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

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        <div xml:id="echoid-div859" type="section" level="1" n="342">
          <head xml:id="echoid-head351" xml:space="preserve">COROLL. I.</head>
          <p>
            <s xml:id="echoid-s8272" xml:space="preserve">HInc colligitur, quod puncta media rectarum quarumlibet applicata-
              <lb/>
            rum in ſectione per axem ducta, cuiuſcunque prædictorum ſolidorũ,
              <lb/>
            ſunt centra baſium earum portionum ſolidarum à planis per eaſdem rectas
              <lb/>
            ductis, atque ad eandem ſectionem per axem erectis abſciſſarum.</s>
            <s xml:id="echoid-s8273" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8274" xml:space="preserve">Nam puncta media G, H, applicatarum E F, C D demonſtrata ſunt
              <lb/>
            eſſe centra prædictarum baſium E O F, C P D, &</s>
            <s xml:id="echoid-s8275" xml:space="preserve">c.</s>
            <s xml:id="echoid-s8276" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div860" type="section" level="1" n="343">
          <head xml:id="echoid-head352" xml:space="preserve">COROLL. II.</head>
          <p>
            <s xml:id="echoid-s8277" xml:space="preserve">PErſpicuum eſt quoque, baſes ſolidarum portionum inter ſe æqualium
              <lb/>
            eiuſdem Coni recti, vel Conoidis Parabolici, aut Hyperbolici, Sphe-
              <lb/>
            ræ, aut Sphæroidis oblongi, habere inter ſe axes minores æquales, ſiue eſſe
              <lb/>
            æqualium latitudinum, ac ideò eſſe inter ſe, vt axes maiores, vel vt baſes
              <lb/>
            rectorum Canonum. </s>
            <s xml:id="echoid-s8278" xml:space="preserve">Baſes verò æqualium portionum eiuſdem Sphæroidis
              <lb/>
            prolati habere maiores axes æquales, ac propterea eſſe inter ſe vt axes mi-
              <lb/>
            nores, vel vt baſes eorundem rectorum Canonum.</s>
            <s xml:id="echoid-s8279" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8280" xml:space="preserve">Etenim, in pręcedentibus figuris, de baſibus E O F, C P D (vel ſint Cir-
              <lb/>
            culi, vel Ellipſes) portionum ſolidarum E A F, C A D, quas æquales eſſe
              <lb/>
            demonſtrauimus, oſtenſum priùs fuit ſemi- axes minores G O, H P in Co-
              <lb/>
            no recto, vel Conoide, aut Sphæroide oblongo eſſe æquales, ac ideò, & </s>
            <s xml:id="echoid-s8281" xml:space="preserve">
              <lb/>
            eorum duplos, hoc eſt integros minores axes æquales eſſe; </s>
            <s xml:id="echoid-s8282" xml:space="preserve">& </s>
            <s xml:id="echoid-s8283" xml:space="preserve">paulò poſt
              <lb/>
            circulum, vel Ellipſim E O F ad C P D eſſe vt maior axis E F ad maiorem
              <lb/>
            C D, vel vt baſis recti Canonis E A F, ad baſim recti Canonis C A D. </s>
            <s xml:id="echoid-s8284" xml:space="preserve">In
              <lb/>
            Sphæroide autem prolato demonſtratum eſt ipſas G O, H P maiores ſemi-
              <lb/>
            axes, item æquales eſſe, ſiue integros maiores axes æquales, & </s>
            <s xml:id="echoid-s8285" xml:space="preserve">poſtea cir-
              <lb/>
            culos, vel Ellipſes E O F, C B D habere inter ſe eandem rationem, ac ipſi
              <lb/>
            minores axes E F, C D; </s>
            <s xml:id="echoid-s8286" xml:space="preserve">nimirum eſſe inter ſe, vt ſunt baſes rectorum
              <lb/>
            Canonum E A F, C A D.</s>
            <s xml:id="echoid-s8287" xml:space="preserve"/>
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        <div xml:id="echoid-div861" type="section" level="1" n="344">
          <head xml:id="echoid-head353" xml:space="preserve">THEOR. L. PROP. LXXIX.</head>
          <p>
            <s xml:id="echoid-s8288" xml:space="preserve">Solidæ portiones eiuſdem Coni recti, vel cuiuſcunque Conoi-
              <lb/>
            dis, vel Sphæræ, aut cuiuslibet Sphæroidis tunc æquales ſunt,
              <lb/>
            qnando, in Cono, portionum axes pertingant ad idem Conoides
              <lb/>
            Hyperbolicum concentricum, &</s>
            <s xml:id="echoid-s8289" xml:space="preserve">c. </s>
            <s xml:id="echoid-s8290" xml:space="preserve">In Conoide verò Parabolico,
              <lb/>
            quando portionum axes ſint æquales. </s>
            <s xml:id="echoid-s8291" xml:space="preserve">At in Conoide Hyperboli-
              <lb/>
            co, Sphæra, aut quocunque Sphæroide, quando portionum axes,
              <lb/>
            ad proprias ſemi- diametros ijſdem axibus in directum poſitas, ſint
              <lb/>
            in vna eademque ratione.</s>
            <s xml:id="echoid-s8292" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8293" xml:space="preserve">ETenim quandò in portionibus eiuſdem cuiuſcunque prædictorum ſoli-
              <lb/>
            dorum diametri rectorum Canonum habuerint relatiuè </s>
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