Cavalieri, Buonaventura, Geometria indivisibilibvs continvorvm : noua quadam ratione promota

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            <s xml:id="echoid-s11926" xml:space="preserve">
              <pb o="467" file="0485" n="485" rhead="LIBER VI."/>
            ſubnectere non inutile mihi viſum fuit. </s>
            <s xml:id="echoid-s11927" xml:space="preserve">Hoc autem tántum circa prę-
              <lb/>
            fatas demonſtrationes dicam, quod licet in Prop. </s>
            <s xml:id="echoid-s11928" xml:space="preserve">_12._ </s>
            <s xml:id="echoid-s11929" xml:space="preserve">& </s>
            <s xml:id="echoid-s11930" xml:space="preserve">_14._ </s>
            <s xml:id="echoid-s11931" xml:space="preserve">indiuiſi-
              <lb/>
            bilibus, nempè omnibus qu adratis parallelogrammorum, quæ ibi de-
              <lb/>
            ſcribuntur, vſus fuerim, tamen etiam modo conſueto potuiſsent de-
              <lb/>
            monſtrari, ſi ex .</s>
            <s xml:id="echoid-s11932" xml:space="preserve">g. </s>
            <s xml:id="echoid-s11933" xml:space="preserve">vice omnium quadratorum parallelogrammi, ED, re-
              <lb/>
            gula, EB, ibi aſſumpta, Vſus fuiſsem parallelepipedo ſub altitudine,
              <lb/>
            DB, baſi autem quadrato, EB, vel pro omnibus quadratis trianguli,
              <lb/>
            CBE, regula eadem, EB, vſus eſſem pyramide ſub altitudine, CE, ba-
              <lb/>
            ſi eodem quadrato, EB, etenim ſimiliter demonſtratio abſolui potuiſ-
              <lb/>
            ſet, hac omnium quadratorum parallelogrammorum ibidem conſide-
              <lb/>
            ratorum dimiſſa congerie, & </s>
            <s xml:id="echoid-s11934" xml:space="preserve">ſubſtitutis parallelepipedis, vel pyrami-
              <lb/>
            dibus, aut earum fruſtis, vbi opus erat. </s>
            <s xml:id="echoid-s11935" xml:space="preserve">Hæc inuenire volui, vt præ-
              <lb/>
            dicta omnia ſtylo veteri demonſtrabilia eſſe, etiam aliter ab Archi-
              <lb/>
            mede patefiat.</s>
            <s xml:id="echoid-s11936" xml:space="preserve"/>
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        <div xml:id="echoid-div1084" type="section" level="1" n="650">
          <head xml:id="echoid-head680" xml:space="preserve">THEOREMA XXI. PROPOS. XXI.</head>
          <p>
            <s xml:id="echoid-s11937" xml:space="preserve">SI exponatur ſeries ſpiralium, & </s>
            <s xml:id="echoid-s11938" xml:space="preserve">circulorum deinceps à
              <lb/>
            primis, in ſpatijs verò ſub ſpiralibus, & </s>
            <s xml:id="echoid-s11939" xml:space="preserve">volutis, cylin-
              <lb/>
            drici, & </s>
            <s xml:id="echoid-s11940" xml:space="preserve">conici in eadem altitudiue ſtantes intelligantur
              <lb/>
            conſtituti tamquam in baſibus, ſimiliter & </s>
            <s xml:id="echoid-s11941" xml:space="preserve">in circulis con-
              <lb/>
            ſtituti eſſe cylindri, & </s>
            <s xml:id="echoid-s11942" xml:space="preserve">coni inte lligantur. </s>
            <s xml:id="echoid-s11943" xml:space="preserve">Cylindri inter
              <lb/>
            ſe, & </s>
            <s xml:id="echoid-s11944" xml:space="preserve">cylindrici pariter inter ſe, ſiue ad cylindros compa-
              <lb/>
            rati, ſiue coni inter ſe, & </s>
            <s xml:id="echoid-s11945" xml:space="preserve">conici inter ſe ſiue ad conos com-
              <lb/>
            parati eandem rationem, quam baſes habebunt.</s>
            <s xml:id="echoid-s11946" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11947" xml:space="preserve">Patet hæc propoſitio, nam cylindrici, & </s>
            <s xml:id="echoid-s11948" xml:space="preserve">conici in eadem alti-
              <lb/>
              <note position="right" xlink:label="note-0485-01" xlink:href="note-0485-01a" xml:space="preserve">B. G. H.
                <lb/>
              Coroll. 4.
                <lb/>
              gener. 34.
                <lb/>
              l. 2.</note>
            tudine conſtituti ſunt inter ſe, vt baſes; </s>
            <s xml:id="echoid-s11949" xml:space="preserve">ſunt autem prædicta ſoli-
              <lb/>
            da per conſtructionem in eadem altitudine poſita, ergo erunt in-
              <lb/>
            ter ſe, vt ipſæ baſes; </s>
            <s xml:id="echoid-s11950" xml:space="preserve">Vocentur autem Cylindri, & </s>
            <s xml:id="echoid-s11951" xml:space="preserve">Cylindrici, nec-
              <lb/>
            non Conici eiuſdem numeri cum ſpatijs, quibus inſiſtunt .</s>
            <s xml:id="echoid-s11952" xml:space="preserve">i. </s>
            <s xml:id="echoid-s11953" xml:space="preserve">pri-
              <lb/>
            mus cylindrus, vel conus, qui eſt in primo circulo, ſecundus cylin-
              <lb/>
            drus, vel conus, qui eſt in ſecundo circulo tamquam in baſi; </s>
            <s xml:id="echoid-s11954" xml:space="preserve">pri-
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            mus cylindricus, vel conicus, qui eſt in ſpatio helico primi circuli
              <lb/>
            tamquam in baſi, ſecundus cylindricus, vel conicus, qui eſt in ſpa-
              <lb/>
            tio ſecundi circuli, & </s>
            <s xml:id="echoid-s11955" xml:space="preserve">ſic deinceps.</s>
            <s xml:id="echoid-s11956" xml:space="preserve"/>
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