Clavius, Christoph, Geometria practica

Table of figures

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        <div xml:id="echoid-div677" type="section" level="1" n="238">
          <p>
            <s xml:id="echoid-s10985" xml:space="preserve">
              <pb o="235" file="265" n="265" rhead="LIBER QVINTVS."/>
            latera aquæ in aſſeribus arcæ, vt habeatur altitudo aquæ vſque ad arcæ fundũ:
              <lb/>
            </s>
            <s xml:id="echoid-s10986" xml:space="preserve">Extracto deinde corpore, ita tamen, vt nihil aquæ extra arcam cadat, notentur
              <lb/>
            rurſum latera aquæ, poſtquam quieuerit. </s>
            <s xml:id="echoid-s10987" xml:space="preserve">Quod ſi per cap. </s>
            <s xml:id="echoid-s10988" xml:space="preserve">1. </s>
            <s xml:id="echoid-s10989" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s10990" xml:space="preserve">metia-
              <lb/>
            mur duo parallelepipeda, quorũ baſis communis eſt arcæ fundus, ſiue baſis, al-
              <lb/>
            titudines vero rectæ à lateribus aquæ notatis vſque ad baſem, & </s>
            <s xml:id="echoid-s10991" xml:space="preserve">minus à maio-
              <lb/>
            re ſubtrahamus, relinquetur parallelepipedũ ſoliditati corporis propoſiti o-
              <lb/>
            mnino æquale. </s>
            <s xml:id="echoid-s10992" xml:space="preserve">quod parallelepipedũ etiam conſequeris, ſi altitu dinem inter
              <lb/>
            latera aquæ bis notata duces in baſem arcæ. </s>
            <s xml:id="echoid-s10993" xml:space="preserve">Sunt, qui infuſa a qua in arcam,@la-
              <lb/>
            tera eius in aſſeribus primo loco notent. </s>
            <s xml:id="echoid-s10994" xml:space="preserve">Deinde impoſito corpore, eiuſdem a-
              <lb/>
            quæ latera ſignent. </s>
            <s xml:id="echoid-s10995" xml:space="preserve">Si enim altitudo inter poſteriora latera, ac priora ducatur in
              <lb/>
            baſem arcæ, pro ducetur ſoliditas corporis impoſiti.</s>
            <s xml:id="echoid-s10996" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10997" xml:space="preserve">2. </s>
            <s xml:id="echoid-s10998" xml:space="preserve">
              <emph style="sc">Pro</emph>
            vrnis, at que amphoris, ſiue eæ lapideæ ſint, ſiue cretaceæ, ita fa cie-
              <lb/>
            mus. </s>
            <s xml:id="echoid-s10999" xml:space="preserve">Impleatur vas arena, & </s>
            <s xml:id="echoid-s11000" xml:space="preserve">eius orificiumita obturetur, vt a qua ingredi nul-
              <lb/>
            lo modo poſsit. </s>
            <s xml:id="echoid-s11001" xml:space="preserve">Impoſito deinde vaſe in aqua intra arcam contenta, ac ſi eſſet
              <lb/>
            corpus quod piam irregulare, inueſtigetur eius ſoliditas, vt Num. </s>
            <s xml:id="echoid-s11002" xml:space="preserve">1. </s>
            <s xml:id="echoid-s11003" xml:space="preserve">diximus. </s>
            <s xml:id="echoid-s11004" xml:space="preserve">De-
              <lb/>
            inde extra cta arena, notentur latera aquæ, antequam vas vacuum impo natur.
              <lb/>
            </s>
            <s xml:id="echoid-s11005" xml:space="preserve">Impoſito denique vaſe vacuo, ſignentur iterum latera a quæ. </s>
            <s xml:id="echoid-s11006" xml:space="preserve">Si namque altitu-
              <lb/>
            do inter poſteriora, ac priora latera multiplicetur per baſem arcæ: </s>
            <s xml:id="echoid-s11007" xml:space="preserve">pro creabitur
              <lb/>
            ſoliditas ſolius vaſis: </s>
            <s xml:id="echoid-s11008" xml:space="preserve">quæ detracta ex priori ſoliditate, notamrelin quet vaſis
              <lb/>
            @apacitatem.</s>
            <s xml:id="echoid-s11009" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div679" type="section" level="1" n="239">
          <head xml:id="echoid-head262" xml:space="preserve">DE SVPERFICIE CONVEXA
            <lb/>
          coni & cylindri recti.</head>
          <head xml:id="echoid-head263" xml:space="preserve">
            <emph style="sc">Capvt</emph>
          XII.</head>
          <p>
            <s xml:id="echoid-s11010" xml:space="preserve">1. </s>
            <s xml:id="echoid-s11011" xml:space="preserve">
              <emph style="sc">QVoniam</emph>
            ex Archimede demonſtrauimus, qua ratione ſuperficies
              <lb/>
              <note position="right" xlink:label="note-265-01" xlink:href="note-265-01a" xml:space="preserve">Superficies co-
                <lb/>
              nica, dempta
                <lb/>
              baſe, cui cir-
                <lb/>
              culo ſit æqua-
                <lb/>
              lis.</note>
            conuexa, ſphæræ eiuſque portionum inueſtiganda ſit: </s>
            <s xml:id="echoid-s11012" xml:space="preserve">non deerit for-
              <lb/>
            taſſe, qui idem deſi deret in cono, ac cylindro recto. </s>
            <s xml:id="echoid-s11013" xml:space="preserve">quod ex ijs, quæ
              <lb/>
            ab eo dem Archimede in lib. </s>
            <s xml:id="echoid-s11014" xml:space="preserve">1. </s>
            <s xml:id="echoid-s11015" xml:space="preserve">de ſphęra, & </s>
            <s xml:id="echoid-s11016" xml:space="preserve">cylindro demonſtrata ſunt, obtine-
              <lb/>
            bit hoc modo. </s>
            <s xml:id="echoid-s11017" xml:space="preserve">Propoſito cono recto quo cunque, erit eius ſuperficies conue-
              <lb/>
            xa conica, ſecluſa baſe, æqualis circulo, cuius ſemidiameter eſt linea media pro-
              <lb/>
            portionalis inter latus coni, & </s>
            <s xml:id="echoid-s11018" xml:space="preserve">ſemidiametrum baſis eiuſdem coni, ex propoſ.
              <lb/>
            </s>
            <s xml:id="echoid-s11019" xml:space="preserve">
              <note position="right" xlink:label="note-265-02" xlink:href="note-265-02a" xml:space="preserve">Superficies
                <lb/>
              fruſti coni,
                <lb/>
              demptis baſi-
                <lb/>
              bus, cui circu-
                <lb/>
              lo æqualis ſit.</note>
            14. </s>
            <s xml:id="echoid-s11020" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s11021" xml:space="preserve">1. </s>
            <s xml:id="echoid-s11022" xml:space="preserve">Archimedis de ſphęra, & </s>
            <s xml:id="echoid-s11023" xml:space="preserve">cylindro.</s>
            <s xml:id="echoid-s11024" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11025" xml:space="preserve">2. </s>
            <s xml:id="echoid-s11026" xml:space="preserve">
              <emph style="sc">Qvod</emph>
            ſi conus rectus ſecetur plano, quod baſi æquidiſtet, erit ſuperfi-
              <lb/>
            cies conuexa fruſti coni, demptis baſibus, æqualis circulo, cuius ſemidiameter
              <lb/>
            eſt linea media proportionalis inter latus conicum fruſti, & </s>
            <s xml:id="echoid-s11027" xml:space="preserve">rectam ex ſemidia-
              <lb/>
            metris duarũ baſum cõflatã, ex ꝓpoſ. </s>
            <s xml:id="echoid-s11028" xml:space="preserve">16. </s>
            <s xml:id="echoid-s11029" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s11030" xml:space="preserve">1. </s>
            <s xml:id="echoid-s11031" xml:space="preserve">Archime. </s>
            <s xml:id="echoid-s11032" xml:space="preserve">de ſphęra, & </s>
            <s xml:id="echoid-s11033" xml:space="preserve">cylindro.
              <lb/>
            </s>
            <s xml:id="echoid-s11034" xml:space="preserve">
              <note position="right" xlink:label="note-265-03" xlink:href="note-265-03a" xml:space="preserve">Propo tio co-
                <lb/>
              nicæ ſuperfi-
                <lb/>
              ciei ad ſuam
                <lb/>
              baſem.</note>
            </s>
          </p>
          <p>
            <s xml:id="echoid-s11035" xml:space="preserve">
              <emph style="sc">Item</emph>
            ſuperficies conica coni recti ad ſuam baſem, proportionẽ habet ean-
              <lb/>
            dem, quam latus coni ad ſemidiametrum baſis coni eiuſdem, ex propoſ. </s>
            <s xml:id="echoid-s11036" xml:space="preserve">15. </s>
            <s xml:id="echoid-s11037" xml:space="preserve">lib.
              <lb/>
            </s>
            <s xml:id="echoid-s11038" xml:space="preserve">1. </s>
            <s xml:id="echoid-s11039" xml:space="preserve">Archimedis de ſphæra, & </s>
            <s xml:id="echoid-s11040" xml:space="preserve">cylindro.</s>
            <s xml:id="echoid-s11041" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11042" xml:space="preserve">4. </s>
            <s xml:id="echoid-s11043" xml:space="preserve">
              <emph style="sc">Deniqve</emph>
            ſuperficies conuexa cylindrirecti, demptis baſibus, æqualis
              <lb/>
              <note position="right" xlink:label="note-265-04" xlink:href="note-265-04a" xml:space="preserve">Superficies cy
                <lb/>
              lindrica dem
                <lb/>
              ptis baſibus,
                <lb/>
              cui circulo ſit
                <lb/>
              æqualis.</note>
            eſt circulo, cuius ſemidia meter eſt linea media proportio nalis inter latus cylin-
              <lb/>
            dri, & </s>
            <s xml:id="echoid-s11044" xml:space="preserve">diametrũ baſis cylin dri eiuſdem, ex propoſ. </s>
            <s xml:id="echoid-s11045" xml:space="preserve">13. </s>
            <s xml:id="echoid-s11046" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s11047" xml:space="preserve">1. </s>
            <s xml:id="echoid-s11048" xml:space="preserve">Archimedis de ſphę-
              <lb/>
            ra & </s>
            <s xml:id="echoid-s11049" xml:space="preserve">cylindro.</s>
            <s xml:id="echoid-s11050" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div683" type="section" level="1" n="240">
          <head xml:id="echoid-head264" xml:space="preserve">FINIS LIBRI QVINTI.</head>
        </div>
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