Clavius, Christoph, Geometria practica

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        <div xml:id="echoid-div99" type="section" level="1" n="45">
          <pb o="53" file="083" n="83" rhead="LIBER SECVNDVS."/>
          <p>
            <s xml:id="echoid-s2153" xml:space="preserve">prodibit diſtantia D F, quæſita, ſiue A B, in eadem menſura differentiæ ſtatio-
              <lb/>
            num: </s>
            <s xml:id="echoid-s2154" xml:space="preserve">cui ſi adij ciatur differentia ſtationum E D, cognita etiam fiet diſtantia E F;
              <lb/>
            </s>
            <s xml:id="echoid-s2155" xml:space="preserve">vel C B, à remotiori ſtatione.</s>
            <s xml:id="echoid-s2156" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div101" type="section" level="1" n="46">
          <head xml:id="echoid-head49" xml:space="preserve">ALITER</head>
          <p>
            <s xml:id="echoid-s2157" xml:space="preserve">2. </s>
            <s xml:id="echoid-s2158" xml:space="preserve">
              <emph style="sc">Posito</emph>
            ſinu toto G F, erit D F, Tangens anguli D G F, complementi
              <lb/>
            anguli obſeruationis G D F. </s>
            <s xml:id="echoid-s2159" xml:space="preserve">quem angulum D G F, in dicat arcus Quadrantis IK,
              <lb/>
              <note symbol="a" position="right" xlink:label="note-083-01" xlink:href="note-083-01a" xml:space="preserve">29. primi.</note>
            à perpendiculo verſus oculum, cum angulus D H I, æqualis ſit angulo D G F, externus interno. </s>
            <s xml:id="echoid-s2160" xml:space="preserve">Eodem modo E F, Tangens erit anguli E G F, complementi
              <lb/>
            alterius anguli obſeruationis GEF. </s>
            <s xml:id="echoid-s2161" xml:space="preserve">At ED, differentia inter eas Tangentes exi-
              <lb/>
            ſtet. </s>
            <s xml:id="echoid-s2162" xml:space="preserve">Si igitur fiat,</s>
          </p>
          <note style="it" position="right" xml:space="preserve">
            <lb/>
          vt E D, differentia \\ inter Tangent{es} \\ angulorũ, qui cõ- \\ plemẽta ſunt angu- \\ lorũ obſeruationũ, # ad D F, Tangentem com- \\ plementi anguli obſerua- \\ tionis G D F, in propin- \\ quiore ſtatione, hoc eſt, ad \\ Tangentem minorem: # Ita E D, diffe- \\ rentia ſtatio- \\ num nota in \\ aliqua men- \\ ſura vulgari. # ad aliud \\ hoc eſt, \\ ad DF,
            <lb/>
          </note>
          <note position="right" xml:space="preserve">Diſtantiæ in-
            <lb/>
          uentio alia
            <lb/>
          per tangen-
            <lb/>
          tes.</note>
          <p>
            <s xml:id="echoid-s2163" xml:space="preserve">procreabitur diſtantia minor quæſita DF, vel A B, in eadem menſura differentiæ
              <lb/>
            ſtationum: </s>
            <s xml:id="echoid-s2164" xml:space="preserve">cui ſi addatur differentia ſtationum E D, nota quo que fiet diſtantia
              <lb/>
            maior E F.</s>
            <s xml:id="echoid-s2165" xml:space="preserve"/>
          </p>
          <note symbol="b" position="right" xml:space="preserve">4. ſexti.</note>
          <note style="it" position="right" xml:space="preserve">
            <lb/>
          #### 3. Rurſus ſi fiat, Vt D N, ſi- \\ n{us} tot{us} # ad N O, Tangentem anguli \\ G D F, in propinquiore ſtatione: # Ita D F, diſtantia \\ inuenta minor # ad aliud, hoc \\ eſt, ad F G;</note>
          <p>
            <s xml:id="echoid-s2166" xml:space="preserve">@ Inuenietur altitudo F G, in menſura diſtantiæ inuentæ D F; </s>
            <s xml:id="echoid-s2167" xml:space="preserve">minoris, cui ſi ad-
              <lb/>
              <note position="right" xlink:label="note-083-06" xlink:href="note-083-06a" xml:space="preserve">Altitudinis in
                <lb/>
              uentio per tã-
