Clavius, Christoph, Geometria practica

Table of contents

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[371.] COROLLARIVM.
Page: 385 (357)
[372.] PROBL. 18. PROPOS. 27.
Page: 385 (357)
[373.] THEOR. 10. PROPOS. 28.
Page: 386 (358)
[374.] SCHOLIVM.
Page: 388 (360)
[375.] THEOR. 11. PROPOS. 29.
Page: 388 (360)
[376.] SCHOLIVM.
Page: 390 (362)
[377.] THEOR. 12. PROPOS. 30.
Page: 390 (362)
[378.] THEOR. 13. PROPOS. 31.
Page: 392 (364)
[379.] THEOR. 14. PROPOS. 32.
Page: 393 (365)
[380.] PROBL. 19. PROPOS. 33.
Page: 393 (365)
[381.] SCHOLIVM.
Page: 394 (366)
[382.] PROBL. 20. PROPOS. 34.
Page: 394 (366)
[383.] PROBL. 21. PROPOS. 35.
Page: 395 (367)
[384.] PROBL. 22. PROPOS. 36.
Page: 396 (368)
[385.] COROLLARIVM I.
Page: 396 (368)
[386.] COROLLARIVM II.
Page: 397 (369)
[387.] PROBL. 23. PROPOS. 37.
Page: 397 (369)
[388.] PROBL. 24. PROPOS. 38.
Page: 397 (369)
[389.] COROLLARIVM.
Page: 397 (369)
[390.] PROBL. 25. PROPOS. 39.
Page: 398 (370)
[391.] COR OLLARIVM.
Page: 398 (370)
[392.] PROBL. 26. PROPOS. 40.
Page: 398 (370)
[393.] COROLLARIVM I.
Page: 399 (371)
[394.] COROLLARIVM II.
Page: 399 (371)
[395.] PROBL. 27. PROPOS. 41.
Page: 400 (372)
[396.] SCHOLIVM.
Page: 400 (372)
[397.] PROBL. 28. PROPOS. 42.
Page: 400 (372)
[398.] PROBL. 29. PROPOS. 43.
Page: 400 (372)
[399.] SCHOLIVM.
Page: 401 (373)
[400.] PROBL. 30. PROPOS. 44.
Page: 401 (373)
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            <s xml:id="echoid-s17595" xml:space="preserve">
              <pb o="372" file="400" n="400" rhead="GEOMETR. PRACT."/>
            corpori regulari æqualis; </s>
            <s xml:id="echoid-s17596" xml:space="preserve"> quippe cum ita ſe habeat tam pyramis hæc
              <note symbol="a" position="left" xlink:label="note-400-01" xlink:href="note-400-01a" xml:space="preserve">6. duodec.</note>
            tera ad vnam pyramidem corporis regularis, quam omnes pyramides corporis
              <lb/>
            regularis ad vnam pyramidem, vt baſis illius vel baſes omnium pyramidum
              <lb/>
            corporis, ad vnam baſem; </s>
            <s xml:id="echoid-s17597" xml:space="preserve">propterea quod in Octaedro proportio eſt vtro-
              <lb/>
            bique octupla: </s>
            <s xml:id="echoid-s17598" xml:space="preserve">In Icoſaedro, vigecupla: </s>
            <s xml:id="echoid-s17599" xml:space="preserve">Et in Dodecaedro, duo decupla. </s>
            <s xml:id="echoid-s17600" xml:space="preserve">Qua-
              <lb/>
            re ſi totiilli pyramidi cubus conſtruatur æqualis, vt paulò ante de Tetraedro di-
              <lb/>
            ctum eſt: </s>
            <s xml:id="echoid-s17601" xml:space="preserve">atque huic tandem cubo ſphæra æqualis fabricetur; </s>
            <s xml:id="echoid-s17602" xml:space="preserve">erit eadem ſphæ-
              <lb/>
            ra illi pyramidi, hoc eſt, corpori regulari æqualis.</s>
            <s xml:id="echoid-s17603" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div1097" type="section" level="1" n="395">
          <head xml:id="echoid-head422" xml:space="preserve">PROBL. 27. PROPOS. 41.</head>
          <p>
            <s xml:id="echoid-s17604" xml:space="preserve">DVOBVS aut pluribus cubis vnum cubum æqualem efficere.</s>
            <s xml:id="echoid-s17605" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s17606" xml:space="preserve">
              <emph style="sc">Si</emph>
            ſupra baſem ſuperiorem primi cubi, conſtruatur parallelepipedum
              <note symbol="b" position="left" xlink:label="note-400-02" xlink:href="note-400-02a" xml:space="preserve">39 hui{us}.</note>
            ctangulum ſecundo cubo æquale, vt fiat vnum parallelepipedum duo bus cu-
              <lb/>
            bis æquale: </s>
            <s xml:id="echoid-s17607" xml:space="preserve">Et ſupra huius parallelepipedi baſem ſuperiorem aliud parallelepi-
              <lb/>
            pedum æquale tertio cubo, & </s>
            <s xml:id="echoid-s17608" xml:space="preserve">ſic deinceps, ſi plures adſint cubi, conſtructum
              <lb/>
            erit parallelepipedum propoſitis cubis æquale. </s>
            <s xml:id="echoid-s17609" xml:space="preserve">Huic ergo ſi fiat cubus
              <note symbol="c" position="left" xlink:label="note-400-03" xlink:href="note-400-03a" xml:space="preserve">38. hui{us}.</note>
            lis, factum erit, quod proponitur.</s>
            <s xml:id="echoid-s17610" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div1099" type="section" level="1" n="396">
          <head xml:id="echoid-head423" xml:space="preserve">SCHOLIVM.</head>
          <p>
            <s xml:id="echoid-s17611" xml:space="preserve">
              <emph style="sc">Eadem</emph>
            arte quotlibet figuris ſolidis non cubis, conſtruetur cubus æqualis:
              <lb/>
            </s>
            <s xml:id="echoid-s17612" xml:space="preserve"> ſi nimirum reuo centur ad vnum parallelepipedum, &</s>
            <s xml:id="echoid-s17613" xml:space="preserve">c.</s>
            <s xml:id="echoid-s17614" xml:space="preserve"/>
          </p>
          <note symbol="d" position="left" xml:space="preserve">37. hui{us}.</note>
        </div>
        <div xml:id="echoid-div1100" type="section" level="1" n="397">
          <head xml:id="echoid-head424" xml:space="preserve">PROBL. 28. PROPOS. 42.</head>
          <p>
            <s xml:id="echoid-s17615" xml:space="preserve">DATO cubo, corpus regulare, quod ex quinque elegeris, æquale con-
              <lb/>
            ſtruere.</s>
            <s xml:id="echoid-s17616" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s17617" xml:space="preserve">
              <emph style="sc">Sit</emph>
            datus cubus, cuius latus A, cui verbi gratia conſtruendum ſit æquale
              <lb/>
            Dodecaedrum. </s>
            <s xml:id="echoid-s17618" xml:space="preserve"> Fiat quodcunque
              <note symbol="e" position="left" xlink:label="note-400-05" xlink:href="note-400-05a" xml:space="preserve">17. tertii-
                <lb/>
              decimi.</note>
            cuius latus B: </s>
            <s xml:id="echoid-s17619" xml:space="preserve">cui per ea, quæ in 2. </s>
            <s xml:id="echoid-s17620" xml:space="preserve">coroll. </s>
            <s xml:id="echoid-s17621" xml:space="preserve">præceden-
              <lb/>
              <note position="right" xlink:label="note-400-06" xlink:href="note-400-06a" xml:space="preserve">
                <lb/>
              C. # A. # B. # D.
                <lb/>
              </note>
            tis propoſ. </s>
            <s xml:id="echoid-s17622" xml:space="preserve">dicta ſunt, fiat æqualis cubus, cuius latus
              <lb/>
            C. </s>
            <s xml:id="echoid-s17623" xml:space="preserve"> Et tribus lateribus C, A, B, reperiatur quarta proportionalis D. </s>
            <s xml:id="echoid-s17624" xml:space="preserve">Dico
              <note symbol="f" position="left" xlink:label="note-400-07" xlink:href="note-400-07a" xml:space="preserve">12. ſexti.</note>
            decaedrum ſupra latus D, conſtructum, æquale eſſe dato cubo lateris A. </s>
            <s xml:id="echoid-s17625" xml:space="preserve">Quo-
              <lb/>
            niam enim, vt ex demonſtratione propoſ. </s>
            <s xml:id="echoid-s17626" xml:space="preserve">37. </s>
            <s xml:id="echoid-s17627" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s17628" xml:space="preserve">11. </s>
            <s xml:id="echoid-s17629" xml:space="preserve">Eucl. </s>
            <s xml:id="echoid-s17630" xml:space="preserve">patet. </s>
            <s xml:id="echoid-s17631" xml:space="preserve">ita eſt cubus la-
              <lb/>
            teris C, ad cubum lateris A, vt Dodecaedrum lateris B, ad Dodecaedrum late-
              <lb/>
            ris D: </s>
            <s xml:id="echoid-s17632" xml:space="preserve">Eſt autem per conſtructionem, cubus lateris C, æqualis Dodecaedro
              <lb/>
            lateris B; </s>
            <s xml:id="echoid-s17633" xml:space="preserve"> erit quo que cubus lateris A, Dodecaedro lateris D, æqualis, quod
              <note symbol="g" position="left" xlink:label="note-400-08" xlink:href="note-400-08a" xml:space="preserve">14. quinti.</note>
            propoſitum.</s>
            <s xml:id="echoid-s17634" xml:space="preserve"/>
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        <div xml:id="echoid-div1102" type="section" level="1" n="398">
          <head xml:id="echoid-head425" xml:space="preserve">PROBL. 29. PROPOS. 43.</head>
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            <s xml:id="echoid-s17635" xml:space="preserve">EX maiori cubo detrahere minorem, reſiduoque cubum æqualem ex-
              <lb/>
            hibere.</s>
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