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

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            <s xml:id="echoid-s7125" xml:space="preserve">
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            ſe æquidiſtant: </s>
            <s xml:id="echoid-s7126" xml:space="preserve">vel tandem ad integram circuli peripheriam à contactibus I,
              <lb/>
            L in figurarum reuolutione deſcriptam in quinta, & </s>
            <s xml:id="echoid-s7127" xml:space="preserve">ſexta vbi axes ſimul
              <lb/>
            congruunt.</s>
            <s xml:id="echoid-s7128" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7129" xml:space="preserve">Cum enim harum ſectionum axes, vel congruant ſimul, vel æquidiſtent,
              <lb/>
            quæ ad vnum ipſorum plana ducentur erecta, alteri quoque erecta erunt,
              <lb/>
            deſcribentque circulos in proprijs ſolidis, quorum centra in ipſ@s ax
              <gap/>
            s ca-
              <lb/>
            dent: </s>
            <s xml:id="echoid-s7130" xml:space="preserve">vnde cum axes ſimul congruent, vt in prima, quinta, & </s>
            <s xml:id="echoid-s7131" xml:space="preserve">ſexta, huiuſ-
              <lb/>
            modi circuli erunt concentrici; </s>
            <s xml:id="echoid-s7132" xml:space="preserve">at ſi æquidiſtent, vt in reliquis, circuli erunt
              <lb/>
            eccentrici, & </s>
            <s xml:id="echoid-s7133" xml:space="preserve">communes ſectiones horum planorum cum ipſis ſectionibus
              <lb/>
            A B C, D E F erunt eorundem circulorum diametri: </s>
            <s xml:id="echoid-s7134" xml:space="preserve">quare ducto quocun-
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            que plano A D F C ad axes erecto, non per contactus I, vel L tranſeunte,
              <lb/>
            efficiente verò in ſectione A B C diametrum A C, in ſectione autem D E F
              <lb/>
            diametrum D F: </s>
            <s xml:id="echoid-s7135" xml:space="preserve">patet in prima, ſecunda, quarta, quinta, & </s>
            <s xml:id="echoid-s7136" xml:space="preserve">ſexta figura,
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            in quibus ſectio D E F inſcripta eſt ſectioni A B C diametrum D F totam
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              <figure xlink:label="fig-0258-01" xlink:href="fig-0258-01a" number="214">
                <image file="0258-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0258-01"/>
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            cadere intra diametrum A C, ac ideo circulum ex D F inſolido D E F
              <lb/>
            diſiunctum eſſe à circulo ex A C in ſolido A B C, vel per armillam A D
              <lb/>
            C, vt in prima, ſecunda, & </s>
            <s xml:id="echoid-s7137" xml:space="preserve">ſexta, ob circulorum concentricitatem, vel
              <lb/>
            per armillam excentricam A D C, in ſecunda, & </s>
            <s xml:id="echoid-s7138" xml:space="preserve">quarta ob ipſorum cir-
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            culorum excentricitatem. </s>
            <s xml:id="echoid-s7139" xml:space="preserve">Rurſus in tertia figura in qua ſectio D E F to-
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            ta cadit extra A B C, prædicta diameter D F tota cadet extra diametrum
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            A C, ideoque circulus ex D F in ſolido D E F totus cadet extra circulum
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            ex A C in ſolido A B C, & </s>
            <s xml:id="echoid-s7140" xml:space="preserve">hoc ſemper: </s>
            <s xml:id="echoid-s7141" xml:space="preserve">quare in ſingulis figuris vbicun-
              <lb/>
            que ductum ſit planum A D F C, præter ad contactus, huiuſmodi ſolida
              <lb/>
            erunt in totum diſiuncta, ex quo nullibi ſe mutuò ſecabunt.</s>
            <s xml:id="echoid-s7142" xml:space="preserve"/>
          </p>
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            <s xml:id="echoid-s7143" xml:space="preserve">Præterea cum in prima figura ſectionum contactus ſit in ipſo axium verti-
              <lb/>
            ce, patet, & </s>
            <s xml:id="echoid-s7144" xml:space="preserve">ſolida circa communem axim ab ipſis ſectionibus genita in eo-
              <lb/>
            dem puncto ſe mutuò contingere. </s>
            <s xml:id="echoid-s7145" xml:space="preserve">In ſecunda verò tertia, & </s>
            <s xml:id="echoid-s7146" xml:space="preserve">quarta ducto
              <lb/>
            plano ad axes erecto per punctum contactus I, in ſolido A B C efficientæ
              <unsure/>
              <lb/>
            circulum, cuius diameter ſit I M, at in ſolido D E F circulum, cuius </s>
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