                <lb/>
              gent{es}.</note>
            datur menſ@ris ſtatura F B, cognita erit tota altitudo B G. </s>
            <s xml:id="echoid-s2168" xml:space="preserve">Item ſi fiat,</s>
          </p>
          <note style="it" position="right" xml:space="preserve">
            <lb/>
          Vt E M, ſi- \\ n{us} tot{us} # ad M H, tangentem anguli G E F, \\ in remotiore ſtatione: # ita E F, diſtantia \\ inuenta maior # ad aliud, hoc \\ est, ad FG,
            <lb/>
          </note>
          <note symbol="c" position="right" xml:space="preserve">4. ſexti.</note>
          <p>
            <s xml:id="echoid-s2169" xml:space="preserve">reperietur eadem altitudo F G, in menſura diſtantiæ inuentæ E F, maioris, cui ſi
              <lb/>
              <note position="right" xlink:label="note-083-09" xlink:href="note-083-09a" xml:space="preserve">Altitudinis
                <lb/>
              inuentio alia
                <lb/>
              per tangent{es}.</note>
            addatur ſtatura menſoris FB, nota fiet tota altitudo B G.</s>
            <s xml:id="echoid-s2170" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div105" type="section" level="1" n="47">
          <head xml:id="echoid-head50" xml:space="preserve">ALITER</head>
          <p>
            <s xml:id="echoid-s2171" xml:space="preserve">4. </s>
            <s xml:id="echoid-s2172" xml:space="preserve">Si per ſolos ſinus idem expedire lubeat, erit operatio aliquando longior.
              <lb/>
            </s>
            <s xml:id="echoid-s2173" xml:space="preserve">Primum enim inuenienda eſt vtra que hypotenuſa E G, D G, in aliqua menſura
              <lb/>
            nota, hoc modo. </s>
            <s xml:id="echoid-s2174" xml:space="preserve"> Quoniam angulus G D F, æqualis eſt duobus angulis
              <note symbol="d" position="right" xlink:label="note-083-10" xlink:href="note-083-10a" xml:space="preserve">32. primi.</note>
            EGD: </s>
            <s xml:id="echoid-s2175" xml:space="preserve">ſi angulus E, in remotiore ſtatione obſeruatus dematur ex angulo GDF,
              <lb/>
            in propinquiore ſtatione deprehenſo, reliquus fiet angulus EGD, differentia ni-
              <lb/>
            miruminter duosangulos obſeruationum. </s>
            <s xml:id="echoid-s2176" xml:space="preserve"> Quod ſi fiat,</s>
          </p>
          <note symbol="c" position="right" xml:space="preserve">10. Triang.
            <lb/>
          rectil.</note>
          <note style="it" position="right" xml:space="preserve">
            <lb/>
          Vt ſin{us} anguli E G D, \\ differentiæ inter an- \\ gulos duos obſeruatio- \\ num # ad E D dif- \\ ferentiam \\ ſtationum \\ notam: # Ita ſin{us} anguli D E G, \\ vel. Ita ſin{us} anguli \\ E D G, cõplementian- \\ guli G D F, ad duos rectos, # ad D G, \\ vel \\ ad E G,
            <lb/>
          </note>
          <p>
            <s xml:id="echoid-s2177" xml:space="preserve">pro ducetur tam D G, quam E G, nota in partibus differentiæ ſtationum. </s>
            <s xml:id="echoid-s2178" xml:space="preserve">Igi-
              <lb/>
              <note position="right" xlink:label="note-083-13" xlink:href="note-083-13a" xml:space="preserve">Inuentio Hy-
                <lb/>
              potenuſarum.</note>
            tur ſi fiat,</s>
          </p>
          <note style="it" position="right" xml:space="preserve">
            <lb/>
          Vt ſin{us} to- \\ t{us} anguli \\ recti F, # ad hypoten@- \\ ſam D G, \\ proxime inuentam # Ita ſin{us} anguli D G F, complementi anguli ob- \\ ſeruationis in propinquiore ſtatione # ad D F,
            <lb/>
          </note>
          <note symbol="f" position="right" xml:space="preserve">10. triang re-
            <lb/>
          ctil.</note>
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    </echo>
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