Clavius, Christoph, Geometria practica

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        <div xml:id="echoid-div670" type="section" level="1" n="235">
          <p>
            <s xml:id="echoid-s10891" xml:space="preserve">
              <pb o="233" file="263" n="263" rhead="LIBER QVINTVS."/>
            de Conoid. </s>
            <s xml:id="echoid-s10892" xml:space="preserve">& </s>
            <s xml:id="echoid-s10893" xml:space="preserve">Sphæroid. </s>
            <s xml:id="echoid-s10894" xml:space="preserve">Federicus Commandinus
              <lb/>
              <figure xlink:label="fig-263-01" xlink:href="fig-263-01a" number="168">
                <image file="263-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/263-01"/>
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            demonſtrauit, planum per AC, ductum, & </s>
            <s xml:id="echoid-s10895" xml:space="preserve">rectum
              <lb/>
            ad axem BD, circulum facit, cuius diameter A C, & </s>
            <s xml:id="echoid-s10896" xml:space="preserve">
              <lb/>
            centrum D: </s>
            <s xml:id="echoid-s10897" xml:space="preserve">erit per propoſ. </s>
            <s xml:id="echoid-s10898" xml:space="preserve">23. </s>
            <s xml:id="echoid-s10899" xml:space="preserve">libri Archim. </s>
            <s xml:id="echoid-s10900" xml:space="preserve">de
              <lb/>
            Conoid. </s>
            <s xml:id="echoid-s10901" xml:space="preserve">& </s>
            <s xml:id="echoid-s10902" xml:space="preserve">Sphæroid. </s>
            <s xml:id="echoid-s10903" xml:space="preserve">Parabolicum Conoides A-
              <lb/>
            BC, ſeſquialterum coni, cuius baſis circulus diame-
              <lb/>
            tri AC, & </s>
            <s xml:id="echoid-s10904" xml:space="preserve">axis BD. </s>
            <s xml:id="echoid-s10905" xml:space="preserve">Igitur ſi fiat, vt 2. </s>
            <s xml:id="echoid-s10906" xml:space="preserve">ad 3. </s>
            <s xml:id="echoid-s10907" xml:space="preserve">ita prædi-
              <lb/>
            ctus conus (quem ex cap. </s>
            <s xml:id="echoid-s10908" xml:space="preserve">2. </s>
            <s xml:id="echoid-s10909" xml:space="preserve">huius libri metiemur)
              <lb/>
            ad aliud; </s>
            <s xml:id="echoid-s10910" xml:space="preserve">proſiliet ſoliditas Conoidis Parabolici A-
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            BC.</s>
            <s xml:id="echoid-s10911" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div672" type="section" level="1" n="236">
          <head xml:id="echoid-head256" xml:space="preserve">DE AREA CONOIDIS
            <lb/>
          Hyperbolici.</head>
          <head xml:id="echoid-head257" xml:space="preserve">
            <emph style="sc">Capvt</emph>
          IX.</head>
          <p>
            <s xml:id="echoid-s10912" xml:space="preserve">
              <emph style="sc">COncipiatvr</emph>
            ſuperior figura eſſe Hyperbola, & </s>
            <s xml:id="echoid-s10913" xml:space="preserve">recta E, æqualis ſe-
              <lb/>
              <note position="right" xlink:label="note-263-01" xlink:href="note-263-01a" xml:space="preserve">Soliditas Co-
                <lb/>
              noidis Hyper-
                <lb/>
              bolici.</note>
            miſsi diametri tranſuerſæ inter duas hyperbolas oppoſitas, hoc eſt, rectæ
              <lb/>
            ex centro hyperbolarum ad verticem B, ductæ. </s>
            <s xml:id="echoid-s10914" xml:space="preserve">Fietque rurſus circu-
              <lb/>
            lus, cuius diameter A C, à plano per AC, ducto, & </s>
            <s xml:id="echoid-s10915" xml:space="preserve">ad axem recto, vt Federicus
              <lb/>
            Commandinus ad propoſ. </s>
            <s xml:id="echoid-s10916" xml:space="preserve">12. </s>
            <s xml:id="echoid-s10917" xml:space="preserve">libri Archim. </s>
            <s xml:id="echoid-s10918" xml:space="preserve">de Conoid. </s>
            <s xml:id="echoid-s10919" xml:space="preserve">& </s>
