Clavius, Christoph, Gnomonices libri octo, in quibus non solum horologiorum solariu[m], sed aliarum quo[quam] rerum, quae ex gnomonis umbra cognosci possunt, descriptiones geometricè demonstrantur

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        <div xml:id="echoid-div347" type="section" level="1" n="127">
          <p>
            <s xml:id="echoid-s5817" xml:space="preserve">
              <pb o="101" file="0121" n="121" rhead="LIBER PRIMVS."/>
            tem; </s>
            <s xml:id="echoid-s5818" xml:space="preserve">inclinatio verò ad Meridianum ſit complementum declinationis eiuſdem plani à Vertica-
              <lb/>
            li circulo. </s>
            <s xml:id="echoid-s5819" xml:space="preserve">In poſteriori autem planum inclinatum E F, tranſit per communes ſectiones A, C, Ho-
              <lb/>
            rizontis, & </s>
            <s xml:id="echoid-s5820" xml:space="preserve">Meridiani, hoc eſt, per polos Verticalis, rectumq́; </s>
            <s xml:id="echoid-s5821" xml:space="preserve">eſt propterea ad Verticalem. </s>
            <s xml:id="echoid-s5822" xml:space="preserve">Vnde
              <lb/>
            ſi loco C, ſumatur litera G, vbi planum inclinatum ſecat Meridianũ, (ita vtarcus Meridiani G H,
              <lb/>
            inter planum & </s>
            <s xml:id="echoid-s5823" xml:space="preserve">polum æqualis ſit altitudini poli ſupra Horizontem, inclinatio verò plani ad
              <lb/>
            Meridianum ſit complementum inclinationis einſdem plani ad Horizontem) erit ſemper eadem
              <lb/>
            proportio ſinus totius, ſeu anguli recti I, ad ſinum arcus G H, quæ ſinus anguli G, ad ſinum arcus
              <lb/>
            H I, &</s>
            <s xml:id="echoid-s5824" xml:space="preserve">c. </s>
            <s xml:id="echoid-s5825" xml:space="preserve">vt demonſtratum eſt.</s>
            <s xml:id="echoid-s5826" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5827" xml:space="preserve">EXEMPLVM prioris. </s>
            <s xml:id="echoid-s5828" xml:space="preserve">Ponatur planum per verticem tranſiens declinare à Verticali circu
              <lb/>
              <note position="right" xlink:label="note-0121-01" xlink:href="note-0121-01a" xml:space="preserve">Exemplum.</note>
            lo grad. </s>
            <s xml:id="echoid-s5829" xml:space="preserve">30. </s>
            <s xml:id="echoid-s5830" xml:space="preserve">& </s>
            <s xml:id="echoid-s5831" xml:space="preserve">idcirco à Meridiano grad. </s>
            <s xml:id="echoid-s5832" xml:space="preserve">60. </s>
            <s xml:id="echoid-s5833" xml:space="preserve">Si igitur fiat vt 100000. </s>
            <s xml:id="echoid-s5834" xml:space="preserve">ſinus totus ad 74314. </s>
            <s xml:id="echoid-s5835" xml:space="preserve">ſinum
              <lb/>
              <note position="left" xlink:label="note-0121-02" xlink:href="note-0121-02a" xml:space="preserve">10</note>
            arcus G H, inter planum, & </s>
            <s xml:id="echoid-s5836" xml:space="preserve">polum interiecti, ita 86602. </s>
            <s xml:id="echoid-s5837" xml:space="preserve">ſinus inclinationis ad Meridianum, ad
              <lb/>
            aliud, inuenietur hic ferè ſinus 64357. </s>
            <s xml:id="echoid-s5838" xml:space="preserve">cuius arcus grad. </s>
            <s xml:id="echoid-s5839" xml:space="preserve">40. </s>
            <s xml:id="echoid-s5840" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s5841" xml:space="preserve">3. </s>
            <s xml:id="echoid-s5842" xml:space="preserve">paulo amplius, oſtendet altitu
              <lb/>
            dinem poli ſupra planum propoſitum. </s>
            <s xml:id="echoid-s5843" xml:space="preserve">Rurſus pro exemplo poſterioris, ponatur planum trãſiens
              <lb/>
            per communes ſectiones Horizontis, ac Meridiani declinare ab Horizonte grad. </s>
