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

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        <div xml:id="echoid-div638" type="section" level="1" n="371">
          <pb o="267" file="0287" n="287" rhead="LIBER III."/>
        </div>
        <div xml:id="echoid-div639" type="section" level="1" n="372">
          <head xml:id="echoid-head389" xml:space="preserve">SECTIO III.</head>
          <p>
            <s xml:id="echoid-s6631" xml:space="preserve">ITem colligimus ſolida ſimilaria genita excirculo, & </s>
            <s xml:id="echoid-s6632" xml:space="preserve">ellipſi, vel
              <lb/>
            ellipſibus, vtcunque iuxta datas regulas .</s>
            <s xml:id="echoid-s6633" xml:space="preserve">i. </s>
            <s xml:id="echoid-s6634" xml:space="preserve">ſphæram, & </s>
            <s xml:id="echoid-s6635" xml:space="preserve">ſphæroi-
              <lb/>
            des, & </s>
            <s xml:id="echoid-s6636" xml:space="preserve">alia quæcunque ſolida ſimilaria genita ex dictis figuris, ha-
              <lb/>
            bere inter ſe rationem ex eorum axibus, vel diametris coniugatis
              <lb/>
            compoſitam.</s>
            <s xml:id="echoid-s6637" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div640" type="section" level="1" n="373">
          <head xml:id="echoid-head390" xml:space="preserve">SECTIO IV.</head>
          <p>
            <s xml:id="echoid-s6638" xml:space="preserve">ITem colligimus ſolida ſimilaria genita ex circulo, vel ellipſi, vel
              <lb/>
            ellipſibus, quæ habeant axes, vel diametros reciprocè quadratis
              <lb/>
            axium illis coniugatorum relpondentes iuxta quæ genita, intelligan-
              <lb/>
            tur, effe æqualia, dummodo vel vna in vtriſque ſumantur axes, vel
              <lb/>
            vna diametri æqualiter ad inuicem inclinatæ: </s>
            <s xml:id="echoid-s6639" xml:space="preserve">& </s>
            <s xml:id="echoid-s6640" xml:space="preserve">ſi hæc ſint æqualia,
              <lb/>
            illa eſſe reciprocè reſpondentia.</s>
            <s xml:id="echoid-s6641" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div641" type="section" level="1" n="374">
          <head xml:id="echoid-head391" xml:space="preserve">SECTIO V.</head>
          <p>
            <s xml:id="echoid-s6642" xml:space="preserve">ITem habemus, quod ſphæræ, & </s>
            <s xml:id="echoid-s6643" xml:space="preserve">ſimilia ſphæroideia, & </s>
            <s xml:id="echoid-s6644" xml:space="preserve">in vni-
              <lb/>
            uerſum, quod ſolida ſimilaria genita ex circulis, vel ellipſibus ha-
              <lb/>
            bentibus axes, vel diametros in ratione ſecundorum axium, vel dia-
              <lb/>
            metrorum, cum quibus æqualiter ſintinclinati, quod, inquam, ſint
              <lb/>
            in tripla ratione axium, vel diametrorum. </s>
            <s xml:id="echoid-s6645" xml:space="preserve">i. </s>
            <s xml:id="echoid-s6646" xml:space="preserve">vt cubi eorundem. </s>
            <s xml:id="echoid-s6647" xml:space="preserve">Hæc
              <lb/>
            enim demonſtrata de omnibus quadratis parallelogrammorum pro
              <lb/>
            omnibus quadratis circulorum, vel ellipſium, tamquam eorundem
              <lb/>
            partibus proportionalibus (dum illis inſcripta intelliguntur) recipi
              <lb/>
            poſiunt.</s>
            <s xml:id="echoid-s6648" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div642" type="section" level="1" n="375">
          <head xml:id="echoid-head392" xml:space="preserve">COROLLARIVM XI.</head>
          <p>
            <s xml:id="echoid-s6649" xml:space="preserve">IN Prop. </s>
            <s xml:id="echoid-s6650" xml:space="preserve">13. </s>
            <s xml:id="echoid-s6651" xml:space="preserve">colligemus ſolidum ſimilare genitum ex, OV, quod
              <lb/>
            poteſt eſſe vel cylindrus, vel prima, ad ſibi ſimilare genitum ex
              <lb/>
            trilineo, DCV, eſſe vt, OV, ad reliquum ſpatium, dempta quarta
              <lb/>
            circuli, vel ellipſis, OCD, cum exceſſu dicti quadrantis ſuper duas
              <lb/>
            tertias, rectanguli, OV, ideſt proximè, vt 21. </s>
            <s xml:id="echoid-s6652" xml:space="preserve">ad 2. </s>
            <s xml:id="echoid-s6653" xml:space="preserve">Exponatur de
              <lb/>
            huius Theor. </s>
            <s xml:id="echoid-s6654" xml:space="preserve">figura tantum rectangulum, OV, cum quarta, OCD,
              <lb/>
            dimiffa, EF, ſi igitur intelligemus, OV, circa, DV, manentem re-
              <lb/>
            uolui, quoad redeat, vnde diſceſſit, defcribetur, ab, OV, cylindrus,
              <lb/>
            OA, ideſt ſolidum ſimilare genitum ex, OV, cuius omnes </s>
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