Clavius, Christoph, Geometria practica

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        <div xml:id="echoid-div1102" type="section" level="1" n="398">
          <pb o="373" file="401" n="401" rhead="LIBER OCTAVVS."/>
          <p>
            <s xml:id="echoid-s17637" xml:space="preserve">
              <emph style="sc">Svpra</emph>
            baſem maioris cubi conſtruatur parallelepipedum cubo
              <note symbol="a" position="right" xlink:label="note-401-01" xlink:href="note-401-01a" xml:space="preserve">39. hui{us}.</note>
            æquale. </s>
            <s xml:id="echoid-s17638" xml:space="preserve">Et ex latere cubi maioris ab ſcindatur recta æqualis altitudini conſtructi
              <lb/>
            parallelepipedi. </s>
            <s xml:id="echoid-s17639" xml:space="preserve">Si enim per punctum abſciſsionis ducatur planum baſibus cu-
              <lb/>
            bi parallelum, detractum erit parallelepip edum parallelepipedo conſtructo æ-
              <lb/>
            quale, cum habeat eandem baſem & </s>
            <s xml:id="echoid-s17640" xml:space="preserve">altitudinem cumillo, hoc eſt, minori cu-
              <lb/>
            bo æquale. </s>
            <s xml:id="echoid-s17641" xml:space="preserve"> Si igitur reliquo parallelepipedo fiat cubus æqualis, factum
              <note symbol="b" position="right" xlink:label="note-401-02" xlink:href="note-401-02a" xml:space="preserve">38. hui{us}.</note>
            quod proponitur.</s>
            <s xml:id="echoid-s17642" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1104" type="section" level="1" n="399">
          <head xml:id="echoid-head426" xml:space="preserve">SCHOLIVM.</head>
          <p>
            <s xml:id="echoid-s17643" xml:space="preserve">
              <emph style="sc">Idem</emph>
            fieri poteſt in aliis figuris ſolidis; </s>
            <s xml:id="echoid-s17644" xml:space="preserve"> ſi prius reducantur ad
              <note symbol="c" position="right" xlink:label="note-401-03" xlink:href="note-401-03a" xml:space="preserve">1. & 2. coroll.
                <lb/>
              36. hui{us}.</note>
            peda rectangula, quando non ſunt parallelepipeda. </s>
            <s xml:id="echoid-s17645" xml:space="preserve"> & </s>
            <s xml:id="echoid-s17646" xml:space="preserve">deinde parallelepi- peda ad cubos, &</s>
            <s xml:id="echoid-s17647" xml:space="preserve">c.</s>
            <s xml:id="echoid-s17648" xml:space="preserve"/>
          </p>
          <note symbol="d" position="right" xml:space="preserve">38. hui{us}.</note>
        </div>
        <div xml:id="echoid-div1106" type="section" level="1" n="400">
          <head xml:id="echoid-head427" xml:space="preserve">PROBL. 30. PROPOS. 44.</head>
          <p>
            <s xml:id="echoid-s17649" xml:space="preserve">DATIS duabus, aut pluribus ſphæris, ſphæram vnam æqualem con-
              <lb/>
            ſtituere.</s>
            <s xml:id="echoid-s17650" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s17651" xml:space="preserve">
              <emph style="sc">Sphæris</emph>
            propoſitis conſtruantur cubi æquales: </s>
            <s xml:id="echoid-s17652" xml:space="preserve"> His deinde
              <note symbol="e" position="right" xlink:label="note-401-05" xlink:href="note-401-05a" xml:space="preserve">40. hui{us}.</note>
              <note symbol="f" position="right" xlink:label="note-401-06" xlink:href="note-401-06a" xml:space="preserve">41. hui{us}.</note>
            cubus æqualis fiat, qui etiam ſphæris datis erit æqualis. </s>
            <s xml:id="echoid-s17653" xml:space="preserve"> Si igitur huic
              <note symbol="g" position="right" xlink:label="note-401-07" xlink:href="note-401-07a" xml:space="preserve">40. hui{us}.</note>
