Clavius, Christoph, Geometria practica

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          <pb o="151" file="181" n="181" rhead="LIBER TERTIVS."/>
          <p>
            <s xml:id="echoid-s5823" xml:space="preserve">LONGITVDINEM trabis ad Horizontem in clinatæ, cuius portio
              <lb/>
            ſuperior tantum conſpiciatur, vna cum angulo inclinationis, diſtan-
              <lb/>
            tia baſis à menſore, & </s>
            <s xml:id="echoid-s5824" xml:space="preserve">altitudine faſtigii ſupra Horizontem, per Qua-
              <lb/>
            dratum metiri.</s>
            <s xml:id="echoid-s5825" xml:space="preserve"/>
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        <div xml:id="echoid-div394" type="section" level="1" n="164">
          <head xml:id="echoid-head167" xml:space="preserve">PROBLEMA XLIII.</head>
          <p>
            <s xml:id="echoid-s5826" xml:space="preserve">1. </s>
            <s xml:id="echoid-s5827" xml:space="preserve">Trabs inclinata ſupra murum CD, ſit AB, & </s>
            <s xml:id="echoid-s5828" xml:space="preserve">menſor in E, conſtitutus è di-
              <lb/>
            recto ipſius trabis, ita, vt ipſe & </s>
            <s xml:id="echoid-s5829" xml:space="preserve">trabs in eodem ſint plano, metiri debeat lon-
              <lb/>
            gitudinẽ A B, angulum in clinationis ABE, diſtantiam B E, & </s>
            <s xml:id="echoid-s5830" xml:space="preserve">altitudinem A F,
              <lb/>
            etiamſi tantum portionem ſupremam A G, videat, baſem ocultante muro C D
              <lb/>
            Si quadratum ad E, bis applicetur, ſemel videlicet in clinatum, vt vnum latus re-
              <lb/>
            cta tendat ad punctum A, & </s>
            <s xml:id="echoid-s5831" xml:space="preserve">iterum demiſſum ad Horizontem, ita vt centrum
              <lb/>
            dioptræ ſit in E, & </s>
            <s xml:id="echoid-s5832" xml:space="preserve">latus E L, Horizontiincumbat. </s>
            <s xml:id="echoid-s5833" xml:space="preserve">Nam inſpecto puncto A, ex
              <lb/>
            a, ſi ſ
              <unsure/>
            iat, vt vmbra verſa e b, ad latus b a, ita latus
              <figure xlink:label="fig-181-01" xlink:href="fig-181-01a" number="112">
                <image file="181-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/181-01"/>
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              <note symbol="a" position="right" xlink:label="note-181-01" xlink:href="note-181-01a" xml:space="preserve">4. ſexti.</note>
            E, ad aliud, gignetur diſtãtia, ſiue hypotenuſa E A.
              <lb/>
            </s>
            <s xml:id="echoid-s5834" xml:space="preserve">Deinde explorata portione dioptræ E I, vt in ſcho-
              <lb/>
            lio Probl. </s>
            <s xml:id="echoid-s5835" xml:space="preserve">7. </s>
            <s xml:id="echoid-s5836" xml:space="preserve">Num. </s>
            <s xml:id="echoid-s5837" xml:space="preserve">2. </s>
            <s xml:id="echoid-s5838" xml:space="preserve">docui; </s>
            <s xml:id="echoid-s5839" xml:space="preserve"> Si fiat, vt E I,
              <note symbol="b" position="right" xlink:label="note-181-02" xlink:href="note-181-02a" xml:space="preserve">2. ſexti. &
                <lb/>
              componendo.</note>
            dio ptræ inuenta ad repertam hypotenuſam EA, ita
              <lb/>
            fI, lateri quadrati æqualis ad aliud, producetur al-
              <lb/>
            titudo AF, quæſita. </s>
            <s xml:id="echoid-s5840" xml:space="preserve">quod eſt quartum.</s>
            <s xml:id="echoid-s5841" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5842" xml:space="preserve">2. </s>
            <s xml:id="echoid-s5843" xml:space="preserve">
              <emph style="sc">Et</emph>
            ſi rurſus fiat, vt EI, portio dioptræ ad hypotenuſam EA, ita Ef, ipſi
              <note symbol="c" position="right" xlink:label="note-181-03" xlink:href="note-181-03a" xml:space="preserve">2. ſexti. &
                <lb/>
              componendo.</note>
            æqualis ad aliud, nota fiet diſtantia EF. </s>
            <s xml:id="echoid-s5844" xml:space="preserve">Non aliter, ſi aliud punctum G, inſpi-
              <lb/>
            ciatur, cognita fiet hypotenuſa E G, & </s>
            <s xml:id="echoid-s5845" xml:space="preserve">altitudo G H, vna cum diſtantia E H, ſi
              <lb/>