            <s xml:id="echoid-s5844" xml:space="preserve">30. </s>
            <s xml:id="echoid-s5845" xml:space="preserve">& </s>
            <s xml:id="echoid-s5846" xml:space="preserve">idcirco à
              <lb/>
            Meridiano grad. </s>
            <s xml:id="echoid-s5847" xml:space="preserve">60. </s>
            <s xml:id="echoid-s5848" xml:space="preserve">Itaque ſi fiat, vt 100000. </s>
            <s xml:id="echoid-s5849" xml:space="preserve">ſinus totus, ad 66913. </s>
            <s xml:id="echoid-s5850" xml:space="preserve">ſinum arcus G H, inter pla
              <lb/>
            num, & </s>
            <s xml:id="echoid-s5851" xml:space="preserve">polum interpoſiti, ita 86602. </s>
            <s xml:id="echoid-s5852" xml:space="preserve">ſinus inclinationis ad Meridianum, ad aliud, inuenietur
              <lb/>
            hic propemodum ſinus 57948, cuius arcus grad. </s>
            <s xml:id="echoid-s5853" xml:space="preserve">35. </s>
            <s xml:id="echoid-s5854" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s5855" xml:space="preserve">25. </s>
            <s xml:id="echoid-s5856" xml:space="preserve">altitudinem poli ſupra propoſitum
              <lb/>
            planum indicabit.</s>
            <s xml:id="echoid-s5857" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5858" xml:space="preserve">QVOD ſi planum ad Horizontem tantum ſit inclinatum, hoc eſt, ſi tranſeat per communes
              <lb/>
              <note position="right" xlink:label="note-0121-03" xlink:href="note-0121-03a" xml:space="preserve">Quando planũ
                <lb/>
              ad Horizon@em
                <lb/>
              tantum eſt incli
                <lb/>
              na@um.</note>
            ſectiones Horizontis, ac Verticalis, rectumq́; </s>
            <s xml:id="echoid-s5859" xml:space="preserve">ſit ad Meridianum, erit ipſe arcus Meridiani inter
              <lb/>
              <note position="left" xlink:label="note-0121-04" xlink:href="note-0121-04a" xml:space="preserve">20</note>
            planum, & </s>
            <s xml:id="echoid-s5860" xml:space="preserve">polum poſitus, altitudo poli ſupra Horizontem, vt ap paret ex figura corollarij propoſ.
              <lb/>
            </s>
            <s xml:id="echoid-s5861" xml:space="preserve">præcedentis. </s>
            <s xml:id="echoid-s5862" xml:space="preserve">Dato igitur plano vel ad Meridianum, vel ad Horizontem inclinato, quanta ſit poli
              <lb/>
            altitudo ſupra ipſum, deprehendimus. </s>
            <s xml:id="echoid-s5863" xml:space="preserve">Quod faciendum erat.</s>
            <s xml:id="echoid-s5864" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div354" type="section" level="1" n="128">
          <head xml:id="echoid-head131" xml:space="preserve">PROBLEMA. 9. PROPOSITIO 30.</head>
          <p>
            <s xml:id="echoid-s5865" xml:space="preserve">DATO plano ad Meridianum inclinato, quantus ſit interceptus
              <lb/>
            arcus ipſius inter Meridianum, & </s>
            <s xml:id="echoid-s5866" xml:space="preserve">circulum maximum, qui per polos
              <lb/>
              <note position="left" xlink:label="note-0121-05" xlink:href="note-0121-05a" xml:space="preserve">30</note>
            ipſius, & </s>
            <s xml:id="echoid-s5867" xml:space="preserve">per polos mundi ducitur, altitudinemq́; </s>
            <s xml:id="echoid-s5868" xml:space="preserve">poli ſupra ipſum di-
              <lb/>
            metitur, tanquam proprius eius Meridianus: </s>
            <s xml:id="echoid-s5869" xml:space="preserve">Et quantum circulus hic
              <lb/>
            maximus ad Meridianum Horizontis, ſeu loci, in quo planum inclina-
              <lb/>
            tum conſideratur, in clinatus ſit, inuenire.</s>
            <s xml:id="echoid-s5870" xml:space="preserve"/>
