Clavius, Christoph, Geometria practica

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          <pb o="86" file="116" n="116" rhead="GEOMETR. PRACT."/>
          <p>
            <s xml:id="echoid-s3322" xml:space="preserve">3. </s>
            <s xml:id="echoid-s3323" xml:space="preserve">
              <emph style="sc">Post</emph>
            hæc è centro A, procedat filum cum perpendiculo, aut certere-
              <lb/>
              <note position="left" xlink:label="note-116-01" xlink:href="note-116-01a" xml:space="preserve">Quadratum
                <lb/>
              pendulum, ac
                <lb/>
              ſtabile.</note>
            gula tenuis, cum linea fiduciæ, quæ pendens libere moueatur, vt lib. </s>
            <s xml:id="echoid-s3324" xml:space="preserve">1. </s>
            <s xml:id="echoid-s3325" xml:space="preserve">capit. </s>
            <s xml:id="echoid-s3326" xml:space="preserve">2.
              <lb/>
            </s>
            <s xml:id="echoid-s3327" xml:space="preserve">Num 6. </s>
            <s xml:id="echoid-s3328" xml:space="preserve">tradidimus: </s>
            <s xml:id="echoid-s3329" xml:space="preserve">& </s>
            <s xml:id="echoid-s3330" xml:space="preserve">in latere A B, duo pinnacidia affigantur, de quibus lib. </s>
            <s xml:id="echoid-s3331" xml:space="preserve">1. </s>
            <s xml:id="echoid-s3332" xml:space="preserve">
              <lb/>
            cap. </s>
            <s xml:id="echoid-s3333" xml:space="preserve">2. </s>
            <s xml:id="echoid-s3334" xml:space="preserve">Num. </s>
            <s xml:id="echoid-s3335" xml:space="preserve">5. </s>
            <s xml:id="echoid-s3336" xml:space="preserve">dictum eſt, ſi quadratum in ſuo vſu debeat eſſe pendulum. </s>
            <s xml:id="echoid-s3337" xml:space="preserve">Nam
              <lb/>
            ſi illud ſtabile eſſe velis, affigenda eſt circa centrum A, dioptra, hoc eſt, regula
              <lb/>
            cum linea fiduciæ, ac duobus pinnacidijs, eodem artificio conſtructis, vt libere
              <lb/>
            poſsit circumduci, & </s>
            <s xml:id="echoid-s3338" xml:space="preserve">in omni ſitu firmari, vt loco ſupra citato in Quadrante ſta-
              <lb/>
            bili faciendum eſſe præcepimus.</s>
            <s xml:id="echoid-s3339" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3340" xml:space="preserve">
              <emph style="sc">Postremo</emph>
            iuxta latus A D, in plano quadrati (Nam ſi hoc fieret extra,
              <lb/>
            prope craſsitiem inſtrumenti, non poſſet quadratum in plano Horizontis lo-
              <lb/>
            carierectum ſupra latus A D. </s>
            <s xml:id="echoid-s3341" xml:space="preserve">quod tamen vt fiat, non raro vſus quadratipoſtu-
              <lb/>
            lat:) </s>
            <s xml:id="echoid-s3342" xml:space="preserve">apponàtur duæ tabellæ perforatæ cumfilo, & </s>
            <s xml:id="echoid-s3343" xml:space="preserve">perpendiculo, vt eius bene-
              <lb/>
            ficio dignoſcere poſsis, numinſtrumentum rectum ſit ad Horizontem, necne.
              <lb/>
            </s>
            <s xml:id="echoid-s3344" xml:space="preserve">quod omnino neceſſarium eſt.</s>
            <s xml:id="echoid-s3345" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3346" xml:space="preserve">4. </s>
            <s xml:id="echoid-s3347" xml:space="preserve">
              <emph style="sc">Sed</emph>
            deceamus, quem ſitum vtraq; </s>
            <s xml:id="echoid-s3348" xml:space="preserve">vmbra in vſu quadrati habeat. </s>
            <s xml:id="echoid-s3349" xml:space="preserve">Res
              <lb/>
              <note position="left" xlink:label="note-116-02" xlink:href="note-116-02a" xml:space="preserve">Vmbrarecta,
                <lb/>
              & verſa, quo
                <lb/>
              pacto in vtro-
                <lb/>
              que quadrato
                <lb/>
              cognoſcenda
                <lb/>
              ſit.</note>
            enim hæc non parui momenti eſt, vt in dimenſionibus nulla confuſio inter vm-
              <lb/>
            bras oriatur. </s>
            <s xml:id="echoid-s3350" xml:space="preserve">In quadrato ergo pendulo vmbra verſa opponitur ſemper lateri
              <lb/>
            pinna cidiorum: </s>
            <s xml:id="echoid-s3351" xml:space="preserve">recta autem cum eodem latere concurrit in puncto à centro A,
              <lb/>
            remotiori, vt in figura latus vmbræ rectæ eſt B C, verſæ autem C D. </s>
