Clavius, Christoph, Geometria practica

Table of Notes

< >
[Note]
Page: 99
[Note]
Page: 99
[Note]
Page: 99
[Note]
Page: 99
[Note]
Page: 99
[Note]
Page: 100
[Note]
Page: 100
[Note]
Page: 100
[Note]
Page: 100
[Note]
Page: 100
[Note]
Page: 100
[Note]
Page: 101
[Note]
Page: 101
[Note]
Page: 101
[Note]
Page: 101
[Note]
Page: 102
[Note]
Page: 102
[Note]
Page: 103
[Note]
Page: 103
[Note]
Page: 103
[Note]
Page: 103
[Note]
Page: 103
[Note]
Page: 103
[Note]
Page: 103
[Note]
Page: 103
[Note]
Page: 103
[Note]
Page: 104
[Note]
Page: 104
[Note]
Page: 104
[Note]
Page: 104
< >
page |< < (252) of 450 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div705" type="section" level="1" n="247">
          <p>
            <s xml:id="echoid-s11631" xml:space="preserve">
              <pb o="252" file="282" n="282" rhead="GEOMETR. PRACT."/>
            ſecundum datam proportionem V, ad X; </s>
            <s xml:id="echoid-s11632" xml:space="preserve">& </s>
            <s xml:id="echoid-s11633" xml:space="preserve">baſis IK, ſexti trianguli (quod pun-
              <lb/>
            ctum Y, cadat in ſextam lineam QR,) ſecetur in Z, vt ſecta eſt QR, in Y; </s>
            <s xml:id="echoid-s11634" xml:space="preserve"> ita
              <note symbol="a" position="left" xlink:label="note-282-01" xlink:href="note-282-01a" xml:space="preserve">1. ſexti.</note>
            ductarecta F Z, triangulum FIK, ſectum ſit, vt ſecta eſt baſis IK, hoc eſt recta QR:
              <lb/>
            </s>
            <s xml:id="echoid-s11635" xml:space="preserve">
              <note symbol="b" position="left" xlink:label="note-282-02" xlink:href="note-282-02a" xml:space="preserve">1. hui{us}.</note>
            Erit figura ABCDEFZKA, ad figuram FZIHGF, vt LY, ad YT, hoc eſt, vt V, ad X, Et ſic de cæteris.</s>
            <s xml:id="echoid-s11636" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div716" type="section" level="1" n="248">
          <head xml:id="echoid-head273" xml:space="preserve">SCHOLIVM.</head>
          <p>
            <s xml:id="echoid-s11637" xml:space="preserve">
              <emph style="sc">His</emph>
            ritè intellectis, licebit nobis quamlibet figuram ſecare in quotuis par-
              <lb/>
              <note position="left" xlink:label="note-282-03" xlink:href="note-282-03a" xml:space="preserve">Quo pacto
                <lb/>
              figura data
                <lb/>
              ſecetur ex da-
                <lb/>
              to angulo vel
                <lb/>
              puncto in late
                <lb/>
              re, in quotuis
                <lb/>
              partes æqua-
                <lb/>
              l{es}.</note>
            tes æquales ex dato angulo, vel pũcto in latere, ex quo duci poſsint ad omnes
              <lb/>
            angulos, exceptis proximis duobus, rectæ lineæ, ita vt nullum figuræ latus ſe-
              <lb/>
            cent. </s>
            <s xml:id="echoid-s11638" xml:space="preserve">Nam ſi propoſita figura ſit ſecanda, verbi gratia in 7. </s>
            <s xml:id="echoid-s11639" xml:space="preserve">partes æquales, di-
              <lb/>
            uidemus eam ſecundum proportionem 1. </s>
            <s xml:id="echoid-s11640" xml:space="preserve">ad 6. </s>
            <s xml:id="echoid-s11641" xml:space="preserve">nimirum ſecundum ſub multi-
              <lb/>
            plicem denominatam à denominatore partium, minus vno, in quas figura diui-
              <lb/>
            denda eſt. </s>
            <s xml:id="echoid-s11642" xml:space="preserve">Ita enim prior pars erit {1/7}. </s>
            <s xml:id="echoid-s11643" xml:space="preserve">totius figuræ, cum poſterior 6. </s>
            <s xml:id="echoid-s11644" xml:space="preserve">eiuſmodi
              <lb/>
            partes complectatur. </s>
            <s xml:id="echoid-s11645" xml:space="preserve">Hanc deinde poſteriorem partem ſecabimus ſecundum
              <lb/>
            proportionem 1. </s>
            <s xml:id="echoid-s11646" xml:space="preserve">ad 5. </s>
            <s xml:id="echoid-s11647" xml:space="preserve">ita vt prior pars contineat {1/6}: </s>
            <s xml:id="echoid-s11648" xml:space="preserve">ipſius, hoc eſt, {1/7}. </s>
            <s xml:id="echoid-s11649" xml:space="preserve">totius fi-
              <lb/>
            guræ. </s>
            <s xml:id="echoid-s11650" xml:space="preserve">Poſt hæc poſteriorem huius ſecundæ diuiſionis partem partiemur ſecũ-
              <lb/>
            dum proportionem 1. </s>
            <s xml:id="echoid-s11651" xml:space="preserve">ad 4. </s>
            <s xml:id="echoid-s11652" xml:space="preserve">Ac rurſus partem huius tertiæ diuiſionis poſterio-
              <lb/>
            rem diuidemus ſecundum proportionem 1. </s>
