Clavius, Christoph, Geometria practica

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        <div xml:id="echoid-div105" type="section" level="1" n="47">
          <pb o="54" file="084" n="84" rhead="GEOMETR. PRACT."/>
          <p>
            <s xml:id="echoid-s2179" xml:space="preserve">nota fiet diſtantia D F, cui ſi a dij ciatur differentia ſtationum E D, cognita etiam
              <lb/>
              <note position="left" xlink:label="note-084-01" xlink:href="note-084-01a" xml:space="preserve">Diſtantiæ in-
                <lb/>
              @entio per ſo-
                <lb/>
              los ſin{us}.</note>
            erit longior diſtantia EF. </s>
            <s xml:id="echoid-s2180" xml:space="preserve">quaminuenies quo que, ſi fiat,</s>
          </p>
          <note style="it" position="right" xml:space="preserve">
            <lb/>
          Vt ſin{us} to- \\ t{us} anguli \\ recti F, # ad hypotenuſam \\ E G, nuper inuen- \\ tam # Ita ſin{us} anguli E G F, complemen- \\ ti anguli obſeruationis in rem@- \\ tiore ſtatione # ad E F.
            <lb/>
          </note>
          <note symbol="a" position="left" xml:space="preserve">10. triang. re-
            <lb/>
          ctil.</note>
          <p>
            <s xml:id="echoid-s2181" xml:space="preserve">Altitudo autem F G, per ſolos ſinus inuenietur, ſi fiat,</s>
          </p>
          <note symbol="b" position="left" xml:space="preserve">10. triang.
            <lb/>
          rectil.
            <lb/>
          Altitudinis in
            <lb/>
          uentio per ſo-
            <lb/>
          los ſin{us}.</note>
          <note style="it" position="right" xml:space="preserve">
            <lb/>
          Vt ſin{us} to- \\ t{us} anguli \\ recti F, # ad hypotenuſam EG, \\ vel ad hypotenuſam \\ D G: # Ita ſin{us} anguli ε, obſeruati \\ minoris, vel ita ſin{us} anguli \\ G D F, obſeruati maioris # ad F G, \\ ad F G.
            <lb/>
          </note>
          <p>
            <s xml:id="echoid-s2182" xml:space="preserve">5. </s>
            <s xml:id="echoid-s2183" xml:space="preserve">
              <emph style="sc">Per</emph>
            Quadrantem ſtabilem eo dem modo dimenſio fit: </s>
            <s xml:id="echoid-s2184" xml:space="preserve">ſolum anguli ob-
              <lb/>
            ſeruationum in duabus ſtationibus hac ra-
              <lb/>
              <figure xlink:label="fig-084-01" xlink:href="fig-084-01a" number="19">
                <image file="084-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/084-01"/>
              </figure>
            tione inueſtigantur. </s>
            <s xml:id="echoid-s2185" xml:space="preserve">Collocato Quadran-
              <lb/>
            te ſupra baſem aliquam planam Horizonti
              <lb/>
            æquidiſtãtem, ita vtrectus ſit ad Horizon-
              <lb/>
            tem; </s>
            <s xml:id="echoid-s2186" xml:space="preserve">quod beneficio alicuius perpendiculi
              <lb/>
            efficies. </s>
            <s xml:id="echoid-s2187" xml:space="preserve">Collocato, inquam, hoc modo
              <lb/>
            Quadrante eleua dioptram, donec per fo-
              <lb/>
            ramina pinnacidiorum faſtigiũ G, videas.
              <lb/>
            </s>
            <s xml:id="echoid-s2188" xml:space="preserve">Ita enim in propinquiore ſtatione D, angulus obſeruationis erit GDF; </s>
            <s xml:id="echoid-s2189" xml:space="preserve">In remo-
              <lb/>
            tiore vero GEF. </s>
            <s xml:id="echoid-s2190" xml:space="preserve">Vtrumque autem metietur arcus Quadrantis inter rectam EF,
              <lb/>
            & </s>
            <s xml:id="echoid-s2191" xml:space="preserve">dioptræ lineam fiduciæ. </s>
            <s xml:id="echoid-s2192" xml:space="preserve">Reliqua omnia fient, ſicut in Quadrante pendulo,
              <lb/>
            vt figura demonſtrat. </s>
            <s xml:id="echoid-s2193" xml:space="preserve">Solum ad altitudinem F G, inuentam adij cienda erit alti-
              <lb/>
            tudo baſis; </s>
            <s xml:id="echoid-s2194" xml:space="preserve">cuiimpoſitus eſt Quadrans, non autem ſtatura menſoris, niſi altitu-
              <lb/>
            dini baſis ſit æqualis.</s>
            <s xml:id="echoid-s2195" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2196" xml:space="preserve">6. </s>
            <s xml:id="echoid-s2197" xml:space="preserve">
              <emph style="sc">Iam</emph>
            vero ſine numeris, id eſt, ſine multiplicatione ac diuiſione numero-
              <lb/>
              <note position="left" xlink:label="note-084-06" xlink:href="note-084-06a" xml:space="preserve">Problema hoc
                <lb/>
              1. quo pacto ſi-
                <lb/>
              ne numeris ab
                <lb/>
              ſolu@@ur.</note>
            rum omnia hæc explorari poterunt, (quod ijs, qui parum in numeris, & </s>
            <s xml:id="echoid-s2198" xml:space="preserve">vſu ſi-
              <lb/>
            nuum, Tangentium, ac ſecantium exercitati ſunt, pergratum fore non dubi-
              <lb/>
            to.) </s>
            <s xml:id="echoid-s2199" xml:space="preserve">hoc modo. </s>
            <s xml:id="echoid-s2200" xml:space="preserve">In charta aliqua, vel plano conſtruatur figura illi omnino ſi-
              <lb/>
            milis, quam ab oculo vſque ad altitudinem ſupra concepimus eſſe conſtructã;
              <lb/>
            </s>
            <s xml:id="echoid-s2201" xml:space="preserve">quod ita fiet. </s>
            <s xml:id="echoid-s2202" xml:space="preserve">Ex inſtrumento partium cap. </s>
            <s xml:id="echoid-s2203" xml:space="preserve">1. </s>
            <s xml:id="echoid-s2204" xml:space="preserve">ſuperioris libri fabricato, vel (ſi
              <lb/>
            inſtrumentum non adſit) ex aliqua recta in particulas plurimas æquales diuiſa
              <lb/>
            capiantur circino tot particulæ æquales, quot palmi, vel pedes inter duas ſtati-
              <lb/>
            ones comprehenduntur; </s>
            <s xml:id="echoid-s2205" xml:space="preserve">transferaturque interuallum illud circini in rectam
              <lb/>
            quamcunque ex E, in D: </s>
            <s xml:id="echoid-s2206" xml:space="preserve">atque in D, & </s>
            <s xml:id="echoid-s2207" xml:space="preserve">E, omni adhibita diligentia, anguli ob-
              <lb/>
            ſeruatioi um GDF, GEF, primæ, & </s>
            <s xml:id="echoid-s2208" xml:space="preserve">ſecundæ ſtationis fiant: </s>
            <s xml:id="echoid-s2209" xml:space="preserve">Punctumque G, in
              <lb/>
            quo rectæ D G, E G, conueniunt, diligenter notetur, (Ne in hoc puncto erretur,
              <lb/>
            propter obliquam ſectionem, docebimus in ſequenti lemmate, quo pacto ex-
              <lb/>
            quiſitiſsime deprehen di poſsit. </s>
            <s xml:id="echoid-s2210" xml:space="preserve">Niſi enim hoc fiat,
              <lb/>
              <figure xlink:label="fig-084-02" xlink:href="fig-084-02a" number="20">
                <image file="084-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/084-02"/>
              </figure>
            mẽſuræ nõ inueniẽtur accurate) ex quo perp ẽdicu-
              <lb/>
            laris demittatur G F Figura ita conſtructa, ſi rectæ
              <lb/>
            D F, EF, F G, D G, E G, per circinum tranſporten-
              <lb/>
            tur in latus 100. </s>
            <s xml:id="echoid-s2211" xml:space="preserve">partium prædicti inſtrumenti, vel in
              <lb/>
            dictam rectam in plurimas partes æquales diuiſam,
              <lb/>
            illico apparebit, quot parriculæ inter pedes </s>
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