            extruatur ſphæra æqualis; </s>
            <s xml:id="echoid-s17654" xml:space="preserve">factum erit, quod iubetur.</s>
            <s xml:id="echoid-s17655" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1108" type="section" level="1" n="401">
          <head xml:id="echoid-head428" xml:space="preserve">PROBL. 31. PROPOS. 45.</head>
          <p>
            <s xml:id="echoid-s17656" xml:space="preserve">EX maiori ſphæra minorem ſphæram detrahere, reſiduoque ſphæram
              <lb/>
            æqualem exhibere.</s>
            <s xml:id="echoid-s17657" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s17658" xml:space="preserve">
              <emph style="sc">Vtraqve</emph>
            ſphæra in cubum reuocetur. </s>
            <s xml:id="echoid-s17659" xml:space="preserve"> Detracto deinde minore
              <note symbol="h" position="right" xlink:label="note-401-08" xlink:href="note-401-08a" xml:space="preserve">40. hui{us}.</note>
            maiore, ſi reſiduo ſphæra fiat æqualis; </s>
            <s xml:id="echoid-s17660" xml:space="preserve">factum erit, quod proponitur.</s>
            <s xml:id="echoid-s17661" xml:space="preserve">
              <note symbol="i" position="right" xlink:label="note-401-09" xlink:href="note-401-09a" xml:space="preserve">43. hui{us}.</note>
              <note symbol="k" position="right" xlink:label="note-401-10" xlink:href="note-401-10a" xml:space="preserve">40. hui{us}.</note>
            </s>
          </p>
        </div>
        <div xml:id="echoid-div1110" type="section" level="1" n="402">
          <head xml:id="echoid-head429" xml:space="preserve">PROBL. 32. PROPOS. 46.</head>
          <p>
            <s xml:id="echoid-s17662" xml:space="preserve">DATVM cubum aut parallelepipedum, ſecundum proportionem da-
              <lb/>
            tam ſecare.</s>
            <s xml:id="echoid-s17663" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s17664" xml:space="preserve">
              <emph style="sc">Si</emph>
            namque vnum latus in baſe cubi, aut parallelepipedi ſecetur ſecundum
              <lb/>
            datam proportionem, & </s>
            <s xml:id="echoid-s17665" xml:space="preserve">per punctum ſectionis ducatur planum duabus baſi-
              <lb/>
            ſibus erectis ſolidi parallelum, diuidens ipſum ſolidum in duo parallelepipeda:
              <lb/>
            </s>
            <s xml:id="echoid-s17666" xml:space="preserve">habebunt hæc parallelepipeda datam proportionem. </s>
            <s xml:id="echoid-s17667" xml:space="preserve"> Habent enim
              <note symbol="l" position="right" xlink:label="note-401-11" xlink:href="note-401-11a" xml:space="preserve">32. vndec.</note>
            tionem inter ſe eandem, quam baſes. </s>
            <s xml:id="echoid-s17668" xml:space="preserve"> Cum ergo baſes habeant eandem
              <note symbol="m" position="right" xlink:label="note-401-12" xlink:href="note-401-12a" xml:space="preserve">@. ſexti.</note>
            portionem, quam ſegmenta lateris ſecundum datam proportionem diuiſi; </s>
            <s xml:id="echoid-s17669" xml:space="preserve">con-
              <lb/>
            ſtat id, quod propoſitum eſt.</s>
            <s xml:id="echoid-s17670" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1112" type="section" level="1" n="403">
          <head xml:id="echoid-head430" xml:space="preserve">SCHOLIVM.</head>
          <p>
            <s xml:id="echoid-s17671" xml:space="preserve">
              <emph style="sc">Non</emph>
            aliter priſma quo dlibet, aut cylindrus ſecundum datam proportio-
              <lb/>
            nem ſecabitur, ſi altitudo in datã ſecetur proportionem, & </s>
            <s xml:id="echoid-s17672" xml:space="preserve">per punctũ </s>
          </p>
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Impressum