Clavius, Christoph, Geometria practica

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        <div xml:id="echoid-div255" type="section" level="1" n="110">
          <pb o="103" file="133" n="133" rhead="LIBER TERTIVS."/>
          <p>
            <s xml:id="echoid-s3998" xml:space="preserve">
              <emph style="sc">Cætervm</emph>
            in ſcholio problematis 7. </s>
            <s xml:id="echoid-s3999" xml:space="preserve">præſcribemus rationẽ, qua eandem
              <lb/>
            diſtantiam A F, metiri licebit per vnicam ſtationem.</s>
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          </p>
          <p>
            <s xml:id="echoid-s4001" xml:space="preserve">DISTANTIAM eandem per duas ſtationes in aliqua altitudine ere-
              <lb/>
            cta factas, ope quadrati perſcrutari.</s>
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          </p>
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        <div xml:id="echoid-div257" type="section" level="1" n="111">
          <head xml:id="echoid-head114" xml:space="preserve">PROBLEMA IV.</head>
          <p>
            <s xml:id="echoid-s4003" xml:space="preserve">1. </s>
            <s xml:id="echoid-s4004" xml:space="preserve">
              <emph style="sc">Qvando</emph>
            in plano commode fieri nequeunt duæ ſtationes, erigatu@
              <lb/>
            haſta aliqua K b, in qua fiant duæ ſtationes oculi menſoris in A, a: </s>
            <s xml:id="echoid-s4005" xml:space="preserve">Vel in dua-
              <lb/>
            bus feneſtris alicuius turris, quarum vna ſuperſtet alteri ad perpendiculum: </s>
            <s xml:id="echoid-s4006" xml:space="preserve">ab-
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            ſcindatur que primum latus vmbræ verſæ in vtraque ſtatione in E, H, Erit que in-
              <lb/>
            ferioris ſtationis vmbra verſa D E, maior, quam vmbra verſa d H, ſtationis ſu-
              <lb/>
            perioris, quod angulus A, maior ſit angulus A, maior ſit angulo a; </s>
            <s xml:id="echoid-s4007" xml:space="preserve">quip pe cũ
              <lb/>
            A G F, minor ſit, quama G M; </s>
            <s xml:id="echoid-s4008" xml:space="preserve">& </s>
            <s xml:id="echoid-s4009" xml:space="preserve">angu-
              <lb/>
            li F, M, recti. </s>
            <s xml:id="echoid-s4010" xml:space="preserve">Sumatur D I, ipſi d H,
              <lb/>
              <figure xlink:label="fig-133-01" xlink:href="fig-133-01a" number="61">
                <image file="133-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/133-01"/>
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              <note symbol="a" position="right" xlink:label="note-133-01" xlink:href="note-133-01a" xml:space="preserve">4. ſexti.</note>
            æqualis; </s>
            <s xml:id="echoid-s4011" xml:space="preserve"> Et quoniam eſt, vt A D, ad D E, ita A F, ad F G: </s>
            <s xml:id="echoid-s4012" xml:space="preserve">erit permutando,
              <lb/>
            vt A D, ad A F, ita D E, ad F G. </s>
            <s xml:id="echoid-s4013" xml:space="preserve">Eadem-
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            que ratione erit, vt ad@ ad a M, ita d H, ad
              <lb/>
            M G. </s>
            <s xml:id="echoid-s4014" xml:space="preserve">Cum ergo eadem ſit proportio
              <lb/>
            A D, ad A F, quę a d, ad a M, propter ę-
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            qualitatem linearum AD, a d, & </s>
            <s xml:id="echoid-s4015" xml:space="preserve">AF, a M;
              <lb/>
            </s>
            <s xml:id="echoid-s4016" xml:space="preserve">
              <note symbol="b" position="right" xlink:label="note-133-02" xlink:href="note-133-02a" xml:space="preserve">11. quinti.</note>
            Erit vt D E, tota ad totam FG, ita
              <note symbol="c" position="right" xlink:label="note-133-03" xlink:href="note-133-03a" xml:space="preserve">19. quinti.</note>
            hoceſt DI, ablata ad ablatam MG. </s>
            <s xml:id="echoid-s4017" xml:space="preserve"> Igi- turerit quoque reliqua I E, ad reliquam F M, hoc eſt, ad reliquam A a, vt tota
              <lb/>
            D E, ad totam F G, hoc eſt, vt A D, ad A F; </s>
            <s xml:id="echoid-s4018" xml:space="preserve">cum oſtenſum ſit eſſe A D, ad A F, vt
              <lb/>
            DE, ad FG. </s>
            <s xml:id="echoid-s4019" xml:space="preserve">Quocirca ſi fiat,</s>
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          <note style="it" position="right" xml:space="preserve">
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          Vt IE, differentia vm- \\ brarum verſarum # ad A a, differen- \\ tiam ſtationum, # Ita AD, lat{us} \\ quadrati # ad A F, @diſtan- \\ tiam,
            <lb/>
          </note>
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            <s xml:id="echoid-s4020" xml:space="preserve">manifeſta colligetur diſtantia AF, in partibus diffe-
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              <figure xlink:label="fig-133-02" xlink:href="fig-133-02a" number="62">
                <image file="133-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/133-02"/>
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            rentię ſtationum Aa.</s>
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          <p>
            <s xml:id="echoid-s4022" xml:space="preserve">2. </s>
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              <emph style="sc">Si</emph>
            in vtraque ſtatione latus vmbrę rectę in-
              <lb/>
            terſecetur in E, H, reducenda eſt vtraque vmbra re-
              <lb/>
            cta B@ E, b H, ad verſam, per ea, quę tradita ſunt ad
              <lb/>
            initium huius libri in conſtructi@ne quadrati
              <lb/>
            Numero 7. </s>
            <s xml:id="echoid-s4024" xml:space="preserve">diuidendo videlicet quadratum nu-
              <lb/>
            merum lateris quadrati per vtramque vmbram
              <lb/>
            rectam abſciſſam ſigillatim. </s>
            <s xml:id="echoid-s4025" xml:space="preserve">Nam ſi produ-
              <lb/>
            cantur latera D C, d c, vmbrę verſę vſque ad
              <lb/>
            radios A G, a G, ad puncta I, K, erit iterum,
              <lb/>
            vt demonſtrauimus Numero 1. </s>
            <s xml:id="echoid-s4026" xml:space="preserve">vt I N, differentia
              <lb/>
            vmbrarum verſarum ad A a, differentiam </s>
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