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

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          <p>
            <s xml:id="echoid-s7907" xml:space="preserve">Nam, ad finem propoſitionis oſtenſum fuit, planum contingens portio-
              <lb/>
            nem ſolidam E F G, & </s>
            <s xml:id="echoid-s7908" xml:space="preserve">baſi E H G I parallelum, eam contingere ad pun-
              <lb/>
            ctum F, quod eſt vertex diametri N F Canonis recti E F G, atque inſuper
              <lb/>
            idem punctum contactus F, iuxta Archim. </s>
            <s xml:id="echoid-s7909" xml:space="preserve">definitiones præmiſſas ad librum
              <lb/>
            de Conoid. </s>
            <s xml:id="echoid-s7910" xml:space="preserve">&</s>
            <s xml:id="echoid-s7911" xml:space="preserve">c. </s>
            <s xml:id="echoid-s7912" xml:space="preserve">iam notum eſt verticem vocari axis portionis ſolidæ E F G.</s>
            <s xml:id="echoid-s7913" xml:space="preserve"/>
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        <div xml:id="echoid-div820" type="section" level="1" n="324">
          <head xml:id="echoid-head333" xml:space="preserve">SCHOLIVM III.</head>
          <p>
            <s xml:id="echoid-s7914" xml:space="preserve">EX his itaque notandum eſt, axim ſolidæ portionis eundem eſſe cum dia-
              <lb/>
            metro prædicti Canonis recti, & </s>
            <s xml:id="echoid-s7915" xml:space="preserve">altitudinem, eandem cum altitudine.</s>
            <s xml:id="echoid-s7916" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s7917" xml:space="preserve">Nam eadem recta F N
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                <image file="0283-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0283-01"/>
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            quæ ex conſtructione diame-
              <lb/>
            ter eſt planæ portionis E F
              <lb/>
            G, eſt quoque axis ſolidæ,
              <lb/>
            cum ab F eius vertice, ad N
              <lb/>
            centrum baſis E H G I ince-
              <lb/>
            dat. </s>
            <s xml:id="echoid-s7918" xml:space="preserve">Præterea ducta ex ha-
              <lb/>
            rum portionum cómuni ver-
              <lb/>
            tice F recta F P ad baſim E
              <lb/>
            G planæ portionis, ſeu recti
              <lb/>
            Canonis E F G perpendicu-
              <lb/>
            lari. </s>
            <s xml:id="echoid-s7919" xml:space="preserve">Patet hanc eſſe Canonis
              <lb/>
            altitudinem, ſed Canon E F
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            G rectus ponitur ad baſim E H G I; </s>
            <s xml:id="echoid-s7920" xml:space="preserve">quare F P, quæ ad communem horum
              <lb/>
            planorum ſectionem E G eſt perpendicularis, recta erit ad planum baſis
              <lb/>
            E H G I, ac propterea ipſa erit quoque altitudo portionis ſolidæ E F G,
              <lb/>
            cum perpendiculariter cadat ex eius vertice F ſuper baſim E H G I, &</s>
            <s xml:id="echoid-s7921" xml:space="preserve">c.</s>
            <s xml:id="echoid-s7922" xml:space="preserve"/>
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        <div xml:id="echoid-div822" type="section" level="1" n="325">
          <head xml:id="echoid-head334" xml:space="preserve">COROLL. III.</head>
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            <s xml:id="echoid-s7923" xml:space="preserve">PAtet denique axim portionis cuiuſcunque prædictorum ſolidorum, & </s>
            <s xml:id="echoid-s7924" xml:space="preserve">
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            axim ſolidi, cuius eſt portio, eſſe in vno eodemque plano, quod per
              <lb/>
            axem eiuſdem ſolidi ad baſim portionis rectum ducitur, ſiue eſſe in plano
              <lb/>
            Canonis recti.</s>
            <s xml:id="echoid-s7925" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s7926" xml:space="preserve">Etenim, & </s>
            <s xml:id="echoid-s7927" xml:space="preserve">B D axis dati ſolidi, & </s>
            <s xml:id="echoid-s7928" xml:space="preserve">F N axis ſolidæ portionis E F G ſunt
              <lb/>
            in plano E B C ducto per axem B D, ſed erecto ſuper baſim E I G H por-
              <lb/>
            tionis ſolidę E F G, quod planum E B C idem eſt, ac planum recti Canonis
              <lb/>
            E F G intra ſolidam portionem intercepti.</s>
            <s xml:id="echoid-s7929" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s7930" xml:space="preserve">Siergo per axim datæ ſolidæ portionis, & </s>
            <s xml:id="echoid-s7931" xml:space="preserve">per axim ſolidi, cuius eſt por-
              <lb/>
            tio ducatur planum, hoc erit ad planum baſis portionis erectum, atque in
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            ſolida portione rectum Canonem exhibebit.</s>
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