Clavius, Christoph, Geometria practica

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        <div xml:id="echoid-div203" type="section" level="1" n="91">
          <pb o="79" file="109" n="109" rhead="LIBER SECVNDVS."/>
          <p>
            <s xml:id="echoid-s3116" xml:space="preserve">DISTANTIAM accliuem montis à loco menſoris vſque ad baſem
              <lb/>
            altitudinis monti impoſitæ, etiam non viſam, vna cumipſa altitudine,
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            quando menſor in aſcenſu montis conſiſtit, prope verum efficere
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            cognitam, beneficio Quadrantis.</s>
            <s xml:id="echoid-s3117" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div204" type="section" level="1" n="92">
          <head xml:id="echoid-head95" xml:space="preserve">PROBLEMA XXII.</head>
          <figure number="45">
            <image file="109-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/109-01"/>
          </figure>
          <p>
            <s xml:id="echoid-s3118" xml:space="preserve">1. </s>
            <s xml:id="echoid-s3119" xml:space="preserve">
              <emph style="sc">Sit</emph>
            turris AB, monti impoſita,
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            in cuius aſcenſu ſeu latere menſor con-
              <lb/>
            ſiſtat in C, ex quo loco baſem turris
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              <note position="right" xlink:label="note-109-01" xlink:href="note-109-01a" xml:space="preserve">In figura duc
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              rectam F A.</note>
            videre non poſsit. </s>
            <s xml:id="echoid-s3120" xml:space="preserve">Erigatur haſta aliqua
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            C G, ad Horizontem, non autem ad la-
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            tus montis perpendicularis, ſitque men-
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            ſoris ſtatura CE. </s>
            <s xml:id="echoid-s3121" xml:space="preserve">Cogitetur ducta E K,
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            ad altitudinem perpendicularis: </s>
            <s xml:id="echoid-s3122" xml:space="preserve">Et in-
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            ſpecto cacumine A, per angulum A EK,
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            fiat alia ſtatio ſuperior in F, ductaque
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            FI, ad altitu dinem perpendiculari, inſpi-
              <lb/>
            ciatur idem cacumen A, per angulum
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              <note symbol="a" position="right" xlink:label="note-109-02" xlink:href="note-109-02a" xml:space="preserve">32. primi.</note>
            A F I, Et quia angulus A F G, duobus angulis FEA, FAE, eſt æqualis: </s>
            <s xml:id="echoid-s3123" xml:space="preserve">ſi dema-
              <lb/>
            tur A EF, complementum maioris anguli
              <lb/>
            A EK, in prima ſtatione obſeruati, reli-
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              <note symbol="b" position="right" xlink:label="note-109-03" xlink:href="note-109-03a" xml:space="preserve">10. triang.
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              rectil.</note>
            quus fiet angulus EAF, Igitur ſi fiat,</s>
          </p>
          <note style="it" position="right" xml:space="preserve">
            <lb/>
          Vt ſin{us} anguli \\ EAF, differen- \\ tiæ complemen- \\ torũ angulorũ \\ obſeruationum # ad EF, diffe- \\ rentiam ſta- \\ tionum: # Ita ſin{us} anguli AFE, confta- \\ ti ex recto E F I, & minore \\ angulo AFI, in ſeounda ſta- \\ tione obſeruati, # ad A E \\ hypote- \\ nuſam.
            <lb/>
          </note>
          <p>
            <s xml:id="echoid-s3124" xml:space="preserve">efficietur nota hypotenuſa AE. </s>
            <s xml:id="echoid-s3125" xml:space="preserve">Poſt hæc erigatur alius baculus DH, ad Hori-
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            zontem rectus, ſumptaque menſoris ſtatura DH, ipſi CE, æquali, & </s>
            <s xml:id="echoid-s3126" xml:space="preserve">ducta recta
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            HL, ad altitudinem perpendiculari, inſpiciatur punctum E, per angulum EHL,
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            & </s>
            <s xml:id="echoid-s3127" xml:space="preserve">perradium HEM, quiipſi BCD, lateri montis parallelus erit. </s>
            <s xml:id="echoid-s3128" xml:space="preserve">
              <note symbol="c" position="right" xlink:label="note-109-05" xlink:href="note-109-05a" xml:space="preserve">33: primi.</note>
            enim ſunt tria puncta B, C, D, in vna recta iacere, ac ſi DC, producta ad baſem
              <lb/>
            turris perueniret. </s>
            <s xml:id="echoid-s3129" xml:space="preserve"> Quia verò angulus EHL, angulo MEK, æqualis eſt:</s>
            <s xml:id="echoid-s3130" xml:space="preserve">ſi hic
              <note symbol="d" position="right" xlink:label="note-109-06" xlink:href="note-109-06a" xml:space="preserve">29. primi.</note>
            maiori angulo obſeruato AEN, inprima ſtatione dematur, reliquus fiet angulus
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            AEM. </s>
            <s xml:id="echoid-s3131" xml:space="preserve">Eſt autem & </s>
            <s xml:id="echoid-s3132" xml:space="preserve">angulus EAN, cognitus, quippe cum ſit complementum
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            maioris anguli obſeruati AEN. </s>
            <s xml:id="echoid-s3133" xml:space="preserve">Igitur & </s>
            <s xml:id="echoid-s3134" xml:space="preserve">AME, reliquus duorum rectorum cog-
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            nitus erit: </s>
            <s xml:id="echoid-s3135" xml:space="preserve">qui quidem etiam relinquitur, ſi complementum anguli M HL, in
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            ſtatione D, obſeruati ex duobusrectis detrahatur. </s>
            <s xml:id="echoid-s3136" xml:space="preserve"> Igitur ſi fiat,</s>
          </p>
          <note symbol="e" position="right" xml:space="preserve">10. triang.
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          rectil.</note>
          <note style="it" position="right" xml:space="preserve">
            <lb/>
          Vtſin{us} anguli A M E, qui \\ velinquitur, ſicomplemen- \\ tum poſtremi anguli obſer- \\ uati MHL, ex duob{us} re- \\ ctis dematur # ad hypotenu- \\ ſam A E, \\ nuper inuẽ- \\ tam: # Ita ſin{us} anguli, \\ E A N, comple- \\ mẽti maioris an- \\ guli obſeruati AEN # ad M E,
            <lb/>
          </note>
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