          </p>
          <figure number="87">
            <image file="0121-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0121-01"/>
          </figure>
          <note position="left" xml:space="preserve">40</note>
          <note position="left" xml:space="preserve">50</note>
          <p>
            <s xml:id="echoid-s5871" xml:space="preserve">SIT Horizon A B C D; </s>
            <s xml:id="echoid-s5872" xml:space="preserve">Meridianus A C; </s>
            <s xml:id="echoid-s5873" xml:space="preserve">planum inclinatum ad Meridianum E F, ſecans
              <lb/>
            Meridianum in G; </s>
            <s xml:id="echoid-s5874" xml:space="preserve">polus mundi H, per quem & </s>
            <s xml:id="echoid-s5875" xml:space="preserve">polum plani inclinati E F, circulus maximus de-
              <lb/>
            ſcribatur B D, ſecans planum inclinatum in I, qui cum per propoſ. </s>
            <s xml:id="echoid-s5876" xml:space="preserve">15. </s>
            <s xml:id="echoid-s5877" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s5878" xml:space="preserve">1. </s>
            <s xml:id="echoid-s5879" xml:space="preserve">Theodoſij, rectus ſit
              <lb/>
            ad ipſum planum inclinatum, metietur altitudinem poli H, ſupra ipſum, per arcum H I. </s>
            <s xml:id="echoid-s5880" xml:space="preserve">Oporter
              <lb/>
              <note position="right" xlink:label="note-0121-08" xlink:href="note-0121-08a" xml:space="preserve">Arcus plani in-
                <lb/>
              clinati iter eius
                <lb/>
              Meridianum &
                <lb/>
              Meridianũ Ho
                <lb/>
              rizontis quo ar-
                <lb/>
              uficio deprehẽ-
                <lb/>
              dacur.</note>
            igitur inuenire quantitatem arcus G I, & </s>
            <s xml:id="echoid-s5881" xml:space="preserve">anguli G H I. </s>
            <s xml:id="echoid-s5882" xml:space="preserve">Quod ita exequemur. </s>
            <s xml:id="echoid-s5883" xml:space="preserve">Quoniam in trian-
              <lb/>
            gulo ſphærico G H I, angulus I, rectus eſt, erit per propoſ. </s>
            <s xml:id="echoid-s5884" xml:space="preserve">19. </s>
            <s xml:id="echoid-s5885" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s5886" xml:space="preserve">4. </s>
            <s xml:id="echoid-s5887" xml:space="preserve">Ioan. </s>
            <s xml:id="echoid-s5888" xml:space="preserve">Regiom. </s>
            <s xml:id="echoid-s5889" xml:space="preserve">vel per propoſ.
              <lb/>
            </s>
            <s xml:id="echoid-s5890" xml:space="preserve">15. </s>
            <s xml:id="echoid-s5891" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s5892" xml:space="preserve">1. </s>
            <s xml:id="echoid-s5893" xml:space="preserve">Gebri, vel certè ex propoſ. </s>
            <s xml:id="echoid-s5894" xml:space="preserve">43. </s>
            <s xml:id="echoid-s5895" xml:space="preserve">noſtrorum triangulorum ſphæricorum, vt ſinus comple
              <lb/>
            menti arcus Meridiani G H, inter planum & </s>
            <s xml:id="echoid-s5896" xml:space="preserve">polum intercepti, ad ſinum complementiarcus H I,
              <lb/>
            altitudinem poli ſupra planum E F, metientis, ita ſinus complementi arcus G I, ad ſinum totum; </s>
            <s xml:id="echoid-s5897" xml:space="preserve">
              <lb/>
            ac propterea & </s>
            <s xml:id="echoid-s5898" xml:space="preserve">conuertendo, vt ſinus complementiarcus H I, altitudinis poli ſupra planum E F,
              <lb/>
            ad ſinum complementi arcus Meridiani G H, inter planum & </s>
            <s xml:id="echoid-s5899" xml:space="preserve">polum, ita ſinus totus ad ſinum </s>
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