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

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        <div xml:id="echoid-div224" type="section" level="1" n="145">
          <p style="it">
            <s xml:id="echoid-s2310" xml:space="preserve">
              <pb o="94" file="0114" n="114" rhead="GEOMETRIÆ"/>
            lineis, vel lateribus homologis deſcriptarum figurarum; </s>
            <s xml:id="echoid-s2311" xml:space="preserve">ſolida, in qui-
              <lb/>
            bus deſcriptæ figuræ ex traiectis planis producentur (quæ in ſequenti li-
              <lb/>
            bro dicuntur, ſolida ad inuicem ſimilaria genita ex dictis ſectionum por-
              <lb/>
            tionibus) erunt ſimilia, & </s>
            <s xml:id="echoid-s2312" xml:space="preserve">figurarum homologarum eorundem regulæ
              <lb/>
              <note position="left" xlink:label="note-0114-01" xlink:href="note-0114-01a" xml:space="preserve">_C. Def. 8._
                <lb/>
              _lib. 2._</note>
            oppoſita tangentia plana dictis iam deſcriptis figuris æquidiſtantia, quo-
              <lb/>
            rum & </s>
            <s xml:id="echoid-s2313" xml:space="preserve">dictorum ſolidorum figuræ incidentes erunt dictæ ſectionum por-
              <lb/>
            tiones, vel in earum planis iacebunt. </s>
            <s xml:id="echoid-s2314" xml:space="preserve">V nde colligimus omnes ſphæras
              <lb/>
            eſſe ſimiles, nam ſi ſecentur planis per axem, conceptæ figuræ fiunt ſimi-
              <lb/>
            les, ideſt circuli, quod ſi ſecentur adhuc planis ad horum circulorum pla-
              <lb/>
              <note position="left" xlink:label="note-0114-02" xlink:href="note-0114-02a" xml:space="preserve">_Lẽma 31._
                <lb/>
              _huius pr._</note>
            na erectis, productæ figuræ fiunt pariter circuli deſcripti tanquam dia-
              <lb/>
            metris eiſdem rectis lineis, in quibus coincidunt circulis per axem du-
              <lb/>
              <note position="left" xlink:label="note-0114-03" xlink:href="note-0114-03a" xml:space="preserve">_33. huius._</note>
            ctis, quæ diametri ſunt etiam incidentes eorundem deſcriptorum circu-
              <lb/>
              <note position="left" xlink:label="note-0114-04" xlink:href="note-0114-04a" xml:space="preserve">_34. huius._</note>
            lorum, & </s>
            <s xml:id="echoid-s2315" xml:space="preserve">oppoſitarum tangentium per eorum extrema ductarum, quæ
              <lb/>
              <note position="left" xlink:label="note-0114-05" xlink:href="note-0114-05a" xml:space="preserve">_Lẽma 31._
                <lb/>
              _huius._</note>
            tangentes omnes inter ſe æquidiſtant, vt facilè patet, & </s>
            <s xml:id="echoid-s2316" xml:space="preserve">ſunt iſtæ inci-
              <lb/>
            dentes, ſiue diametri deſcriptorum circulorum, quæ axem diuidunt fi-
              <lb/>
            militer ad eandem partem, vt ipſi axes, igitur ſpbæræ omnes ſunt ſimi-
              <lb/>
            les, & </s>
            <s xml:id="echoid-s2317" xml:space="preserve">ductis duobus planis oppoſitis tangentibus vtcumq; </s>
            <s xml:id="echoid-s2318" xml:space="preserve">& </s>
            <s xml:id="echoid-s2319" xml:space="preserve">per axem,
              <lb/>
              <note position="left" xlink:label="note-0114-06" xlink:href="note-0114-06a" xml:space="preserve">_Lẽma 31._
                <lb/>
              _huius._</note>
            qui iungit puncta contactuum ductis planis, hinc effecti circuli erunt
              <lb/>
            figuræ incidentes dictorum tangentium, & </s>
            <s xml:id="echoid-s2320" xml:space="preserve">ſphærarum, & </s>
            <s xml:id="echoid-s2321" xml:space="preserve">dicta plana
              <lb/>
            tangentia erunt regulæ homologarum figurarum earundem, vnde tan-
              <lb/>
            dem patet quoſuis circulos in ſphæris per centrum tranſeuntes poſſe eſſe
              <lb/>
            figuras incidentes earundem ſphærarum, & </s>
            <s xml:id="echoid-s2322" xml:space="preserve">planorum oppoſitorum tan-
              <lb/>
            gentium ſphæras in extremis punctis diametrorum quorumuis dictorum
              <lb/>
            circulorum per centrum tr anſeuntium.</s>
            <s xml:id="echoid-s2323" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div226" type="section" level="1" n="146">
          <head xml:id="echoid-head157" xml:space="preserve">THEOREMA XLVI. PROPOS. XLIX.</head>
          <p>
            <s xml:id="echoid-s2324" xml:space="preserve">POſita definitione particulari ſimilium ſphæroidum, ſe-
              <lb/>
            quitur & </s>
            <s xml:id="echoid-s2325" xml:space="preserve">generalis ſimilium ſolidorum.</s>
            <s xml:id="echoid-s2326" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2327" xml:space="preserve">Sint ſimiles ſphæroides
              <lb/>
              <figure xlink:label="fig-0114-01" xlink:href="fig-0114-01a" number="63">
                <image file="0114-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0114-01"/>
              </figure>
            iuxta definitionem particu-
              <lb/>
            larem de ipſis allatam, AB
              <lb/>
            CD, FEHG. </s>
            <s xml:id="echoid-s2328" xml:space="preserve">Dico has
              <lb/>
            eſſe ſimiles iuxta definitio.
              <lb/>
            </s>
            <s xml:id="echoid-s2329" xml:space="preserve">nem generalem ſimilium
              <lb/>
            ſolidorum; </s>
            <s xml:id="echoid-s2330" xml:space="preserve">ductis enim pla-
              <lb/>
            nis per axes, AC, FH,
              <lb/>
            producantur in eiſdem el-
              <lb/>
            lipſes, ABCD, FEHG,
              <lb/>
              <note position="left" xlink:label="note-0114-07" xlink:href="note-0114-07a" xml:space="preserve">33 huius.</note>
            quæ erunt eædem illis, ex quarum reuolutione circa axes, AC, FH,
              <lb/>
              <note position="left" xlink:label="note-0114-08" xlink:href="note-0114-08a" xml:space="preserve">38. huius.</note>
            </s>
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