Clavius, Christoph, Geometria practica

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        <div xml:id="echoid-div394" type="section" level="1" n="164">
          <pb o="152" file="182" n="182" rhead="GEOMETR. PRACT."/>
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        <div xml:id="echoid-div400" type="section" level="1" n="165">
          <head xml:id="echoid-head168" xml:space="preserve">PROBLEMA XLIV.</head>
          <p>
            <s xml:id="echoid-s5872" xml:space="preserve">1. </s>
            <s xml:id="echoid-s5873" xml:space="preserve">
              <emph style="sc">Sint</emph>
            duæ turres A F, GH, quarum ſola faſtigia A, G, cernantur exloco
              <lb/>
            Horizontis B. </s>
            <s xml:id="echoid-s5874" xml:space="preserve">Oportet inueſtigare & </s>
            <s xml:id="echoid-s5875" xml:space="preserve">diſtantiam F H, & </s>
            <s xml:id="echoid-s5876" xml:space="preserve">interuallum A G, & </s>
            <s xml:id="echoid-s5877" xml:space="preserve">v-
              <lb/>
            triuſq; </s>
            <s xml:id="echoid-s5878" xml:space="preserve">turris altitudinem. </s>
            <s xml:id="echoid-s5879" xml:space="preserve">Sit primum minor turris A F, inter maiorem, & </s>
            <s xml:id="echoid-s5880" xml:space="preserve">men-
              <lb/>
            ſorem, ita vt menſor in eodem cum turribus ſit plano, & </s>
            <s xml:id="echoid-s5881" xml:space="preserve">minor non occultet fa-
              <lb/>
            ſtigium G, maioris. </s>
            <s xml:id="echoid-s5882" xml:space="preserve">Per ſchol. </s>
            <s xml:id="echoid-s5883" xml:space="preserve">probl. </s>
            <s xml:id="echoid-s5884" xml:space="preserve">7. </s>
            <s xml:id="echoid-s5885" xml:space="preserve">inuenietur & </s>
            <s xml:id="echoid-s5886" xml:space="preserve">vtraque diſtantia B F, BH,
              <lb/>
            & </s>
            <s xml:id="echoid-s5887" xml:space="preserve">vtra que altitudo A F, G H: </s>
            <s xml:id="echoid-s5888" xml:space="preserve">ſi nimirum in B, Quadratum ita locetur, vt vnum
              <lb/>
            eius latus cum hypotenuſis BA, BG, coincidat, &</s>
            <s xml:id="echoid-s5889" xml:space="preserve">c. </s>
            <s xml:id="echoid-s5890" xml:space="preserve">quod eſt quartum, ac terti-
              <lb/>
            um. </s>
            <s xml:id="echoid-s5891" xml:space="preserve">Et quia tria puncta B, F, H, ponuntur in eadem recta, erit diſtantiarum diffe-
              <lb/>
            rentia F H, cognita, hoc eſt, diſtantia inter turrium baſes, quod eſt primum. </s>
            <s xml:id="echoid-s5892" xml:space="preserve">Rur-
              <lb/>
            ſus differentia altitudinum GC, nota erit, ac propterea in triangulo
              <note symbol="a" position="left" xlink:label="note-182-01" xlink:href="note-182-01a" xml:space="preserve">6. triang. re-
                <lb/>
              ctil.</note>
            lo ACG, ex duobus lateribus. </s>
            <s xml:id="echoid-s5893" xml:space="preserve">A C, C G, cognitis, baſis quo que A G, efficietur
              <lb/>
            nota. </s>
            <s xml:id="echoid-s5894" xml:space="preserve">quod eſt ſecundum.</s>
            <s xml:id="echoid-s5895" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5896" xml:space="preserve">2. </s>
            <s xml:id="echoid-s5897" xml:space="preserve">
              <emph style="sc">Deinde</emph>
            conſiſtat menſor in D, ita vtipſe, ac baſes F, H, non iaceant in
              <lb/>
            vna linea recta. </s>
            <s xml:id="echoid-s5898" xml:space="preserve">Per ſcholium problem. </s>
            <s xml:id="echoid-s5899" xml:space="preserve">7.
