Clavius, Christoph, Geometria practica

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        <div xml:id="echoid-div301" type="section" level="1" n="130">
          <pb o="123" file="153" n="153" rhead="LIBER TERTIVS."/>
        </div>
        <div xml:id="echoid-div303" type="section" level="1" n="131">
          <head xml:id="echoid-head134" xml:space="preserve">PROBLEMA XIV.</head>
          <p>
            <s xml:id="echoid-s4794" xml:space="preserve">1. </s>
            <s xml:id="echoid-s4795" xml:space="preserve">
              <emph style="sc">Sit</emph>
            mons, aut turris D E, ſitque pri-
              <lb/>
              <figure xlink:label="fig-153-01" xlink:href="fig-153-01a" number="82">
                <image file="153-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/153-01"/>
              </figure>
            mum è directo menſoris in faſtigio D, exi-
              <lb/>
            ſtentis interuallum F G, notum. </s>
            <s xml:id="echoid-s4796" xml:space="preserve">Accom-
              <lb/>
            modetur quadratum ſtabile in ſummitate
              <lb/>
            D, ita vt latus A D, perpendiculare ſit ad
              <lb/>
            Horizontem, & </s>
            <s xml:id="echoid-s4797" xml:space="preserve">C D, Horizonti paralle-
              <lb/>
            lum. </s>
            <s xml:id="echoid-s4798" xml:space="preserve">Inſpecto igitur per dioptram vtroq;
              <lb/>
            </s>
            <s xml:id="echoid-s4799" xml:space="preserve">
              <note symbol="a" position="right" xlink:label="note-153-01" xlink:href="note-153-01a" xml:space="preserve">ſchol. 4. ſe-
                <lb/>
              xti.</note>
            termino F, G, ſecetur vmbra recta in H, I. </s>
            <s xml:id="echoid-s4800" xml:space="preserve"> Quoniam igitur eſt, vt I H, ad H D, ita G F,
              <lb/>
              <note symbol="b" position="right" xlink:label="note-153-02" xlink:href="note-153-02a" xml:space="preserve">4. ſexti.</note>
            ad F E: </s>
            <s xml:id="echoid-s4801" xml:space="preserve"> Item ob triangulorum ſimilitu- dinem, vt H D, ad D A, ita FE, ad EA; </s>
            <s xml:id="echoid-s4802" xml:space="preserve">erit ex
              <lb/>
            æquo, vt I H, ad D A, ita G F, ad E A. </s>
            <s xml:id="echoid-s4803" xml:space="preserve">Igitur ſi fiat,
              <lb/>
              <note style="it" position="right" xlink:label="note-153-03" xlink:href="note-153-03a" xml:space="preserve">
                <lb/>
              Vt I H, d@fferentia vm- \\ brarum rectarum # ad D A, lat{us} qua- \\ drati # Ita interuallum G F, \\ cognitum # ad E A
                <lb/>
              </note>
            exibit nota recta E A. </s>
            <s xml:id="echoid-s4804" xml:space="preserve">Et ſi dematur Iatus quadrati D A, (quod fieri debet notum
              <lb/>
            in partibus interualli G F,) reliqua fiet nota altitudo D E, in partibus interualli
              <lb/>
            G F.</s>
            <s xml:id="echoid-s4805" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4806" xml:space="preserve">2. </s>
            <s xml:id="echoid-s4807" xml:space="preserve">
              <emph style="sc">Sit</emph>
            tota deinde diſtantia E G, nota. </s>
            <s xml:id="echoid-s4808" xml:space="preserve">Inſpiciendum ergo ſolum eſt extre-
              <lb/>
            mum G. </s>
            <s xml:id="echoid-s4809" xml:space="preserve"> Nam ſi
              <note symbol="c" position="right" xlink:label="note-153-04" xlink:href="note-153-04a" xml:space="preserve">4. ſexti.</note>
              <note style="it" position="right" xlink:label="note-153-05" xlink:href="note-153-05a" xml:space="preserve">
                <lb/>
              Vt I D, vmbrarecta # ad D A, lat{us} quadrati # Ita diſtantia no- \\ ta G E, # ad E A,
                <lb/>
              </note>
            efficietur rurſus nota recta E A, &</s>
            <s xml:id="echoid-s4810" xml:space="preserve">c.</s>
            <s xml:id="echoid-s4811" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4812" xml:space="preserve">3. </s>
            <s xml:id="echoid-s4813" xml:space="preserve">
              <emph style="sc">Qvando</emph>
            vmbra verſa B C, interſecatur, vt ſi ſpatium notum ſit L N, re-
              <lb/>
            ducenda eſt vtra que vmbra verſa ad rectas D K, D M. </s>
            <s xml:id="echoid-s4814" xml:space="preserve">Nam rurſus erit, vt K M,
              <lb/>
            differentia vmbrarum rectarum ad latus D A, ita ſpatium notum L N, ad E A.</s>
            <s xml:id="echoid-s4815" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4816" xml:space="preserve">
              <emph style="sc">Sic</emph>
            etiam quando vnus radius vmbram rectam, & </s>
            <s xml:id="echoid-s4817" xml:space="preserve">alter verſam interſecat,
              <lb/>
            vt in ſpatio L G, contingit, reuo canda erit vmbra verſa ad rectam DK, vtiterum
              <lb/>
            ſit K I, differentia vmbrarum rectarum ad D A, latus, vt ſpatium notum L G, ad
              <lb/>
            E A.</s>
            <s xml:id="echoid-s4818" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4819" xml:space="preserve">4. </s>
            <s xml:id="echoid-s4820" xml:space="preserve">
              <emph style="sc">Si</emph>
            denique radius per C, tranſiret, ſumendum eſſet totumlatus CD, pro
              <lb/>
            vmbra recta, at vmbra verſa, ſi qua eſſet, ad rectam reducenda.</s>
            <s xml:id="echoid-s4821" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4822" xml:space="preserve">DISTANTIAM ab oculo, vel pede menſoris (vbicunque exiſtat)
              <lb/>
            ad quoduis punctum in aliqua altitudine notatum per quadratum ex-
              <lb/>
            quirere.</s>
            <s xml:id="echoid-s4823" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div306" type="section" level="1" n="132">
          <head xml:id="echoid-head135" xml:space="preserve">PROBLEMA XV.</head>
          <p>
            <s xml:id="echoid-s4824" xml:space="preserve">1. </s>
            <s xml:id="echoid-s4825" xml:space="preserve">
              <emph style="sc">Exploranda</emph>
            ſit diſtantia puncti F, in muro aliquo ſiue perpendicu-
              <lb/>
            lariad Horizontem, ſiue in clinato, vel etiam in tecto quo piam ab oculo A, vel à
              <lb/>
            pede E, poſita ſtatura menſoris A E. </s>
            <s xml:id="echoid-s4826" xml:space="preserve">Et ſit primum altius punctum F, quam ocu-
              <lb/>
            lus A. </s>
            <s xml:id="echoid-s4827" xml:space="preserve">Concipiatur ex F, demiſſa perpendicularis F G, & </s>
            <s xml:id="echoid-s4828" xml:space="preserve">ad hanc ducta ab ocu-
              <lb/>
            lo A, alia perpendicularis A H. </s>
            <s xml:id="echoid-s4829" xml:space="preserve">Collocato ergo ita quadrato, vt latus A D, Ho-
              <lb/>
            rizonti æquidiſtet, inſpiciatur punctum F, radiuſque A F, vel dioptra </s>
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