            <s xml:id="echoid-s3352" xml:space="preserve">At in qua-
              <lb/>
            drato ſtabili, ſi metienda ſit altitudo, & </s>
            <s xml:id="echoid-s3353" xml:space="preserve">centrum A, inferiorem obtineatlo cum,
              <lb/>
            in eoque oculus ponatur, latus vmbræ rectæ ſupremam occupabit ſedem; </s>
            <s xml:id="echoid-s3354" xml:space="preserve">la-
              <lb/>
            tus vero vmbræ verſæ vergere debebit verſusip ſam altitudinem: </s>
            <s xml:id="echoid-s3355" xml:space="preserve">ita vt tunc ba-
              <lb/>
            ſis inſtrumenti ſit A D. </s>
            <s xml:id="echoid-s3356" xml:space="preserve">quo pacto iterum vmbra recta eſt B C, & </s>
            <s xml:id="echoid-s3357" xml:space="preserve">verſa C D. </s>
            <s xml:id="echoid-s3358" xml:space="preserve">Si
              <lb/>
            autem centrum A, ſuperiorem locum poſsideat, & </s>
            <s xml:id="echoid-s3359" xml:space="preserve">oculus in extremitate dio-
              <lb/>
            ptræ exiſtat, (quod etiam fieri poteſt) latus vmbræ rectæ erit baſis C D, & </s>
            <s xml:id="echoid-s3360" xml:space="preserve">latus
              <lb/>
            vmbræ verſæ B C, prope oculum, & </s>
            <s xml:id="echoid-s3361" xml:space="preserve">ab altitudine metienda remotius. </s>
            <s xml:id="echoid-s3362" xml:space="preserve">Siau-
              <lb/>
            tem longitudo metienda proponatur, centrumque A, in ſuperiori loco ſitum
              <lb/>
            ſit, & </s>
            <s xml:id="echoid-s3363" xml:space="preserve">in eo oculus collocetur, erit quoque baſis C D, latus vmbræ rectæ: </s>
            <s xml:id="echoid-s3364" xml:space="preserve">latus
              <lb/>
            autem B C, vmbræ verſæ deputabitur, quod quidem verſus longitudinem me-
              <lb/>
            tiendam vergere debebit, & </s>
            <s xml:id="echoid-s3365" xml:space="preserve">longius ab oculo abeſſe. </s>
            <s xml:id="echoid-s3366" xml:space="preserve">At vero ſi centrum A,
              <lb/>
            ponaturinloco inferiori, ita vt baſis ſit A D, oculus autem in extremitate dio-
              <lb/>
            ptræ conſiſtat, (quod etiam fieri poteſt, præſertim ſi quadratum in ſublimi fue-
              <lb/>
            rit poſitum, vt in monte, vel turri aliqua) latus vmbræ rectæ erit B C, baſi A D,
              <lb/>
            oppoſitum, vmbrævero verſæ latus erit C D, quod ſcilicet longius à longitudi-
              <lb/>
            ne metienda recedit. </s>
            <s xml:id="echoid-s3367" xml:space="preserve">In vtro que porro quadrato centrum A, per diametrum
              <lb/>
            opponitur puncto, in quo vmbra recta cum verſa concurrit: </s>
            <s xml:id="echoid-s3368" xml:space="preserve">& </s>
            <s xml:id="echoid-s3369" xml:space="preserve">in ſtabili vm-
              <lb/>
            brarecta perpetuo vel ſupremum locum occupat, quando videlicet centrum
              <lb/>
            A, infimam ſedem tenet; </s>
            <s xml:id="echoid-s3370" xml:space="preserve">(vel infimum locum, quando ſcilicet centrum A, in
              <lb/>
            ſuperioriloco exiſtit, vt ex dictis liquet. </s>
            <s xml:id="echoid-s3371" xml:space="preserve">Hæcnon negligenter conſideranda
              <lb/>
            ſunt, ne in vario inſtrumentivſu vmbram rectam pro verſa accipias, aut contra;
              <lb/>
            </s>
            <s xml:id="echoid-s3372" xml:space="preserve">quando quidem pro diuerſo ſitu quadrati ſtabilis tamlatus BC, quam CD, mo-
              <lb/>
            do vmbrærectæ, modo verſæ munus obire poteſt, vt diximus.</s>
            <s xml:id="echoid-s3373" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3374" xml:space="preserve">5. </s>
            <s xml:id="echoid-s3375" xml:space="preserve">
              <emph style="sc">Qvamvis</emph>
            autem vel ſola vmbrarecta, vel verſa ſatis ſit ad altitudines,
              <lb/>
            longitudines, profunditateſque perueſtigandas, vt ex ſequentibus fiet mani-
              <lb/>
              <handwritten xlink:label="hd-116-1" xlink:href="hd-116-1a" number="46"/>
            feſtum: </s>
            <s xml:id="echoid-s3376" xml:space="preserve">vtraque tamen aſſumitur à Geometris, eo quod interdum vmbrarecta
              <lb/>
            excedit latus B C, nimirum quando filum perpendiculi, aut linea fiduciæ </s>
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