            <s xml:id="echoid-s11653" xml:space="preserve">ad 3. </s>
            <s xml:id="echoid-s11654" xml:space="preserve">Atq; </s>
            <s xml:id="echoid-s11655" xml:space="preserve">poſteriorem huius quar-
              <lb/>
            tæ diuiſionis partem ſecabimus ſecundum proportionem 1. </s>
            <s xml:id="echoid-s11656" xml:space="preserve">ad 2. </s>
            <s xml:id="echoid-s11657" xml:space="preserve">Ac poſtremo
              <lb/>
            partem poſteriorem huius quintæ diuiſionis partiemur in duas partes æquales,
              <lb/>
            nimirum ſecundum proportionem 1. </s>
            <s xml:id="echoid-s11658" xml:space="preserve">ad 1.</s>
            <s xml:id="echoid-s11659" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11660" xml:space="preserve">
              <emph style="sc">Non</emph>
            aliter figuram irregularem, in qua à nullo angulo, vel puncto in late-
              <lb/>
            re, duci poſſunt rectæ ad angulos oppoſitos, quin aliqua figuræ latera ſecentur,
              <lb/>
            diuidere licebit in partes quotuis æquales, ex diuerſis angulis, vel punctis. </s>
            <s xml:id="echoid-s11661" xml:space="preserve">Nam
              <lb/>
            ſi verbi gratia vltima figura huius propoſitionis diuidenda ſit in 5. </s>
            <s xml:id="echoid-s11662" xml:space="preserve">partes æqua-
              <lb/>
            les; </s>
            <s xml:id="echoid-s11663" xml:space="preserve">reſecabimus ex ea, ab aliquo angulo, vel puncto, quintã partem. </s>
            <s xml:id="echoid-s11664" xml:space="preserve">Deinde
              <lb/>
            ex maiore parte complectente {4/5}. </s>
            <s xml:id="echoid-s11665" xml:space="preserve">totius figuræ, ab aliquo eius angulo, vel pun-
              <lb/>
            cto, detrahemus quartam partem: </s>
            <s xml:id="echoid-s11666" xml:space="preserve">Item tertiam partem ex maiore parte huius
              <lb/>
            diuiſionis: </s>
            <s xml:id="echoid-s11667" xml:space="preserve">Ac tandem ſemiſſem ex vltima parte poſtremæ huius diuiſionis. </s>
            <s xml:id="echoid-s11668" xml:space="preserve">Hac
              <lb/>
            enim ratione diuiſa erit tota figura in 5. </s>
            <s xml:id="echoid-s11669" xml:space="preserve">partes: </s>
            <s xml:id="echoid-s11670" xml:space="preserve">non ſecus atq; </s>
            <s xml:id="echoid-s11671" xml:space="preserve">in linea recta A B,
              <lb/>
            contingit. </s>
            <s xml:id="echoid-s11672" xml:space="preserve">Si namque eam partiri iubeamur in 7. </s>
            <s xml:id="echoid-s11673" xml:space="preserve">partes æquales, efficiemus
              <lb/>
              <figure xlink:label="fig-282-01" xlink:href="fig-282-01a" number="186">
                <image file="282-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/282-01"/>
              </figure>
            id, ſi primo loco ſeptimam partem AC, detrahemus; </s>
            <s xml:id="echoid-s11674" xml:space="preserve">deinde {1/6}. </s>
            <s xml:id="echoid-s11675" xml:space="preserve">C D, ex reliqua
              <lb/>
            linea CB; </s>
            <s xml:id="echoid-s11676" xml:space="preserve">& </s>
            <s xml:id="echoid-s11677" xml:space="preserve">ex reliqua DB, quintam partem DE: </s>
            <s xml:id="echoid-s11678" xml:space="preserve">& </s>
            <s xml:id="echoid-s11679" xml:space="preserve">ex reliqua EB, quartam par-
              <lb/>
            tem DE: </s>
            <s xml:id="echoid-s11680" xml:space="preserve">& </s>
            <s xml:id="echoid-s11681" xml:space="preserve">ex reliqua FB, tertiam partem F G: </s>
            <s xml:id="echoid-s11682" xml:space="preserve">Ac deniq; </s>
            <s xml:id="echoid-s11683" xml:space="preserve">relin quam lineam GB,
              <lb/>
            bifariam ſecabimus in H, hoc eſt, ſemiſſem GH, ex ea abſcindemus.</s>
            <s xml:id="echoid-s11684" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11685" xml:space="preserve">
              <emph style="sc">Facilivs</emph>
            idem exequemur, quando ex dato angulo, vel puncto, duci
              <lb/>
            poſſunt rectæ ad omnes angulos, duo bus proximis exceptis, nullum figuræ la-
              <lb/>
            tus ſecantes, hacratione. </s>
            <s xml:id="echoid-s11686" xml:space="preserve">Lineam ex rectis, quę triangulis figuræ proportiona-
              <lb/>
            les ſunt, cõflatã ſecabim
              <emph style="sub">9</emph>
            in tot partes æquales, in quot figurã partiriiubemur. </s>
            <s xml:id="echoid-s11687" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum