Clavius, Christoph, Geometria practica

Table of figures

< >
[Figure 111]
[Figure 112]
[Figure 113]
[Figure 114]
[Figure 115]
[Figure 116]
[Figure 117]
[Figure 118]
[Figure 119]
[Figure 120]
[Figure 121]
[Figure 122]
[Figure 123]
[Figure 124]
[Figure 125]
[Figure 126]
[Figure 127]
[Figure 128]
[Figure 129]
[Figure 130]
[Figure 131]
[Figure 132]
[Figure 133]
[Figure 134]
[Figure 135]
[Figure 136]
[Figure 137]
[Figure 138]
[Figure 139]
[Figure 140]
< >
page |< < (171) of 450 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div455" type="section" level="1" n="173">
          <pb o="171" file="201" n="201" rhead="LIBER QVARTVS."/>
        </div>
        <div xml:id="echoid-div462" type="section" level="1" n="174">
          <head xml:id="echoid-head178" xml:space="preserve">DE AREA MVLTIL ATERARVM
            <lb/>
          figurarum irregularium.</head>
          <head xml:id="echoid-head179" xml:space="preserve">
            <emph style="sc">Capvt</emph>
          IV.</head>
          <p>
            <s xml:id="echoid-s7118" xml:space="preserve">1. </s>
            <s xml:id="echoid-s7119" xml:space="preserve">FIGVRAS multilateras irregulares, quæ videlicet plura latera habent
              <lb/>
              <note position="right" xlink:label="note-201-01" xlink:href="note-201-01a" xml:space="preserve">Area multi
                <lb/>
              lateræ figuræ.</note>
            inæqualia, quam quatuor, etiamſi valdè irregulares ſint, metiemur, vt
              <lb/>
            trapezia irregularia, reſoluendo nimirum illasin triangula, & </s>
            <s xml:id="echoid-s7120" xml:space="preserve">ſingulorũ
              <lb/>
            triangulorum areas inueſtigando. </s>
            <s xml:id="echoid-s7121" xml:space="preserve">Nam omnes hæ areæ in vnam ſummam col-
              <lb/>
            lectæ æquales ſunt areæ totius figuræ propoſitæ. </s>
            <s xml:id="echoid-s7122" xml:space="preserve">Vt ſi figura ſeptem laterum A-
              <lb/>
            BCDEFG, reſoluatur in quin que triangula ABG, GBD, DBC, DEF, FDG, ita
              <lb/>
              <note position="right" xlink:label="note-201-02" xlink:href="note-201-02a" xml:space="preserve">Quando figu-
                <lb/>
              ra in triangu-
                <lb/>
              la reſolui po-
                <lb/>
              teſt, quo m@-
                <lb/>
              do ei{us} area
                <lb/>
              colligatur.</note>
            vteorum latera ſe mutuo non interſecent, in quirendæ ſunt areæ ſingulorũ hoc
              <lb/>
              <figure xlink:label="fig-201-01" xlink:href="fig-201-01a" number="129">
                <image file="201-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/201-01"/>
              </figure>
            modo. </s>
            <s xml:id="echoid-s7123" xml:space="preserve">Quando omnia latera triangulorum nota effici poſſunt per aliquam
              <lb/>
            menſuram, ſiue figura agrum aliquem repræſentet, ſiue in charta ſolum ſit de-
              <lb/>
            ſcripta, demittantur ex angulis ad latera oppoſita perpendiculares AH, DI, CK,
              <lb/>
            DM, FL, ſingulæ in ſingulis triangulis. </s>
            <s xml:id="echoid-s7124" xml:space="preserve">Deinde in triangulo ABG,
              <note symbol="a" position="right" xlink:label="note-201-03" xlink:href="note-201-03a" xml:space="preserve">9. triang. re-
                <lb/>
              ctil.</note>
            ex tribus lateribus notis ſegmenta B H, H G; </s>
            <s xml:id="echoid-s7125" xml:space="preserve">& </s>
            <s xml:id="echoid-s7126" xml:space="preserve">ex his perpendicularis A H, vt
              <lb/>
            cap. </s>
            <s xml:id="echoid-s7127" xml:space="preserve">2. </s>
            <s xml:id="echoid-s7128" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s7129" xml:space="preserve">Num. </s>
            <s xml:id="echoid-s7130" xml:space="preserve">2. </s>
            <s xml:id="echoid-s7131" xml:space="preserve">declarauimus. </s>
            <s xml:id="echoid-s7132" xml:space="preserve">Nam AH, in ſemiſſem baſis B G, ducta
              <lb/>
            producet aream trianguli A B G. </s>
            <s xml:id="echoid-s7133" xml:space="preserve">Eadem que ratione aliorum triangulorum areæ
              <lb/>
            perueſtigentur: </s>
            <s xml:id="echoid-s7134" xml:space="preserve">atque omnes areæ in vnam redigantur ſummam, vt area toti-
              <lb/>
            us figuræ habeatur. </s>
            <s xml:id="echoid-s7135" xml:space="preserve">Quod ſi malueris, poteris omnium triangulorum areas in-
              <lb/>
            dagare ex tribus lateribus cognitis, per ea, quæ capit. </s>
            <s xml:id="echoid-s7136" xml:space="preserve">2. </s>
            <s xml:id="echoid-s7137" xml:space="preserve">Numer. </s>
            <s xml:id="echoid-s7138" xml:space="preserve">1. </s>
            <s xml:id="echoid-s7139" xml:space="preserve">ſcripſimus,
              <lb/>
            etiamſi neque perpendiculares ductæ ſint, neque ſegmenta B H, G H, in-
              <lb/>
            uenta.</s>
            <s xml:id="echoid-s7140" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7141" xml:space="preserve">2. </s>
            <s xml:id="echoid-s7142" xml:space="preserve">
              <emph style="sc">Qvando</emph>
            latera triangulorum interiora menſurarinequeunt, immo ne-
              <lb/>
              <note position="right" xlink:label="note-201-04" xlink:href="note-201-04a" xml:space="preserve">Quando figu-
                <lb/>
              ra in triangu-
                <lb/>
              la reſolui non
                <lb/>
              poteſt quo mo
                <lb/>
              do ei{us} area
                <lb/>
              deprehenda-
                <lb/>
              tur.</note>
            que duci, vt non raro accidit in campis, aut agris, qui vel propter arbores, vel
              <lb/>
            paludes interiectas, rectis itineribus pertranſirinon poſſunt; </s>
            <s xml:id="echoid-s7143" xml:space="preserve">alia ratione ſco-
              <lb/>
            pum attingemus, hac videlicet. </s>
            <s xml:id="echoid-s7144" xml:space="preserve">Cognitis lateribus figuram ambientibus
              <lb/>
            per aliquam menſuram, inueſtigentur quoque anguli ab ipſis comprehenſi
              <lb/>
            beneficio quadrantis alicuius in gradus diuiſi. </s>
            <s xml:id="echoid-s7145" xml:space="preserve">In propoſita figura angulus
              <lb/>
            C D E, indagandus non eſt, quod ſit extra figuram. </s>
            <s xml:id="echoid-s7146" xml:space="preserve">Reſoluta deinde figura
              <lb/>
            mente. </s>
            <s xml:id="echoid-s7147" xml:space="preserve">aut cogitatione in triangula, ac ſi latera interiora ducta eſſent, vt p@us:</s>
            <s xml:id="echoid-s7148" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>