Clavius, Christoph, Geometria practica

Table of figures

< >
[Figure 291]
Page: 402
[Figure 292]
Page: 403
[Figure 293]
Page: 404
[Figure 294]
Page: 445
< >
page |< < (261) of 450 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div744" type="section" level="1" n="253">
          <pb o="261" file="291" n="291" rhead="LIBER SEXTVS."/>
        </div>
        <div xml:id="echoid-div746" type="section" level="1" n="254">
          <head xml:id="echoid-head279" xml:space="preserve">THEOR. 3. PROPOS. 7.</head>
          <p>
            <s xml:id="echoid-s12020" xml:space="preserve">SI in triangulo baſi parallela ducatur, & </s>
            <s xml:id="echoid-s12021" xml:space="preserve">extrema parallelarum rectis
              <lb/>
            iungantur ſe ſeinterſecantibus: </s>
            <s xml:id="echoid-s12022" xml:space="preserve">habebit vtriuſuis harum rectarum ſe-
              <lb/>
            gmentur ab angulo incipiens ad reliquum in latere terminatum ean-
              <lb/>
            dem proportionem, quam latus ab illa recta diuiſum ad partem eius
              <lb/>
            ſuperiorem. </s>
            <s xml:id="echoid-s12023" xml:space="preserve">Recta autem ex tertio angulo per interſectionem dicta-
              <lb/>
            rum rectarum extenſa ſecabit vtramque parallelam bifariam.</s>
            <s xml:id="echoid-s12024" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12025" xml:space="preserve">
              <emph style="sc">In</emph>
            triangulo ABC, ducta ſit DE, baſi BC, parallela, & </s>
            <s xml:id="echoid-s12026" xml:space="preserve">iunctæ rectæ BE, CD,
              <lb/>
            ſeinterſecent in F. </s>
            <s xml:id="echoid-s12027" xml:space="preserve">Dico eſſe BF, ad FE, vt AC, ad AE: </s>
            <s xml:id="echoid-s12028" xml:space="preserve">Item CF, ad FD, vt AB,
              <lb/>
            ad AD. </s>
            <s xml:id="echoid-s12029" xml:space="preserve">Et iunctam rectam AF, ſecare parallelas DE, BC, bi-
              <lb/>
            fariam in G, & </s>
            <s xml:id="echoid-s12030" xml:space="preserve">H. </s>
            <s xml:id="echoid-s12031" xml:space="preserve"> Quoniam enim triangula B D C, C E B,
              <figure xlink:label="fig-291-01" xlink:href="fig-291-01a" number="194">
                <image file="291-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/291-01"/>
              </figure>
              <note symbol="a" position="right" xlink:label="note-291-01" xlink:href="note-291-01a" xml:space="preserve">37. primi.</note>
            qualia ſunt; </s>
            <s xml:id="echoid-s12032" xml:space="preserve">ablato communi BFC, reliqua BDF, CEF, æqua-
              <lb/>
            lia quoque erunt. </s>
            <s xml:id="echoid-s12033" xml:space="preserve"> Quia verò eſt, vt B D, ad D A, ita C E,
              <note symbol="b" position="right" xlink:label="note-291-02" xlink:href="note-291-02a" xml:space="preserve">2. ſexti.</note>
            EA: </s>
            <s xml:id="echoid-s12034" xml:space="preserve"> Vt autem BD, ad DA, ita eſt triangulum BFD, ad
              <note symbol="c" position="right" xlink:label="note-291-03" xlink:href="note-291-03a" xml:space="preserve">1. ſexti.</note>
            gulum AFD: </s>
            <s xml:id="echoid-s12035" xml:space="preserve">Et vt CE, ad EA, ita triangulum CFE, ad trian-
              <lb/>
            gulum AFE; </s>
            <s xml:id="echoid-s12036" xml:space="preserve">erit quoque triangulum BFD, ad triangulum AFD, vt triangulum
              <lb/>
            CFE, ad triangulum AFE. </s>
            <s xml:id="echoid-s12037" xml:space="preserve">Cum ergo triangulum BFD, triangulo CFE, oſten-
              <lb/>
            ſum ſit æquale; </s>
            <s xml:id="echoid-s12038" xml:space="preserve"> erit quoque triangulum AFD, triangulo AFE, æquale. </s>
            <s xml:id="echoid-s12039" xml:space="preserve">
              <note symbol="d" position="right" xlink:label="note-291-04" xlink:href="note-291-04a" xml:space="preserve">14. quinti.</note>
            tur DE, in G, ſecta eſt bifariam: </s>
            <s xml:id="echoid-s12040" xml:space="preserve"> ac proinde & </s>
            <s xml:id="echoid-s12041" xml:space="preserve">parallela BC, ſecta erit
              <note symbol="e" position="right" xlink:label="note-291-05" xlink:href="note-291-05a" xml:space="preserve">6. hui{us}.</note>
            in H. </s>
            <s xml:id="echoid-s12042" xml:space="preserve"> Et quoniam triangulum AFB, ad triangula æqualia AFD, AFE,
              <note symbol="f" position="right" xlink:label="note-291-06" xlink:href="note-291-06a" xml:space="preserve">ſchol. 4. ſexti.</note>
            habetproportionem; </s>
            <s xml:id="echoid-s12043" xml:space="preserve"> eſt que vt AFB, ad AFD, ita AB, ad AD: </s>
            <s xml:id="echoid-s12044" xml:space="preserve">Et vt AFB,
              <note symbol="g" position="right" xlink:label="note-291-07" xlink:href="note-291-07a" xml:space="preserve">7. quinti.</note>
            AFE, ita BF, ad FE: </s>
            <s xml:id="echoid-s12045" xml:space="preserve">erit quoque BA, ad AD, ideoque AC, ad AE, vt BF, ad FE:
              <lb/>
            </s>
            <s xml:id="echoid-s12046" xml:space="preserve">
              <note symbol="h" position="right" xlink:label="note-291-08" xlink:href="note-291-08a" xml:space="preserve">1. ſexti.</note>
            Eademque ratione erit A B, ad A D, vel A C, ad A E, vt C F, ad F D. </s>
            <s xml:id="echoid-s12047" xml:space="preserve">quod
              <lb/>
              <note symbol="i" position="right" xlink:label="note-291-09" xlink:href="note-291-09a" xml:space="preserve">1. ſexti.</note>
            etiam inde patet; </s>
            <s xml:id="echoid-s12048" xml:space="preserve"> cum ſit vt C F, ad F D, ita C F E, ad D E F, hoc eſt, ita B F
              <note symbol="k" position="right" xlink:label="note-291-10" xlink:href="note-291-10a" xml:space="preserve">1. ſexti.</note>
            ipſi CFE, æquale ad idem DEF, hoc eſt, ita BF, ad FE. </s>
            <s xml:id="echoid-s12049" xml:space="preserve">quod erat dum.</s>
            <s xml:id="echoid-s12050" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div748" type="section" level="1" n="255">
          <head xml:id="echoid-head280" xml:space="preserve">THEOR. 4. PROPOS. 8.</head>
          <p>
            <s xml:id="echoid-s12051" xml:space="preserve">SI in triangulo à duobus angulis duæ rectæ ducantur ad media puncta
              <lb/>
            oppoſitorum laterum: </s>
            <s xml:id="echoid-s12052" xml:space="preserve">Recta ex angulo reliquo perinterſectionem
              <lb/>
            earum deducta ſecat quoque reliquum latus bifariam. </s>
            <s xml:id="echoid-s12053" xml:space="preserve">Cuiuslibet au-
              <lb/>
            tem illarum trium linearum ſegmentum prope angulum adreliquum
              <lb/>
            ſegmentum duplam habet proportionem. </s>
            <s xml:id="echoid-s12054" xml:space="preserve">Triangulum denique per
              <lb/>
            rectas ab interſectione ad angulos ductas in tria triangula æqualia di-
              <lb/>
            uiditur.</s>
            <s xml:id="echoid-s12055" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12056" xml:space="preserve">
              <emph style="sc">In</emph>
            triangulo præcedentis propoſ. </s>
            <s xml:id="echoid-s12057" xml:space="preserve">ABC, duærectæ BE, CD,
              <lb/>
            ſecent latera AC, AB, bifariamin E, D, ſe autem mutuo interſe-
              <lb/>
              <figure xlink:label="fig-291-02" xlink:href="fig-291-02a" number="195">
                <image file="291-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/291-02"/>
              </figure>
            cet in F. </s>
            <s xml:id="echoid-s12058" xml:space="preserve">Dico rectam ductam AF, ſecare quoque latus BC, bi-
              <lb/>
            fariamin H, &</s>
            <s xml:id="echoid-s12059" xml:space="preserve">c. </s>
            <s xml:id="echoid-s12060" xml:space="preserve"> Iuncta enim recta D E, parallela erit ipſi B
              <note symbol="l" position="right" xlink:label="note-291-11" xlink:href="note-291-11a" xml:space="preserve">2. ſexti.</note>
            cum ſecet latera A B, A C, proportionaliter, in partes videlicet
              <lb/>
            æquales: </s>
            <s xml:id="echoid-s12061" xml:space="preserve"> Quamobrem A F, vtramque parallelam D E, B
              <note symbol="m" position="right" xlink:label="note-291-12" xlink:href="note-291-12a" xml:space="preserve">7. hui{us}.</note>
            bifariam ſecabit. </s>
            <s xml:id="echoid-s12062" xml:space="preserve">quod eſt primum.</s>
            <s xml:id="echoid-s12063" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum