Clavius, Christoph, Geometria practica

List of thumbnails

< >
391
391 (363) 		392
392 (364)
393
393 (365) 		394
394 (366)
395
395 (367) 		396
396 (368)
397
397 (369) 		398
398 (370)
399
399 (371) 		400
400 (372)
< >
page |< < (368) of 450 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div1068" type="section" level="1" n="383">
          <pb o="368" file="396" n="396" rhead="GEOMETR. PRACT."/>
          <p>
            <s xml:id="echoid-s17393" xml:space="preserve">
              <emph style="sc">Si</emph>
            baſi priſmatis, vel pyramidis conſtruatur circulus æqualis, per ea, quæ ad
              <lb/>
            finem lib. </s>
            <s xml:id="echoid-s17394" xml:space="preserve">7. </s>
            <s xml:id="echoid-s17395" xml:space="preserve">ſcripſimus: </s>
            <s xml:id="echoid-s17396" xml:space="preserve">Et ſuper hunc circulum extruatur cylindrus, vel conus
              <lb/>
            eiuſdem altitu dinis cum priſmate, vel pyramide; </s>
            <s xml:id="echoid-s17397" xml:space="preserve">erit cylindrus priſmati, & </s>
            <s xml:id="echoid-s17398" xml:space="preserve">co-
              <lb/>
            nus pyramidi æqualis. </s>
            <s xml:id="echoid-s17399" xml:space="preserve">Cum enim tam baſes, quam altitudines æquales ſint:
              <lb/>
            </s>
            <s xml:id="echoid-s17400" xml:space="preserve">pro ducatur autem priſma, & </s>
            <s xml:id="echoid-s17401" xml:space="preserve">Cylindrus ex baſe in altitudinem multiplicata, & </s>
            <s xml:id="echoid-s17402" xml:space="preserve">
              <lb/>
            pyramis, atque conus ex tertia parte baſis in altitudinem multiplicata, vt lib. </s>
            <s xml:id="echoid-s17403" xml:space="preserve">5. </s>
            <s xml:id="echoid-s17404" xml:space="preserve">
              <lb/>
            cap. </s>
            <s xml:id="echoid-s17405" xml:space="preserve">1. </s>
            <s xml:id="echoid-s17406" xml:space="preserve">declarauimus; </s>
            <s xml:id="echoid-s17407" xml:space="preserve">manifeſtum eſt, cylindrum priſmati, & </s>
            <s xml:id="echoid-s17408" xml:space="preserve">conum pyramidi
              <lb/>
            eſſe æqualem.</s>
            <s xml:id="echoid-s17409" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s17410" xml:space="preserve">
              <emph style="sc">Si</emph>
            viciſsim baſi cylindri, vel coni conſtituatur quadratum, aut alia quæuis
              <lb/>
            rectilinea figura æqualis, per ea, quæ ad finem lib. </s>
            <s xml:id="echoid-s17411" xml:space="preserve">7. </s>
            <s xml:id="echoid-s17412" xml:space="preserve">diximus, & </s>
            <s xml:id="echoid-s17413" xml:space="preserve">ſuper hoc qua-
              <lb/>
            dratum, aut figuram rectilineam fiat priſma, vel pyramis eiuſdem altitudinis
              <lb/>
            cum cylindro, vel cono, erit priſma cylindro, & </s>
            <s xml:id="echoid-s17414" xml:space="preserve">pyramis cono æqualis. </s>
            <s xml:id="echoid-s17415" xml:space="preserve">quod eſt
              <lb/>
            propoſitum.</s>
            <s xml:id="echoid-s17416" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1069" type="section" level="1" n="384">
          <head xml:id="echoid-head411" xml:space="preserve">PROBL. 22. PROPOS. 36.</head>
          <p>
            <s xml:id="echoid-s17417" xml:space="preserve">DATO Cylindro, aut priſmati æqualem conum, vel pyramidem ſub
              <lb/>
            eadem altitudine. </s>
            <s xml:id="echoid-s17418" xml:space="preserve">Et viciſsim dato cono, vel pyramidi æqualem cy-
              <lb/>
            lindrum, aut priſma eiuſdem altitudinis conſtituere.</s>
            <s xml:id="echoid-s17419" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s17420" xml:space="preserve">
              <emph style="sc">Si</emph>
            tam baſis cylindri, quam priſmatis tripletur, & </s>
            <s xml:id="echoid-s17421" xml:space="preserve">ſuper triplicatam
              <note symbol="a" position="left" xlink:label="note-396-01" xlink:href="note-396-01a" xml:space="preserve">16. ſexti.
                <lb/>
              hui{us}.</note>
            tur conus, vel pyramis eiuſdem altitudinis, factum erit, quod in prima paite
              <lb/>
            proponitur. </s>
            <s xml:id="echoid-s17422" xml:space="preserve"> Cumenim cylindrus ttiplus ſit coni eandem cumillo baſem, &</s>
            <s xml:id="echoid-s17423" xml:space="preserve">
              <note symbol="b" position="left" xlink:label="note-396-02" xlink:href="note-396-02a" xml:space="preserve">10. duode-
                <lb/>
              cimi.</note>
            altitudinem habentis: </s>
            <s xml:id="echoid-s17424" xml:space="preserve"> Item priſma triplum pyramidis eandem cum illo ba- ſem, atque altitudinem habentis: </s>
            <s xml:id="echoid-s17425" xml:space="preserve"> Sit autem & </s>
            <s xml:id="echoid-s17426" xml:space="preserve">conus extructus eiuſdem
              <note symbol="c" position="left" xlink:label="note-396-03" xlink:href="note-396-03a" xml:space="preserve">coroll. 7.
                <lb/>
              duodec.</note>
            lius coni triplus; </s>
            <s xml:id="echoid-s17427" xml:space="preserve">necnon & </s>
            <s xml:id="echoid-s17428" xml:space="preserve">pyramis conſtructa eiuſdem illius pyramidis tri-
              <lb/>
            pla. </s>
            <s xml:id="echoid-s17429" xml:space="preserve"> Erit tam conus extructus cylindro æqualis, quam pyramis
              <note symbol="d" position="left" xlink:label="note-396-04" xlink:href="note-396-04a" xml:space="preserve">11. & 6. duo-
                <lb/>
              dec.</note>
            priſmati. </s>
            <s xml:id="echoid-s17430" xml:space="preserve">quod eſt propoſitum.</s>
            <s xml:id="echoid-s17431" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s17432" xml:space="preserve">
              <emph style="sc">Si</emph>
            viciſsim baſes coni, & </s>
            <s xml:id="echoid-s17433" xml:space="preserve">pyramidis in tripla proportione minuantur, &</s>
            <s xml:id="echoid-s17434" xml:space="preserve">
              <note symbol="e" position="left" xlink:label="note-396-05" xlink:href="note-396-05a" xml:space="preserve">9. quinti.</note>
              <note symbol="f" position="left" xlink:label="note-396-06" xlink:href="note-396-06a" xml:space="preserve">16. ſexti.
                <lb/>
              hui{us}.</note>
            ſuper tertias has partes cylindrus erigatur, & </s>
            <s xml:id="echoid-s17435" xml:space="preserve">priſma: </s>
            <s xml:id="echoid-s17436" xml:space="preserve">Erit tam cylindrus dato
              <lb/>
            cono, quam priſma datæ pyramidi æquale. </s>
            <s xml:id="echoid-s17437" xml:space="preserve"> Quoniam enim tam conus
              <note symbol="g" position="left" xlink:label="note-396-07" xlink:href="note-396-07a" xml:space="preserve">11. & 10.
                <lb/>
              duodec.</note>
            quam cylindrus extructus, triplus eſt coni eandem baſem, altitudinem que ha-
              <lb/>
            bentis cum cylindro extructo. </s>
            <s xml:id="echoid-s17438" xml:space="preserve"> Item tam data pyramis, quam priſma
              <note symbol="h" position="left" xlink:label="note-396-08" xlink:href="note-396-08a" xml:space="preserve">6. & 7. duo-
                <lb/>
              dec.</note>
            ctum, triplum eſt pyramidis eandem habentis baſem, atque altitudinem cum
              <lb/>
            priſmate extructo. </s>
            <s xml:id="echoid-s17439" xml:space="preserve"> Erit tam cylindrus extructus dato cono æqualis,
              <note symbol="i" position="left" xlink:label="note-396-09" xlink:href="note-396-09a" xml:space="preserve">9. quinti.</note>
            priſma conſtructum datæ pyramidis æquale. </s>
            <s xml:id="echoid-s17440" xml:space="preserve">quod eſt propoſitum.</s>
            <s xml:id="echoid-s17441" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1072" type="section" level="1" n="385">
          <head xml:id="echoid-head412" xml:space="preserve">COROLLARIVM I.</head>
          <p>
            <s xml:id="echoid-s17442" xml:space="preserve">
              <emph style="sc">Qvia</emph>
            igitur omne priſma in cylindrum, & </s>
            <s xml:id="echoid-s17443" xml:space="preserve">pyramis in conum
              <note symbol="k" position="left" xlink:label="note-396-10" xlink:href="note-396-10a" xml:space="preserve">35. hui{us}.</note>
            tur: </s>
            <s xml:id="echoid-s17444" xml:space="preserve">Et contra cylindrus in priſma, & </s>
            <s xml:id="echoid-s17445" xml:space="preserve">conus in pyramidem: </s>
            <s xml:id="echoid-s17446" xml:space="preserve"> Item
              <note symbol="l" position="left" xlink:label="note-396-11" xlink:href="note-396-11a" xml:space="preserve">36. hui{us}.</note>
            in conum, & </s>
            <s xml:id="echoid-s17447" xml:space="preserve">priſma in pyramidem: </s>
            <s xml:id="echoid-s17448" xml:space="preserve">Et contra conus in cylindrum, & </s>
            <s xml:id="echoid-s17449" xml:space="preserve">pyramis
              <lb/>
            in priſma conuerti poteſt; </s>
            <s xml:id="echoid-s17450" xml:space="preserve">fit vt indifferenter tam cylindrus, quam priſma tranſ-
              <lb/>
            mutari poſsit in pyramidem, aut conum, ac pyramis in cylindrum, aut priſma
              <lb/>
            æquale.</s>
            <s xml:id="echoid-s17451" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum