Clavius, Christoph, Geometria practica

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          <p>
            <s xml:id="echoid-s9272" xml:space="preserve">
              <pb o="207" file="237" n="237" rhead="LIBER QVINTVS."/>
            quinque triangula ABF, BCF, CDF, DEF, AEF, tot nimirum, quot in baſe ſunt
              <lb/>
            latera, dicitur pyramis.</s>
            <s xml:id="echoid-s9273" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9274" xml:space="preserve">
              <emph style="sc">Convs</emph>
            autem eſt figura ſolida rotunda ad vnum punctum conſtituta, ſu-
              <lb/>
              <note position="right" xlink:label="note-237-01" xlink:href="note-237-01a" xml:space="preserve">Area pyra-
                <lb/>
              midis, & co-
                <lb/>
              ni.</note>
            pra baſem circularem, inſtar pyramidis rotundæ,
              <lb/>
              <figure xlink:label="fig-237-01" xlink:href="fig-237-01a" number="153">
                <image file="237-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/237-01"/>
              </figure>
            qualis eſt figura ABCDE.</s>
            <s xml:id="echoid-s9275" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9276" xml:space="preserve">
              <emph style="sc">Tam</emph>
            autem pyramidis, quam Coni area pro-
              <lb/>
            ducitur ex multiplicatione baſis in tertiã partem
              <lb/>
            altitudinis. </s>
            <s xml:id="echoid-s9277" xml:space="preserve">Cũ enim, vt in præcedenti cap. </s>
            <s xml:id="echoid-s9278" xml:space="preserve">oſten-
              <lb/>
            dimus, ex baſe in totam altitudinem gignatur
              <lb/>
            priſma vel Cylindrus eandem habens cum pyra-
              <lb/>
            mide, & </s>
            <s xml:id="echoid-s9279" xml:space="preserve">cono altitudinem; </s>
            <s xml:id="echoid-s9280" xml:space="preserve"> producetur ex eadem baſe in tertiam partem
              <note symbol="a" position="right" xlink:label="note-237-02" xlink:href="note-237-02a" xml:space="preserve">ſchol. 14.
                <lb/>
              duodec.</note>
            titudinis tertia pars illius priſmatis, vel Cylindri. </s>
            <s xml:id="echoid-s9281" xml:space="preserve">, Cum ergo pyramisſit
              <handwritten xlink:label="hd-237-2" xlink:href="hd-237-2a" number="71"/>
              <handwritten xlink:label="hd-237-2" xlink:href="hd-237-2a" number="72"/>
            pars illius priſmatis, & </s>
            <s xml:id="echoid-s9282" xml:space="preserve">Conus tertia pars Cylindri, liquet tam pyramidẽ,
              <note symbol="b" position="right" xlink:label="note-237-03" xlink:href="note-237-03a" xml:space="preserve">corol. 7.
                <lb/>
              duodec.</note>
            Conum produci ex baſe in tertiam partem altitudinis. </s>
            <s xml:id="echoid-s9283" xml:space="preserve">Ex quo fit, ſi baſis duca-
              <lb/>
            tur in totam altitudinem, tertiam partem numeri producti, eſſe quoque aream
              <lb/>
              <note symbol="c" position="right" xlink:label="note-237-04" xlink:href="note-237-04a" xml:space="preserve">10. duodec.
                <lb/>
              Areapyrami-
                <lb/>
              dis, & coni
                <lb/>
              aliter.</note>
            pyramidis, vel Coni. </s>
            <s xml:id="echoid-s9284" xml:space="preserve">Item eandem produci ex tota altitudine in tertiam par-
              <lb/>
            tem baſis: </s>
            <s xml:id="echoid-s9285" xml:space="preserve"> quod hac ratione tertia pars priſmatis, vel Conigignatur.</s>
            <s xml:id="echoid-s9286" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9287" xml:space="preserve">2. </s>
            <s xml:id="echoid-s9288" xml:space="preserve">
              <emph style="sc">Basis</emph>
            porro pyramidis, ſi triangularis eſt, cognoſcetur, vt lib. </s>
            <s xml:id="echoid-s9289" xml:space="preserve">4. </s>
            <s xml:id="echoid-s9290" xml:space="preserve">2. </s>
            <s xml:id="echoid-s9291" xml:space="preserve">tra-
              <lb/>
            ditum eſt: </s>
            <s xml:id="echoid-s9292" xml:space="preserve">ſi multilatera, reperietur, per ea, quæ eodem lib. </s>
            <s xml:id="echoid-s9293" xml:space="preserve">cap. </s>
            <s xml:id="echoid-s9294" xml:space="preserve">3. </s>
            <s xml:id="echoid-s9295" xml:space="preserve">4. </s>
            <s xml:id="echoid-s9296" xml:space="preserve">& </s>
            <s xml:id="echoid-s9297" xml:space="preserve">5. </s>
            <s xml:id="echoid-s9298" xml:space="preserve">ſcripſi-
              <lb/>
              <note symbol="d" position="right" xlink:label="note-237-05" xlink:href="note-237-05a" xml:space="preserve">1. ſchol. 7.
                <lb/>
              duodec. & 11.
                <lb/>
              duodec.</note>
            mus. </s>
            <s xml:id="echoid-s9299" xml:space="preserve">Baſis autem Coni inueſtigabitur ex cap. </s>
            <s xml:id="echoid-s9300" xml:space="preserve">7. </s>
            <s xml:id="echoid-s9301" xml:space="preserve">eiuſdem lib. </s>
            <s xml:id="echoid-s9302" xml:space="preserve">At verò altitudo
              <lb/>
            tam pyramidis, quam Coni, obtinebitur, ſi in vertice ſtatuatur planum baſi æ-
              <lb/>
            quidiſtans, ab eoque ad planum, in quo baſis, perpendicularis demittatur, ea-
              <lb/>
              <note position="right" xlink:label="note-237-06" xlink:href="note-237-06a" xml:space="preserve">Altitudo py-
                <lb/>
              ramidis, &
                <lb/>
              coni.</note>
              <handwritten xlink:label="hd-237-2" xlink:href="hd-237-2a" number="71"/>
              <handwritten xlink:label="hd-237-2" xlink:href="hd-237-2a" number="72"/>
            que exquiſitè menſuretur. </s>
            <s xml:id="echoid-s9303" xml:space="preserve">Quamuis enim eadem hæc altitudo inda
              <unsure/>
            gari poſsit
              <lb/>
            Geo metrice, ſi inclinatio vnius lateris ad baſem, & </s>
            <s xml:id="echoid-s9304" xml:space="preserve">magnitudo quoque eiuſdem
              <lb/>
            lateris cognoſcatur: </s>
            <s xml:id="echoid-s9305" xml:space="preserve">quia tamen hęc ipſa exploranda ſunt materialiter per ali-
              <lb/>
            quodinſtrumentum, præſtatipſam quoque altitudinem ſtatim per inſtrumen-
              <lb/>
            tum exquirere, pręſertim per inſtrumentum partium, quod lib. </s>
            <s xml:id="echoid-s9306" xml:space="preserve">1. </s>
            <s xml:id="echoid-s9307" xml:space="preserve">cap. </s>
            <s xml:id="echoid-s9308" xml:space="preserve">1. </s>
            <s xml:id="echoid-s9309" xml:space="preserve">deſcri
              <lb/>
            pſimus: </s>
            <s xml:id="echoid-s9310" xml:space="preserve">cum inuentio illa Geometrica difficilior ſit, procedatq; </s>
            <s xml:id="echoid-s9311" xml:space="preserve">ex inclinatio-
              <lb/>
            ne, ac latere per inſtrumentum cognitis.</s>
            <s xml:id="echoid-s9312" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9313" xml:space="preserve">3. </s>
            <s xml:id="echoid-s9314" xml:space="preserve">
              <emph style="sc">Atqve</emph>
            hæc, quę diximus, intelligivolumus tam de pyramidibus, C@-
              <lb/>
            niſque rectis, quam de obliquis, & </s>
            <s xml:id="echoid-s9315" xml:space="preserve">Scalenis.</s>
            <s xml:id="echoid-s9316" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div570" type="section" level="1" n="206">
          <head xml:id="echoid-head221" xml:space="preserve">DL AREA FRVSTI PYRA-
            <lb/>
          midis, & Coni.</head>
          <head xml:id="echoid-head222" xml:space="preserve">
            <emph style="sc">Capvt</emph>
          III.</head>
          <p>
            <s xml:id="echoid-s9317" xml:space="preserve">1. </s>
            <s xml:id="echoid-s9318" xml:space="preserve">
              <emph style="sc">FRvstvm</emph>
            pyramidis, & </s>
            <s xml:id="echoid-s9319" xml:space="preserve">Coni appello id, quod alij pyramidem decur-
              <lb/>
            tatam, & </s>
            <s xml:id="echoid-s9320" xml:space="preserve">Conum decurtatum dicunt. </s>
            <s xml:id="echoid-s9321" xml:space="preserve">Sit ergo fruſtum pyramidis
              <lb/>
            ABCDEF, cuius baſes ABC, DEF, ſint parallelæ, & </s>
            <s xml:id="echoid-s9322" xml:space="preserve">ſimiles, & </s>
            <s xml:id="echoid-s9323" xml:space="preserve">cuius
              <lb/>
            area inueſtiganda ſit. </s>
            <s xml:id="echoid-s9324" xml:space="preserve">Quod duobus modis fieri poteſt. </s>
            <s xml:id="echoid-s9325" xml:space="preserve">Primũ cogitetur integra
              <lb/>
            pyramis ABCH, cuius altitudinẽ HG, perpendicularem ad baſem (licet pyramis
              <lb/>
            actu nõ ſit integrata) ita inueniem
              <emph style="sub">9</emph>
            . </s>
            <s xml:id="echoid-s9326" xml:space="preserve"> Quoniã eſt, vt ab AB, ad AH, ita DE, ad
              <note symbol="e" position="right" xlink:label="note-237-07" xlink:href="note-237-07a" xml:space="preserve">4. ſexti.</note>
            & </s>
            <s xml:id="echoid-s9327" xml:space="preserve">permutando, vt AB, ad DE, ita AH, ad DH; </s>
            <s xml:id="echoid-s9328" xml:space="preserve">erit quoq; </s>
            <s xml:id="echoid-s9329" xml:space="preserve">diuidẽdo (ſumpta </s>
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