Clavius, Christoph, Geometria practica

Table of figures

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          <pb o="111" file="141" n="141" rhead="LIBER TERTIVS."/>
          <note style="it" position="right" xml:space="preserve">
            <lb/>
          Vt P, numer{us}, qui relinquitur, ſi \\ product{us} ex vmbra verſa D E, \\ in vmbrã rectam b H, ex qua- \\ drato 1,000,000. d{et}rahatur. # ad Q, numerum, \\ qui fit ex vmbra \\ verſa D E, in la- \\ t{us} A B, 1000. # Ita Aa, diffe- \\ rentia ſtatio- \\ num # ad F G, al- \\ titudinem,
            <lb/>
          </note>
          <p>
            <s xml:id="echoid-s4358" xml:space="preserve">producetur altitudo F G, nota in partibus differentię ſtationum A a: </s>
            <s xml:id="echoid-s4359" xml:space="preserve">cui ſi ad-
              <lb/>
            iicietur ſtatura menſoris F L, tota altitudo GL, nota efficietur.</s>
            <s xml:id="echoid-s4360" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4361" xml:space="preserve">
              <emph style="sc">In</emph>
            ſcholio porro ſequentis problematis idem hoc problema per vnicam
              <lb/>
            ſtationem abſoluemus.</s>
            <s xml:id="echoid-s4362" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4363" xml:space="preserve">ALTITVDINEM eandem, quando diſtantia ab oculo menſoris ne-
              <lb/>
            que data eſt, neque inuenta, neque è directo altitudinis duæ ſtationes
              <lb/>
            fieri poſſunt, per duas ſtationes in aliqua haſta erecta factas, indagare
              <lb/>
            per Quadratum.</s>
            <s xml:id="echoid-s4364" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div280" type="section" level="1" n="121">
          <head xml:id="echoid-head124" xml:space="preserve">PROBLEMA VII.</head>
          <p>
            <s xml:id="echoid-s4365" xml:space="preserve">1. </s>
            <s xml:id="echoid-s4366" xml:space="preserve">
              <emph style="sc">Cvm</emph>
            in plano duæ ſtationes fieri commodè nequeunt erigatur haſta ali-
              <lb/>
            qua K b, ad Horizontem recta, niſi fortè ad ſit aliquod ædificium erectum, ibi-
              <lb/>
              <figure xlink:label="fig-141-01" xlink:href="fig-141-01a" number="68">
                <image file="141-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/141-01"/>
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            que fiant duæ ſtationes in A, & </s>
            <s xml:id="echoid-s4367" xml:space="preserve">a, vt in
              <lb/>
            problemate 4. </s>
            <s xml:id="echoid-s4368" xml:space="preserve">Cadat autem primum
              <lb/>
            dioptra, vel filum perpendiculi in vtra-
              <lb/>
            que ſtatione in vmbram verſam, vt in 1.
              <lb/>
            </s>
            <s xml:id="echoid-s4369" xml:space="preserve">figura problematis 4. </s>
            <s xml:id="echoid-s4370" xml:space="preserve">quę hic repetita eſt. </s>
            <s xml:id="echoid-s4371" xml:space="preserve">
              <lb/>
            Et quoniã propter triangulorũ
              <note symbol="a" position="right" xlink:label="note-141-02" xlink:href="note-141-02a" xml:space="preserve">4. ſexti.</note>
            tudinẽ eſt, vt A D, ad D E, ita AF, ad F G;
              <lb/>
            </s>
            <s xml:id="echoid-s4372" xml:space="preserve">erit permutando vt AD, ad AF, ita DE, ad
              <lb/>
            FG. </s>
            <s xml:id="echoid-s4373" xml:space="preserve">Eademque ratione erit vt, a d, ad
              <lb/>
            a M, ita d H, ad M G. </s>
            <s xml:id="echoid-s4374" xml:space="preserve">Cumergo eadem
              <lb/>
            ſit proportio A D, ad A F, quæ a d, ad a M,
              <lb/>
            propter ęqualitatem rectarum AD, ad, & </s>
            <s xml:id="echoid-s4375" xml:space="preserve">AF, a M; </s>
            <s xml:id="echoid-s4376" xml:space="preserve"> erit vt tota D E, ad
              <note symbol="b" position="right" xlink:label="note-141-03" xlink:href="note-141-03a" xml:space="preserve">11. quinti.</note>
            F G, ita d H, hoc eſt, ita D I, ablata ad ablatam MG. </s>
            <s xml:id="echoid-s4377" xml:space="preserve"> Igitur erit quo que
              <note symbol="c" position="right" xlink:label="note-141-04" xlink:href="note-141-04a" xml:space="preserve">19. quinti.</note>
            I E, ad reliquam F M, hoc eſt, ad D d, vt tota D E, ad totam F G. </s>
            <s xml:id="echoid-s4378" xml:space="preserve">Quocirca ſi
              <lb/>
            fiat,</s>
          </p>
          <note style="it" position="right" xml:space="preserve">
            <lb/>
          Vt IE, differentia vm- \\ brarum verſarum # ad Dd, differentiam \\ ſtationum: # Ita D E, mæior vm- \\ bra verſa # ad F G, altitu- \\ dinem
            <lb/>
          </note>
          <p>
            <s xml:id="echoid-s4379" xml:space="preserve">euadet cognita altitudo F G, in partibus differentiæ ſtationum D d. </s>
            <s xml:id="echoid-s4380" xml:space="preserve">Appoſita
              <lb/>
            autem ſtatura menſoris FL, tota altitudo G L, quæſita cognita erit.</s>
            <s xml:id="echoid-s4381" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4382" xml:space="preserve">2. </s>
            <s xml:id="echoid-s4383" xml:space="preserve">
              <emph style="sc">Abscindat</emph>
            deinde dioptra in vtraque ſtatione vmbram rectam, vt
              <lb/>
            in 2. </s>
            <s xml:id="echoid-s4384" xml:space="preserve">figura problematis 4. </s>
            <s xml:id="echoid-s4385" xml:space="preserve">quæ poſita eſt in pagina 103. </s>
            <s xml:id="echoid-s4386" xml:space="preserve"> Et quia propter
              <note symbol="d" position="right" xlink:label="note-141-06" xlink:href="note-141-06a" xml:space="preserve">4. ſexti.</note>
            gulorum ſimilitudinem eſt vt b H, ad ab, ita a M, ad M G: </s>
            <s xml:id="echoid-s4387" xml:space="preserve"> erit
              <note symbol="e" position="right" xlink:label="note-141-07" xlink:href="note-141-07a" xml:space="preserve">16. ſexti.</note>
            lum ſub b H, M G, æquale rectangulo ſub a b, a M. </s>
            <s xml:id="echoid-s4388" xml:space="preserve">Eadem ratione erit rectan-
              <lb/>
            gulum ſub B E, F G, æquale rectangulo ſub A B, A F, quod eadem quo
              <note symbol="f" position="right" xlink:label="note-141-08" xlink:href="note-141-08a" xml:space="preserve">4. ſexti.</note>
            fit proportio B E, ad A B, quæ A F, ad F G. </s>
            <s xml:id="echoid-s4389" xml:space="preserve">Cum ergo rectangulum ſub a b,
              <lb/>
            a M, rectangulo ſub A B, AF, æquale ſit, ob æqualitatem rectarum a b, A B, & </s>
            <s xml:id="echoid-s4390" xml:space="preserve">
              <lb/>
            a M, AF, erit etiam rectangulum ſub b H, M G; </s>
            <s xml:id="echoid-s4391" xml:space="preserve">rectangulo ſub BE, FG, </s>
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