            <s xml:id="echoid-s10920" xml:space="preserve">Sphæroid. </s>
            <s xml:id="echoid-s10921" xml:space="preserve">demon-
              <lb/>
            ſtrauit. </s>
            <s xml:id="echoid-s10922" xml:space="preserve">Soliditatem igitur Conoidis Hyperbolici, quod ab hyperbola ABC,
              <lb/>
            circa axem BD, circumuoluta effi citur, ita venabimur. </s>
            <s xml:id="echoid-s10923" xml:space="preserve">Quoniam per pro-
              <lb/>
            poſ. </s>
            <s xml:id="echoid-s10924" xml:space="preserve">27. </s>
            <s xml:id="echoid-s10925" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s10926" xml:space="preserve">Archimedis de Conoid. </s>
            <s xml:id="echoid-s10927" xml:space="preserve">& </s>
            <s xml:id="echoid-s10928" xml:space="preserve">Sphæroid. </s>
            <s xml:id="echoid-s10929" xml:space="preserve">Conoides Hyperbolicum A-
              <lb/>
            BC, ad conum, cuius baſis eadem cum baſe Conoidis, circulus videlicet diame-
              <lb/>
            tri A C, & </s>
            <s xml:id="echoid-s10930" xml:space="preserve">axis idem B D, proportionem habet eandem, quam linea conflata ex
              <lb/>
            axe B D, & </s>
            <s xml:id="echoid-s10931" xml:space="preserve">tripla ipſius E, ad lineam conflatam ex axe BD, & </s>
            <s xml:id="echoid-s10932" xml:space="preserve">dupla ipſius E. </s>
            <s xml:id="echoid-s10933" xml:space="preserve">Si
              <lb/>
            fiat, vt linea conflata ex axe B D, & </s>
            <s xml:id="echoid-s10934" xml:space="preserve">duplaipſius E, ad lineam conflatam ex
              <lb/>
            axe BD, & </s>
            <s xml:id="echoid-s10935" xml:space="preserve">tripla ipſius E, ita prædictus conus (quem ex cap. </s>
            <s xml:id="echoid-s10936" xml:space="preserve">2. </s>
            <s xml:id="echoid-s10937" xml:space="preserve">huius libri dime-
              <lb/>
            tiemur) ad aliud; </s>
            <s xml:id="echoid-s10938" xml:space="preserve">gignetur ſoliditas Conoidis Hyperbolici ABC.</s>
            <s xml:id="echoid-s10939" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div674" type="section" level="1" n="237">
          <head xml:id="echoid-head258" xml:space="preserve">DE AREA DOLIORVM.</head>
          <head xml:id="echoid-head259" xml:space="preserve">
            <emph style="sc">Capvt</emph>
          X.</head>
          <p>
            <s xml:id="echoid-s10940" xml:space="preserve">
              <emph style="sc">QVoniam</emph>
            dolia non eandem formam vbiq; </s>
            <s xml:id="echoid-s10941" xml:space="preserve">ſeruant, vix præſcribi po-
              <lb/>
            teſt ratio, qua dolij propoſiti capacitas accurate inueniatur. </s>
            <s xml:id="echoid-s10942" xml:space="preserve">Argumen-
              <lb/>
              <note position="right" xlink:label="note-263-02" xlink:href="note-263-02a" xml:space="preserve">Capacit{as} do-
                <lb/>
              lii.</note>
            to eſt, quod ſcriptores variè de eius Dimenſione ſcripſerunt. </s>
            <s xml:id="echoid-s10943" xml:space="preserve">Dicam er-
              <lb/>
            go etiam ego id, quod mihi veriſimile videtur. </s>
            <s xml:id="echoid-s10944" xml:space="preserve">Sit dolium ABCDEF, in extre-
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            mitatibus habens circulos AF, CD, orificium B, per quod cogitetur planum du-
              <lb/>
            ctum rectum ad lineam KL, centra circulorum AF, CD, coniungentem, ſecans
              <lb/>
            dolium bifariam. </s>
            <s xml:id="echoid-s10945" xml:space="preserve">Si igitur aſſeres dolij in B, & </s>
            <s xml:id="echoid-s10946" xml:space="preserve">E, curuentur, & </s>
            <s xml:id="echoid-s10947" xml:space="preserve">deinde ſecun-
              <lb/>
            dum lineas quaſi rectas extendantur, cuiuſmo di dolia non pauca Romæ vidi:</s>
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