Clavius, Christoph, Geometria practica

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        <div xml:id="echoid-div235" type="section" level="1" n="105">
          <pb o="96" file="126" n="126" rhead="GEOMETR. PRACT."/>
        </div>
        <div xml:id="echoid-div237" type="section" level="1" n="106">
          <head xml:id="echoid-head109" xml:space="preserve">PROBLEMA II.</head>
          <p>
            <s xml:id="echoid-s3652" xml:space="preserve">1. </s>
            <s xml:id="echoid-s3653" xml:space="preserve">
              <emph style="sc">Sit</emph>
            diſtantia metienda FG. </s>
            <s xml:id="echoid-s3654" xml:space="preserve">Hocper quadratum pendulum ſic fiet. </s>
            <s xml:id="echoid-s3655" xml:space="preserve">Eri-
              <lb/>
            gatur ex F, altitudo quæpiam nota F A, Horizonti ad angulos rectos, ſiue ea ſit
              <lb/>
            ſtatura menſoris ab oculo ad planum, ſiue maior quædam altitudo. </s>
            <s xml:id="echoid-s3656" xml:space="preserve">Inſpiciatur
              <lb/>
            extremũ G, per radium AG, ab oculo A, per foramina pinna @ diorum inceden-
              <lb/>
            tem, filo perpendiculari liberè pendente, & </s>
            <s xml:id="echoid-s3657" xml:space="preserve">inſtrumentum radente, punctum-
              <lb/>
              <figure xlink:label="fig-126-01" xlink:href="fig-126-01a" number="54">
                <image file="126-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/126-01"/>
              </figure>
            que E, notetur, vbi filum latus quadrati interſecat, quod fiet vel in latere B C,
              <lb/>
            vmbræ rectæ, vel in angulo C, vel in latere DC, vmbræ verſæ. </s>
            <s xml:id="echoid-s3658" xml:space="preserve">Cadente namque
              <lb/>
            filo in vmbram rectam, vel in punctum C, vt in 1. </s>
            <s xml:id="echoid-s3659" xml:space="preserve">& </s>
            <s xml:id="echoid-s3660" xml:space="preserve">2. </s>
            <s xml:id="echoid-s3661" xml:space="preserve">figura, fiet triangulum
              <lb/>
            ABE, triangulo AFG, æquiangulum, cum anguli B, F, ſint recti, & </s>
            <s xml:id="echoid-s3662" xml:space="preserve">angulus A,
              <lb/>
            communis. </s>
            <s xml:id="echoid-s3663" xml:space="preserve"> Si igitur fiat,</s>
          </p>
          <note symbol="a" position="left" xml:space="preserve">4. ſexti.</note>
          <note style="it" position="right" xml:space="preserve">
            <lb/>
          Vt lat{us} A B, par- \\ tium 1000. # ad vmbramrectam \\ abſciſſam B E, # Ita altitudo no- \\ ta A F, # ad F G, diſtan- \\ tiam,
            <lb/>
          </note>
          <p>
            <s xml:id="echoid-s3664" xml:space="preserve">euadet nota diſtantia quæſita F G, in partibus altitudinis AF. </s>
            <s xml:id="echoid-s3665" xml:space="preserve">Cadente autem
              <lb/>
            puncto E, in vmbram verſam, vt in 3. </s>
            <s xml:id="echoid-s3666" xml:space="preserve">figura, abſcindetur rurſus triangulum ADE,
              <lb/>
            triangulo AF G, æquiangulum, cum anguli D, F, rectiſint, & </s>
            <s xml:id="echoid-s3667" xml:space="preserve">alterni
              <note symbol="b" position="left" xlink:label="note-126-03" xlink:href="note-126-03a" xml:space="preserve">29. primi.</note>
            FAG, æquales. </s>
            <s xml:id="echoid-s3668" xml:space="preserve"> Ergo ſi fiat.</s>
            <s xml:id="echoid-s3669" xml:space="preserve"/>
          </p>
          <note symbol="c" position="left" xml:space="preserve">4. ſexti.</note>
          <note style="it" position="right" xml:space="preserve">
            <lb/>
          Vt vmbra verſa \\ abſciſſa D E, # ad lat{us} D A, partium \\ 1000. # Ita altitudo \\ nota AF. # ad FG, diſtantiam ′
            <lb/>
          </note>
          <note position="left" xml:space="preserve">Quando al-
            <lb/>
          titudo maior
            <lb/>
          eſt, quam di-
            <lb/>
          ſtantia, &
            <lb/>
          quando æqua-
            <lb/>
          lis, & quando
            <lb/>
          minor.</note>
          <p>
            <s xml:id="echoid-s3670" xml:space="preserve">nota quoque effi cietur diſtantia quæſita F G, in partibus altitudinis A F. </s>
            <s xml:id="echoid-s3671" xml:space="preserve">Ex
              <lb/>
            quo illud intelligere poteris, quando punctum E, interſectionis fili cum latere
              <lb/>
            quadrati cadit in vmbram rectam, altitudinem AF, maiorem eſſe diſtantia F G:
              <lb/>
            </s>
            <s xml:id="echoid-s3672" xml:space="preserve">quando in punctum C, æqualem; </s>
            <s xml:id="echoid-s3673" xml:space="preserve">quando denique in vmbram verſam, mi-
              <lb/>
            norem.</s>
            <s xml:id="echoid-s3674" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3675" xml:space="preserve">2. </s>
            <s xml:id="echoid-s3676" xml:space="preserve">
              <emph style="sc">Qvadrato</emph>
            ſtabili ita eandem diſtantiam explorabimus. </s>
            <s xml:id="echoid-s3677" xml:space="preserve">Erigatur in
              <lb/>
            extremo diſtantiæ E, altitudo quædam perpendicularis notarum partium, & </s>
            <s xml:id="echoid-s3678" xml:space="preserve">
              <lb/>
            quadratum ita accommodetur, vt centrum A, ſuperiorem locum occupet, & </s>
            <s xml:id="echoid-s3679" xml:space="preserve">
              <lb/>
            vmbra recta DC, Horizonti æquidiſtet. </s>
            <s xml:id="echoid-s3680" xml:space="preserve">Directa igitur dioptra ad ſignum pro-
              <lb/>
            poſitum, notetur diligenter vmbra abſciſſa: </s>
            <s xml:id="echoid-s3681" xml:space="preserve">quæ ſi recta fuerit, nimirum D I,
              <lb/>
            erit altitudo AE, maior, quam diſtantia EG, triangulumque A D I,
              <note symbol="d" position="left" xlink:label="note-126-07" xlink:href="note-126-07a" xml:space="preserve">coroll. 4.
                <lb/>
              ſexti.</note>
            AEG, ſimile erit. </s>
            <s xml:id="echoid-s3682" xml:space="preserve"> Si gitur fiat.</s>
            <s xml:id="echoid-s3683" xml:space="preserve"/>
          </p>
          <note symbol="e" position="left" xml:space="preserve">4. ſexti.</note>
          <note position="right" xml:space="preserve">
            <lb/>
          Vt lat{us} quadrati \\ AD, 1000. # ad part{es} vmbræ \\ rectæ D I: # Ita altitudo A E, \\ cognita # ad E G, diſtan- \\ tiam
            <lb/>
          </note>
          <p>
            <s xml:id="echoid-s3684" xml:space="preserve">reperietur diſtantia quæſita EG, in partibus altitudinis aſſumptæ AE.</s>
            <s xml:id="echoid-s3685" xml:space="preserve"/>
          </p>
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