Clavius, Christoph, Geometria practica

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            <s xml:id="echoid-s5183" xml:space="preserve">
              <pb o="133" file="163" n="163" rhead="LIBER TERTIVS."/>
            Horizonti æquidiſtans. </s>
            <s xml:id="echoid-s5184" xml:space="preserve">Applicato autem quadrato ſtabili ad haſtam in puncto
              <lb/>
            E, (ſi pendulum adhibeatur, cõſtituendus etiam erit oculus in E.) </s>
            <s xml:id="echoid-s5185" xml:space="preserve">dirigatur dio-
              <lb/>
            ptra verſus cacumen A; </s>
            <s xml:id="echoid-s5186" xml:space="preserve">& </s>
            <s xml:id="echoid-s5187" xml:space="preserve">per vmbram
              <lb/>
              <figure xlink:label="fig-163-01" xlink:href="fig-163-01a" number="94">
                <image file="163-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/163-01"/>
              </figure>
            abſciſſaminueniatur angulus AEK, vt in
              <lb/>
            problemate 1. </s>
            <s xml:id="echoid-s5188" xml:space="preserve">tradidimus. </s>
            <s xml:id="echoid-s5189" xml:space="preserve">Deinde fiat
              <lb/>
            alia ſtatio ſuperior in F, in haſta, ductaq;
              <lb/>
            </s>
            <s xml:id="echoid-s5190" xml:space="preserve">per cogitationẽ recta F I, ad altitudinem
              <lb/>
              <note position="right" xlink:label="note-163-01" xlink:href="note-163-01a" xml:space="preserve">In figura duc
                <lb/>
              lineam ex F.
                <lb/>
              ad A.</note>
            perpendiculari, dirigatur rurſus dioptra
              <lb/>
            verſus A, atque eo dem modo angulus e-
              <lb/>
            ruatur AFI, Et quia angulus AFG, duo- bus angulis FEA, FAE, æqualis eſt, ſi au-
              <lb/>
              <note symbol="a" position="right" xlink:label="note-163-02" xlink:href="note-163-02a" xml:space="preserve">32. primi.</note>
            feratur AEF, complementum prioris an-
              <lb/>
            guli AEK, in ſtatione inferiori E, inuenti,
              <lb/>
            ex A F G, complemento poſterioris an-
              <lb/>
            guli in ſuperiori ſtatione F, deprehenſi,
              <lb/>
            reliquus fiet angulus E A F, cognitus.
              <lb/>
            </s>
            <s xml:id="echoid-s5191" xml:space="preserve">Quoniam igitur in trangulo A E F, duo
              <lb/>
            anguli A, E, cogniti ſunt, vna cum latere
              <lb/>
            E F, hoc eſt, cum differentia ſtationum, nota fientreliqua latera AE, AF.</s>
            <s xml:id="echoid-s5192" xml:space="preserve"/>
          </p>
          <note symbol="b" position="right" xml:space="preserve">10. triang.
            <lb/>
          rectil.</note>
          <p>
            <s xml:id="echoid-s5193" xml:space="preserve">2. </s>
            <s xml:id="echoid-s5194" xml:space="preserve">
              <emph style="sc">Post</emph>
            hæc erigatur alius baculus D H, ad Horizontem rectus, ſumptaq;
              <lb/>
            </s>
            <s xml:id="echoid-s5195" xml:space="preserve">menſoris ſtatura ipſi C E, æquali, & </s>
            <s xml:id="echoid-s5196" xml:space="preserve">ducta recta HL, ad altitu dinem perpendicu-
              <lb/>
            lari, applicetur ad H, quadratum, ac dioptra in punctum E, dirigatur, rurſumque
              <lb/>
            per problema 1. </s>
            <s xml:id="echoid-s5197" xml:space="preserve">ex vmbra abſciſſa angulus eliciatur EHL, acradius viſualis HE,
              <lb/>
            altitudini occurrere concipiatur in M, qui ipſi B C D, lateri montis parallelus erit. </s>
            <s xml:id="echoid-s5198" xml:space="preserve">Concipienda etenim ſunt tria puncta B, C, D, in vna recta linea iacere, ac ſi
              <lb/>
              <note symbol="c" position="right" xlink:label="note-163-04" xlink:href="note-163-04a" xml:space="preserve">33. primi.</note>
            D C, producta ad baſem turris pertineret. </s>
            <s xml:id="echoid-s5199" xml:space="preserve"> Quia vero angulus E H L,
              <note symbol="d" position="right" xlink:label="note-163-05" xlink:href="note-163-05a" xml:space="preserve">29. primi.</note>
            M E K, internus externo æqualis eſt, ſi E H L, cognitus hoc eſt M E K,
              <lb/>
            ex angulo A E N, in priori ſtatione E, obſeruato, detrahatur, notus relin-
              <lb/>
            quetur angulus AEM: </s>
            <s xml:id="echoid-s5200" xml:space="preserve">Eſt autem & </s>
            <s xml:id="echoid-s5201" xml:space="preserve">angulus EAM, cum complementum ſit an-
              <lb/>
            guli AEN, in priori ſtatione E, obſeruati, cognitus. </s>
            <s xml:id="echoid-s5202" xml:space="preserve">Igitur & </s>
            <s xml:id="echoid-s5203" xml:space="preserve">AME, reliquus duo-
              <lb/>
            rum rectorum cognitus erit: </s>
            <s xml:id="echoid-s5204" xml:space="preserve">quiquidem etiam relinquitur, ſi N M H, comple-
              <lb/>
            mentum anguli M H L, in ſtatione poſtrema H, inuenti ex duobus rectis detra-
              <lb/>
            hatur. </s>
            <s xml:id="echoid-s5205" xml:space="preserve">Quapropter cumin triangulo AEM, omnes anguli noti ſint, vna cumla-
              <lb/>
            tere A E, quod paulo ante inuenimus, cognoſcentur quoque reliqua duo
              <note symbol="e" position="right" xlink:label="note-163-06" xlink:href="note-163-06a" xml:space="preserve">10. triang.
                <lb/>
              rectil.</note>
            tera ME, AM: </s>
            <s xml:id="echoid-s5206" xml:space="preserve">ac propterea diſtantia E M, vel C B, inuenta erit. </s>
            <s xml:id="echoid-s5207" xml:space="preserve">Et ſi rectæ A M,
              <lb/>
            inuentæ addatur menſoris ſtatura MB, tota turris altitudo A B, cognita erit.</s>
            <s xml:id="echoid-s5208" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5209" xml:space="preserve">
              <emph style="sc">Cvrandvm</emph>
            autem eſt magnopere, vt tria puncta B, C, D, in vna linea re-
              <lb/>
            ctaiaceant, id quod in problemate 22. </s>
            <s xml:id="echoid-s5210" xml:space="preserve">lib 2. </s>
            <s xml:id="echoid-s5211" xml:space="preserve">faciendum eſſe monuimus.</s>
            <s xml:id="echoid-s5212" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5213" xml:space="preserve">3. </s>
            <s xml:id="echoid-s5214" xml:space="preserve">
              <emph style="sc">Qvod</emph>
            ſi baſis altitudinis ex latere montis videri poſsit, nullo ferme la-
              <lb/>
            bore problema per vnicam ſtationem efficiemus. </s>
            <s xml:id="echoid-s5215" xml:space="preserve">Nam ſi in D, ſtatuatur qua-
              <lb/>
            dratum, ita vt centrum dioptræ ſit ſuperius, & </s>
            <s xml:id="echoid-s5216" xml:space="preserve">latus infimum recta in B, feratur,
              <lb/>
              <note symbol="f" position="right" xlink:label="note-163-07" xlink:href="note-163-07a" xml:space="preserve">4. ſexti.</note>
            dirigenda erit dioptra verſus idem punctum B. </s>
            <s xml:id="echoid-s5217" xml:space="preserve"> Nam ſi
              <note style="it" position="right" xlink:label="note-163-08" xlink:href="note-163-08a" xml:space="preserve">
                <lb/>
              Vt vmbra verſa \\ abſciſſa # Ad lat{us} quadra- \\ ti: # Ita lat{us} qua- \\ drati # a
                <unsure/>
              daliud,
                <lb/>
              </note>
            inuenietur diſtantia DB, in partibus lateris quadrati, vt liquido cõſtat ex ijs, quæ
              <lb/>
            in problem. </s>
            <s xml:id="echoid-s5218" xml:space="preserve">15. </s>
            <s xml:id="echoid-s5219" xml:space="preserve">Num. </s>
            <s xml:id="echoid-s5220" xml:space="preserve">5. </s>
            <s xml:id="echoid-s5221" xml:space="preserve">ſcripſimus, patetque in 1. </s>
            <s xml:id="echoid-s5222" xml:space="preserve">figura eiuſdem problematis; </s>
            <s xml:id="echoid-s5223" xml:space="preserve"/>
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