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

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        <div xml:id="echoid-div814" type="section" level="1" n="320">
          <head xml:id="echoid-head329" xml:space="preserve">SCHOLIVM I.</head>
          <p>
            <s xml:id="echoid-s7883" xml:space="preserve">CVm huiuſmodi ſolida portio E F G de quolibet prędictorum ſolidorum
              <lb/>
            abſciſſa, ſit ſolidum ad alteram partem F deficiens, circa Acuminatũ
              <lb/>
            planum E F G deſcriptum, cumque omnia plana eius baſi E H G I æquidi-
              <lb/>
            ſtantia, ſint plana Acuminata, vt in prima proximè præcedentium definitio-
              <lb/>
              <note symbol="a" position="left" xlink:label="note-0282-01" xlink:href="note-0282-01a" xml:space="preserve">Coroll.
                <lb/>
              15. Arch.
                <lb/>
              de Conoi.
                <lb/>
              &c.</note>
            num monuimus, ſintque omnia inter ſe ſimilia, ac ſimiliter poſita, eò quod vel ſint circuli, vel Ellipſes, quarum homologi axes ſunt eædem applicatæ in Acuminato E F G, idcircò per ſecundam prædictarum definit. </s>
            <s xml:id="echoid-s7884" xml:space="preserve">talis ſoli-
              <lb/>
              <note symbol="b" position="left" xlink:label="note-0282-02" xlink:href="note-0282-02a" xml:space="preserve">13. 14.
                <lb/>
              15. ibid.</note>
            da portio in poſterum vocari poterit aliquandò ſolidum Acuminatum; </s>
            <s xml:id="echoid-s7885" xml:space="preserve">& </s>
            <s xml:id="echoid-s7886" xml:space="preserve">
              <lb/>
            planum Acuminatum, ſeu portio plana E F G, cum ſit recta ad baſim E H
              <lb/>
            G I, dicetur Canon rectus ſolidæ portionis.</s>
            <s xml:id="echoid-s7887" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div816" type="section" level="1" n="321">
          <head xml:id="echoid-head330" xml:space="preserve">COROLL. I.</head>
          <p>
            <s xml:id="echoid-s7888" xml:space="preserve">EX hac elicitur, qua methodo per axem cuiuslibet Conoidis, aut Sphæ-
              <lb/>
            roidis, vel Sphæræ, aut etiam Coni recti duci poſſit planum, quod ad
              <lb/>
            datum quodcunque planum non per axem ductum, & </s>
            <s xml:id="echoid-s7889" xml:space="preserve">ſolidum ſecans, re-
              <lb/>
            ctum ſit, etiam ſi ſecans planum in Conoide Parabolico, aut Hyperbolico,
              <lb/>
            vel Cono non ſit circulus, neque Ellipſis: </s>
            <s xml:id="echoid-s7890" xml:space="preserve">ſimulque patet, quod prædictum
              <lb/>
            planum per axem, aliud non per axem ductum omnino ſecat intra ſolidum:
              <lb/>
            </s>
            <s xml:id="echoid-s7891" xml:space="preserve">quæ omnia, velleuiter perpendenti manifeſta ſunt ex dictis, quæque ab ip-
              <lb/>
            ſo Archimede tanquam poſſibilia, & </s>
            <s xml:id="echoid-s7892" xml:space="preserve">iam nota paſſim ſupponuntur in libro
              <lb/>
            de Conoid. </s>
            <s xml:id="echoid-s7893" xml:space="preserve">&</s>
            <s xml:id="echoid-s7894" xml:space="preserve">c.</s>
            <s xml:id="echoid-s7895" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div817" type="section" level="1" n="322">
          <head xml:id="echoid-head331" xml:space="preserve">SCHOLIVM II.</head>
          <p>
            <s xml:id="echoid-s7896" xml:space="preserve">POterat quidem prima pars huius Problematis breuiùs perſolui. </s>
            <s xml:id="echoid-s7897" xml:space="preserve">Nam
              <lb/>
            ex vertice B, vel ex quolibet alio axis puncto, ſuper planum ſe-
              <lb/>
            cans E H G I ducta perpẽdiculari, per quàm, & </s>
            <s xml:id="echoid-s7898" xml:space="preserve">per axem B D ducto plano;
              <lb/>
            </s>
            <s xml:id="echoid-s7899" xml:space="preserve">conſtat hoc idem ſuper planum ſecans rectum eſſe. </s>
            <s xml:id="echoid-s7900" xml:space="preserve">Verùm cum ſæpe
              <note symbol="c" position="left" xlink:label="note-0282-03" xlink:href="note-0282-03a" xml:space="preserve">18. vnd.
                <lb/>
              Elem.</note>
            niat, quod ipſa perpendicularis occurrat ſecanti plano non intra ſolidum,
              <lb/>
            ſed vel in eius ſuperficie, vel extra, cumq; </s>
            <s xml:id="echoid-s7901" xml:space="preserve">omnino oſtendere opus ſit, quod
              <lb/>
            huiuſmodi planum per axem, rectum ad planum ſecans, hoc idem planum
              <lb/>
            ſecat ſemper intra ſolidum, idcircò prò huius Problematis ſolutione ſupe-
              <lb/>
            riorem viam elegimus, quæ ad vtrunq; </s>
            <s xml:id="echoid-s7902" xml:space="preserve">ſimul nos perduceret vnica conſtru-
              <lb/>
            ctione.</s>
            <s xml:id="echoid-s7903" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div819" type="section" level="1" n="323">
          <head xml:id="echoid-head332" xml:space="preserve">COROLL. II.</head>
          <p>
            <s xml:id="echoid-s7904" xml:space="preserve">COlligitur quoque planum, quod baſi portionis cuiuslibet prædicto-
              <lb/>
            rum ſolidorum æquidiſtat, atque eius conuexam ſuperficiem con-
              <lb/>
            tingit, eam contingere ad verticem diametri recti Canonis; </s>
            <s xml:id="echoid-s7905" xml:space="preserve">hoc eſt tan-
              <lb/>
            gere ad verticem axis portionis ſolidæ.</s>
            <s xml:id="echoid-s7906" xml:space="preserve"/>
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