe Ellipſis Sphæroidis, & </s>
            <s xml:id="echoid-s8598" xml:space="preserve">_MAXIMVS_, qui congruat cum
              <lb/>
            maiori: </s>
            <s xml:id="echoid-s8599" xml:space="preserve">quare ſi primùm axes harum omnium equalium portionum, dempta
              <lb/>
            ea circa _MINIMV M_ axem, huic _MINIMO_ axi æquales ſecentur, atque ex
              <lb/>
            interſectionibus ducantur plana baſibus portionum æquidiſtantia, auferen-
              <lb/>
            tur ab ipſis portiones ſolidæ æqualium axium, ſed vnaquæque erit minor
              <lb/>
            quacunque æqualium portionum, (cum ſit pars ſuo toto minor) ac propte-
              <lb/>
            rea minor ea, è cuius, axe, ſiue à qua portione nihil ablatũ ſuit, quę quidem
              <lb/>
            ea eſt, cuius axis congruit cum axe Coni recti, vel Conoidis Hyperbolici,
              <lb/>
            & </s>
            <s xml:id="echoid-s8600" xml:space="preserve">in Sphæroide cum minori axe Ellipſis genìtricis. </s>
            <s xml:id="echoid-s8601" xml:space="preserve">Si ergo omnes aliæ por-
              <lb/>
            tiones æqualium axium ſunt hac portione minores, erit è contra hæc ipſa
              <lb/>
            portio, cuius axis congruit cum axe dati Coni, vel Conoidis Hyperbolici,
              <lb/>
            & </s>
            <s xml:id="echoid-s8602" xml:space="preserve">pro Sphæroide, cum minori axe genitricis Ellipſis, earundem omnium
              <lb/>
            portionum, æqualium axium, _MAXIMA_. </s>
            <s xml:id="echoid-s8603" xml:space="preserve">Quod primò erat, &</s>
            <s xml:id="echoid-s8604" xml:space="preserve">c.</s>
            <s xml:id="echoid-s8605" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8606" xml:space="preserve">PRæterea ſi axes omnium æqualium portionum eiuſdem Sphæroidis pro-
              <lb/>
            ducantur, ac prædicto _MAXIMO_ axi (qui iam, vt ſuperiùs </s>
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