            nimirum quadratum primo ita applicetur ad E, vt vnum latus tendat recta ad
              <lb/>
            G, &</s>
            <s xml:id="echoid-s5846" xml:space="preserve">c. </s>
            <s xml:id="echoid-s5847" xml:space="preserve">quemadmo dum in ſcholio probl. </s>
            <s xml:id="echoid-s5848" xml:space="preserve">7. </s>
            <s xml:id="echoid-s5849" xml:space="preserve">oſtendimus.</s>
            <s xml:id="echoid-s5850" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5851" xml:space="preserve">3. </s>
            <s xml:id="echoid-s5852" xml:space="preserve">
              <emph style="sc">Iam</emph>
            ſi E F, inuenta ex cognita E H, ſubducatur, nota relinquetur F H, id
              <lb/>
            eſt, GI, quæ in ſublimi duci cogitetur parallela Horizonti Eodem modo ſi G H,
              <lb/>
            cognita, vel illi æqualis FI, ex inuenta AF, dematur, reliqua AI, nota fiet. </s>
            <s xml:id="echoid-s5853" xml:space="preserve">Cum
              <lb/>
            igitur in triangulo rectangulo AGI, in ſublimi conſtituto duo latera AI, IG, co-
              <lb/>
              <note symbol="d" position="right" xlink:label="note-181-04" xlink:href="note-181-04a" xml:space="preserve">6. triang. re-
                <lb/>
              ctil.</note>
            gnita ſint, cognoſcetur & </s>
            <s xml:id="echoid-s5854" xml:space="preserve">baſis A G, & </s>
            <s xml:id="echoid-s5855" xml:space="preserve">angulus AGI, quiæ qualis eſt angu- lo in clinationis ABE, qui quæritur. </s>
            <s xml:id="echoid-s5856" xml:space="preserve">quod eſt ſecundum.</s>
            <s xml:id="echoid-s5857" xml:space="preserve"/>
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          <note symbol="e" position="right" xml:space="preserve">29. primi.</note>
          <p>
            <s xml:id="echoid-s5858" xml:space="preserve">4. </s>
            <s xml:id="echoid-s5859" xml:space="preserve">
              <emph style="sc">Itaqve</emph>
            cum in triangulo rectangulo ABF, latus A F, notũ ſit factum,
              <lb/>
              <note symbol="f" position="right" xlink:label="note-181-06" xlink:href="note-181-06a" xml:space="preserve">4. triang. re-
                <lb/>
              ctil.</note>
            vna cum angulo B, ac proinde & </s>
            <s xml:id="echoid-s5860" xml:space="preserve">cum eius complemento BAF, cognitum fiet alterum quo que latus B F, cui ſi adij cietur diſtantia E F, inuenta, tota diſtantia
              <lb/>
            quæſita E B, manifeſta erit. </s>
            <s xml:id="echoid-s5861" xml:space="preserve">quod eſt tertium.</s>
            <s xml:id="echoid-s5862" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s5863" xml:space="preserve">5. </s>
            <s xml:id="echoid-s5864" xml:space="preserve">
              <emph style="sc">Deniqve</emph>
            in eodem triangulo ABF, rectangulo, ex latere A F, & </s>
            <s xml:id="echoid-s5865" xml:space="preserve">angu-
              <lb/>
            lo B, ac proinde & </s>
            <s xml:id="echoid-s5866" xml:space="preserve">eius complemento BAF, cognitis, cognoſcetur etiam
              <note symbol="g" position="right" xlink:label="note-181-07" xlink:href="note-181-07a" xml:space="preserve">4. triang re-
                <lb/>
              ctil.</note>
            AB, longitudo videlicet trabis. </s>
            <s xml:id="echoid-s5867" xml:space="preserve">quod eſt primum. </s>
            <s xml:id="echoid-s5868" xml:space="preserve">Hæc autem nota etiam effi-
              <lb/>
            cietur, ſi fiat, vt AI, differentia altitudinum cognitarum AF, GH, ad AF,
              <note symbol="h" position="right" xlink:label="note-181-08" xlink:href="note-181-08a" xml:space="preserve">2. ſexti. &
                <lb/>
              componendo.</note>
            rem altitudinem, ita AG, paulo ante nota effecta, ad A B.</s>
            <s xml:id="echoid-s5869" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5870" xml:space="preserve">VISIS duarum turrium ſummitatibus, etiamſi baſes propter ædificia
              <lb/>
            interiecta occultentur, diſtantiam tam inter earum baſes, quam inter
              <lb/>
            earundem faſtigia, vna cum ipſarum altitudinibus, ac diſtãtiis à men-
              <lb/>
            ſore coniicere.</s>
            <s xml:id="echoid-s5871" xml:space="preserve"/>
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