Clavius, Christoph, Geometria practica

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        <div xml:id="echoid-div262" type="section" level="1" n="113">
          <pb o="105" file="135" n="135" rhead="LIBER TERTIVS."/>
          <note style="it" position="right" xml:space="preserve">
            <lb/>
          Vt A a, differentia Quotientum \\ qui fiunt, ſilat{us} quadrati \\ per vtramque vmbram rectam \\ diuidatur, # ad A a, differentiam \\ ſtationum notam in \\ menſura aliqua: # ita A F, \\ vt 1. # ad AF, \\ diſtan- \\ tiam,@
            <lb/>
          </note>
          <figure number="63">
            <image file="135-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/135-01"/>
          </figure>
          <p>
            <s xml:id="echoid-s4079" xml:space="preserve">hoc eſt, ſi differentia ſtationum diuidatur per dif-
              <lb/>
            ferentiam Quotientum, efficietur nota diſtantia
              <lb/>
            AF, in partibus differentiæ ſtationum A a, &</s>
            <s xml:id="echoid-s4080" xml:space="preserve">c.</s>
            <s xml:id="echoid-s4081" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4082" xml:space="preserve">3. </s>
            <s xml:id="echoid-s4083" xml:space="preserve">
              <emph style="sc">Si</emph>
            denique in ſtatione inferiori latus vm-
              <lb/>
            brærectæ ſecetur in E, & </s>
            <s xml:id="echoid-s4084" xml:space="preserve">in ſuperiori ſtatione latus
              <lb/>
            vmbræ verſæ in H, reducenda quo que erit vmbra
              <lb/>
            recta ad verſam, vt diximus, & </s>
            <s xml:id="echoid-s4085" xml:space="preserve">producendum la-
              <lb/>
            tus D C, vmbræ verſæ vſque ad punctum N, ſu-
              <lb/>
            mendaque D I, ipſi d H, æqualis. </s>
            <s xml:id="echoid-s4086" xml:space="preserve">Nam vt Num. </s>
            <s xml:id="echoid-s4087" xml:space="preserve">1.
              <lb/>
            </s>
            <s xml:id="echoid-s4088" xml:space="preserve">oſtendimus, ſi fiat,</s>
          </p>
          <note style="it" position="right" xml:space="preserve">
            <lb/>
          Vt N I, differentia vm- \\ brarum verſarum # ad Aa, differentiam \\ ſtationum: # Ita A D, lat{us} \\ quadrati # ad A F, di- \\ ſtantiam,
            <lb/>
          </note>
          <p>
            <s xml:id="echoid-s4089" xml:space="preserve">cognita rurſus erit diſtantia A F, in partibus differentiæ ſtationum A a.</s>
            <s xml:id="echoid-s4090" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div263" type="section" level="1" n="114">
          <head xml:id="echoid-head117" xml:space="preserve">ALITER.</head>
          <p>
            <s xml:id="echoid-s4091" xml:space="preserve">
              <emph style="sc">Sine</emph>
            reductione vmbræ rectæ ad verſam ita quoque agemus. </s>
            <s xml:id="echoid-s4092" xml:space="preserve">Numerus
              <lb/>
            qui fit ex recta vmbra B E, in vmbram verſam d H, auferatur ex 1000000. </s>
            <s xml:id="echoid-s4093" xml:space="preserve">qua-
              <lb/>
            drato lateris 1000. </s>
            <s xml:id="echoid-s4094" xml:space="preserve">reſiduumque ſit, O. </s>
            <s xml:id="echoid-s4095" xml:space="preserve">Item ex vmbra recta B E, in latus qua-
              <lb/>
            drati 1000. </s>
            <s xml:id="echoid-s4096" xml:space="preserve">fiat P. </s>
            <s xml:id="echoid-s4097" xml:space="preserve">Et quoniam, vt initio huius libro in conſtructione quadrati
