Clavius, Christoph, Geometria practica
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          <pb o="52" file="082" n="82" rhead="GEOMETR. PRACT."/>
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          <head xml:id="echoid-head48" xml:space="preserve">PROBLEMA I.</head>
          <p>
            <s xml:id="echoid-s2120" xml:space="preserve">
              <emph style="sc">Sit</emph>
            diſtantia ſiue longitu-
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              <figure xlink:label="fig-082-01" xlink:href="fig-082-01a" number="18">
                <image file="082-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/082-01"/>
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            do inueſtiganda A B, in
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            plano C B, erectaque ſit in
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            extremo B, altitudo quæ-
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            piam perpendicularis B G,
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            licet extremum B, non ap-
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            pareat. </s>
            <s xml:id="echoid-s2121" xml:space="preserve">Statura menſoris
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            ſit D A, ab oculo ad pedes
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            vſque. </s>
            <s xml:id="echoid-s2122" xml:space="preserve">Neautem hæc ſta-
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            tura mutetur, ſed eadem
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            ſemper maneat, recte fe-
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            ceris, ſi pro ea ſtatura ba-
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            culum eidem æqualem ac-
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            cipias, ad cuius extremum
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            oculum applices. </s>
            <s xml:id="echoid-s2123" xml:space="preserve">Ducta autem cogitatione per D, ipſi C B, parallela E F, fiat
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            prima ſtatio in D, Secunda verò in E, puncto remotiore: </s>
            <s xml:id="echoid-s2124" xml:space="preserve">ſitquerecta D E, quæ
              <lb/>
              <note position="left" xlink:label="note-082-01" xlink:href="note-082-01a" xml:space="preserve">Differentia
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              ſtationum.</note>
            differentia ſtationum dicitur, nota ſecundum aliquam menſuram vulgarem.
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            </s>
            <s xml:id="echoid-s2125" xml:space="preserve">Deinde dirigatur latus quadrantis H K, in quo ſunt pinnacidia, verſus faſti-
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            gium G, ita vt oculus in D, poſitus per vtriuſque pinnacidij foramina, fafti-
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            gium G videat, libere pendente perpendiculo H I: </s>
            <s xml:id="echoid-s2126" xml:space="preserve">diligenterque per ea,
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            quæ cap. </s>
            <s xml:id="echoid-s2127" xml:space="preserve">2. </s>
            <s xml:id="echoid-s2128" xml:space="preserve">libr. </s>
            <s xml:id="echoid-s2129" xml:space="preserve">1. </s>
            <s xml:id="echoid-s2130" xml:space="preserve">Num. </s>
            <s xml:id="echoid-s2131" xml:space="preserve">7. </s>
            <s xml:id="echoid-s2132" xml:space="preserve">& </s>
            <s xml:id="echoid-s2133" xml:space="preserve">10. </s>
            <s xml:id="echoid-s2134" xml:space="preserve">tradita ſunt, notetur in gradibus, ac minu-
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            tis angulus G D F, quem arcus I L, in Quadrante manifeſtabit, complemen-
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            tum videlicet arcus I K, Cum enim filum perpendiculi H I, ſit ad D F, rectum,
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            erit angulus G D F, complementum anguli D H I, ęqualis nimirum angulo
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            I H L, qui eiuſdem anguli D H I, complementum etiam eſt. </s>
            <s xml:id="echoid-s2135" xml:space="preserve">Atque hunc an-
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            gulum G D F, angulum obſeruationis dicemus. </s>
            <s xml:id="echoid-s2136" xml:space="preserve">Eodem modo obſeruetur in
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              <note position="left" xlink:label="note-082-02" xlink:href="note-082-02a" xml:space="preserve">Angul{us} ob-
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              ſeruationis.</note>
            ſecunda ſtatione angulus G E F, per radium viſualem ab oculo, & </s>
            <s xml:id="echoid-s2137" xml:space="preserve">per pinna-
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            cidia Quadrantis ad faſtigium G, directum. </s>
            <s xml:id="echoid-s2138" xml:space="preserve">Sumptis autem E M, D N, æquali-
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            bus, erigantur perpendiculares M N, N O, (in figura conincidit M H, cum fi-
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            lo perpendiculi; </s>
            <s xml:id="echoid-s2139" xml:space="preserve">quod nihil refert.) </s>
            <s xml:id="echoid-s2140" xml:space="preserve">Si igitur E M, D N, ſtatuantur ſinus to-
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            ti, erunt M H, N O, Tangentes angulorum obſeruationum E, & </s>
            <s xml:id="echoid-s2141" xml:space="preserve">D. </s>
            <s xml:id="echoid-s2142" xml:space="preserve">Ducta
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            quoque D Q, ipſi E G, parallela ſecante N O, in P, erit angulus N D P,
              <note symbol="a" position="left" xlink:label="note-082-03" xlink:href="note-082-03a" xml:space="preserve">29. primi.</note>
            gulo E, æqualis. </s>
            <s xml:id="echoid-s2143" xml:space="preserve">Cum ergo duo anguli N. </s>
            <s xml:id="echoid-s2144" xml:space="preserve">D, trianguli N D P, duobus angu-
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            lis M, E, trianguli M E H, ſint æquales, (eſt enim & </s>
            <s xml:id="echoid-s2145" xml:space="preserve">rectus N, recto M, æqua-
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            lis) lateraque D N, E M, quibus adiacent, æqualia; </s>
            <s xml:id="echoid-s2146" xml:space="preserve"> erunt latera N P, M H;</s>
            <s xml:id="echoid-s2147" xml:space="preserve">
              <note symbol="b" position="left" xlink:label="note-082-04" xlink:href="note-082-04a" xml:space="preserve">26. primi.</note>
            æqualia: </s>
            <s xml:id="echoid-s2148" xml:space="preserve">ac proinde O P, differentia erit inter Tangentes angulorum obſer-
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            uationum. </s>
            <s xml:id="echoid-s2149" xml:space="preserve"> Quia verò eſt, vt O P, ad P N, ita G Q, ad Q F: </s>
            <s xml:id="echoid-s2150" xml:space="preserve"> Et vt G
              <note symbol="c" position="left" xlink:label="note-082-05" xlink:href="note-082-05a" xml:space="preserve">Schol. 4.
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              lib. 6.</note>
            ad Q F, ita E D, ad D F; </s>
            <s xml:id="echoid-s2151" xml:space="preserve">erit quo que vt O P, differentia Tangentium angulis
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            obſeruationum reſpondentium ad P N, ſiue ad H M, Tangentem remotioris
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              <note symbol="d" position="left" xlink:label="note-082-06" xlink:href="note-082-06a" xml:space="preserve">2. ſext.</note>
            ſtationis, ita E D, differentia ſtationum ad D F, diſtantiam quæſitam. </s>
            <s xml:id="echoid-s2152" xml:space="preserve">Quo-
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            cir ca ſi fiat,</s>
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          <note style="it" position="right" xml:space="preserve">
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          Vt O P, differentia \\ inter Tangent{es} an- \\ gulorum obſeruatio- \\ num. # ad P N, vel \\ H M, Tan- \\ gentem mi- \\ norem: # Ita E D, differentia \\ ſtationum nota in \\ menſura aliqua vul- \\ gari # ad aliud; \\ hoc eſt ad \\ D F,
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          </note>
          <note position="left" xml:space="preserve">Diſtantiæ in-
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          uentio per
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          tangentes.</note>
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