              <lb/>
            Numer. </s>
            <s xml:id="echoid-s4098" xml:space="preserve">6. </s>
            <s xml:id="echoid-s4099" xml:space="preserve">oſtendimus, latus quadrati medio loco proportionale eſt inter vm-
              <lb/>
            bras B E, D N: </s>
            <s xml:id="echoid-s4100" xml:space="preserve"> Erit rectangulum ſub B E, D N, quadrato lateris æquale. </s>
            <s xml:id="echoid-s4101" xml:space="preserve">
              <note symbol="a" position="right" xlink:label="note-135-03" xlink:href="note-135-03a" xml:space="preserve">16. ſexti.</note>
              <note symbol="b" position="right" xlink:label="note-135-04" xlink:href="note-135-04a" xml:space="preserve">1. ſecundum.</note>
            ergo rectangulum ſub B E, D N, æquale ſitrectangulis ſub D E, D I, & </s>
            <s xml:id="echoid-s4102" xml:space="preserve">ſub B E,
              <lb/>
            N I: </s>
            <s xml:id="echoid-s4103" xml:space="preserve">ſi rectangulum ſub B E, D I, auferatur ex rectangulo ſub B E, DN, id eſt,
              <lb/>
            ex 1000000. </s>
            <s xml:id="echoid-s4104" xml:space="preserve">quadrato lateris A D, reliquum fiet rectangulum ſub
              <lb/>
            B E, N I; </s>
            <s xml:id="echoid-s4105" xml:space="preserve">ac proinde cum D I, ipſi d H, ſi æqualis, fiet rectangulum ſub B E, D I,
              <lb/>
            ex vmbra B E, in vmbram d H; </s>
            <s xml:id="echoid-s4106" xml:space="preserve">atque idcirco reliquum rectangulum ſub B E,
              <lb/>
            N I, (quod videlicet relin quitur, ſi rectangulum ſub B E, D I, ex quadrato late-
              <lb/>
            ris detrahatur, vt dictum eſt,) numero O, æquale erit. </s>
            <s xml:id="echoid-s4107" xml:space="preserve">Eſt autem ex conſtru-
              <lb/>
            ctione rectangulum quo que ſub B E, vmbrarecta, & </s>
            <s xml:id="echoid-s4108" xml:space="preserve">latere A D, numero P, æ-
              <lb/>
            quale. </s>
            <s xml:id="echoid-s4109" xml:space="preserve">Igitur cum numerus B E, multiplicans N I, A D, producat O, P,
              <note symbol="c" position="right" xlink:label="note-135-05" xlink:href="note-135-05a" xml:space="preserve">17. ſept.</note>
            erit O, ad P, vt N I, ad AD. </s>
            <s xml:id="echoid-s4110" xml:space="preserve">Sed vt Numero 1. </s>
            <s xml:id="echoid-s4111" xml:space="preserve">huius problematis demonſtra-
              <lb/>
            uimus, vt NI, differentia vmbrarum verſarum ad A a, differentiam ſtationum, ita
              <lb/>
            eſt AD, latus quadrati ad AF, & </s>
            <s xml:id="echoid-s4112" xml:space="preserve">permutando vt NI, ad AD, ita A a, ad AF. </s>
            <s xml:id="echoid-s4113" xml:space="preserve">Igi-
              <lb/>
            tur erit quoque O, ad P, vt A a, ad A F. </s>
            <s xml:id="echoid-s4114" xml:space="preserve">Quamobrem ſi fiat,</s>
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          <note style="it" position="right" xml:space="preserve">
            <lb/>
          Vt O, numer{us}, quirelinquitur \\ ſinumer{us} genit{us} ex vmbra \\ recta in verſam ex quadrato \\ lateris de@rahatur, # ad numerum P, \\ qui ex vmbra re- \\ cta B E, in lat{us} AD, \\ producitur: # Ita A a, diffe- \\ @entiaſtatio- \\ tionum # Ad AF, \\ diſtan- \\ tiam
            <lb/>
          </note>
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