              <lb/>
            </s>
            <s xml:id="echoid-s5900" xml:space="preserve">iterum tam altitu dines AF, GH, quam di-
              <lb/>
            ſtantiæ D F, D H, congitæ fient, ſi videlicet
              <lb/>
              <figure xlink:label="fig-182-01" xlink:href="fig-182-01a" number="113">
                <image file="182-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/182-01"/>
              </figure>
            quadrati vnum latus hypotenuſis D A,
              <lb/>
            D G, congruet, &</s>
            <s xml:id="echoid-s5901" xml:space="preserve">c. </s>
            <s xml:id="echoid-s5902" xml:space="preserve">quod eſt tertium, ac
              <lb/>
            quartum. </s>
            <s xml:id="echoid-s5903" xml:space="preserve">Inueſtigatis autem hypotenuſis
              <lb/>
            DA, DG, vt in eodem ſcholio traditũ eſt,
              <lb/>
            cognoſcetur per problema 16. </s>
            <s xml:id="echoid-s5904" xml:space="preserve">præſertim
              <lb/>
            per ea, quæ Num. </s>
            <s xml:id="echoid-s5905" xml:space="preserve">2. </s>
            <s xml:id="echoid-s5906" xml:space="preserve">eiuſdem problematis
              <lb/>
            ſcripſimus, interuallum A G, ſi nimirum in
              <lb/>
            hypotenuſis accipentur portiones D I,
              <lb/>
            D E, ipſis hypotenuſis proportionales, vt in illo Num. </s>
            <s xml:id="echoid-s5907" xml:space="preserve">2. </s>
            <s xml:id="echoid-s5908" xml:space="preserve">diximus, &</s>
            <s xml:id="echoid-s5909" xml:space="preserve">c. </s>
            <s xml:id="echoid-s5910" xml:space="preserve">quod eſt
              <lb/>
            ſecundum. </s>
            <s xml:id="echoid-s5911" xml:space="preserve">Et quoniam altitudines AF, GH, notæ factæ ſunt, erit etiam earum
              <lb/>
            differentia G C, nota. </s>
            <s xml:id="echoid-s5912" xml:space="preserve">Quam obrem ex baſe A G, & </s>
            <s xml:id="echoid-s5913" xml:space="preserve">latere G C, in triangulo re-
              <lb/>
            ctangulo ACG, cognitis, latus quoq; </s>
            <s xml:id="echoid-s5914" xml:space="preserve">AC, hoc eſt, diſtantia F H, inter baſes no-
              <lb/>
            ta erit: </s>
            <s xml:id="echoid-s5915" xml:space="preserve">quod eſt primum.</s>
            <s xml:id="echoid-s5916" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5917" xml:space="preserve">SI turres eſſent AF, CH, æquales, eſſet diſtantia A C, inter faſtigia diſtantiæ
              <lb/>
            FH, inter baſes æqualis.</s>
            <s xml:id="echoid-s5918" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div403" type="section" level="1" n="166">
          <head xml:id="echoid-head169" xml:space="preserve">SCHOLIVM.</head>
          <p>
            <s xml:id="echoid-s5919" xml:space="preserve">1. </s>
            <s xml:id="echoid-s5920" xml:space="preserve">Ex omnibus, quæ demonſtrata ſuntin hoc 3. </s>
            <s xml:id="echoid-s5921" xml:space="preserve">libro, colligi poteſt regula
              <lb/>
              <note position="left" xlink:label="note-182-02" xlink:href="note-182-02a" xml:space="preserve">Vnica regula
                <lb/>
              adomnes re-
                <lb/>
              ct{as} dimetien-
                <lb/>
              d{as}, quando
                <lb/>
              earum extre-
                <lb/>
              ma videntur.</note>
            generalis ad dimetiendas omnes longitudines, ſiue eæ ſint diſtantię in Horizon-
              <lb/>
            te, ſiue altitudines, profunditateſue, ſiue hypotenuſę, id eſt, diſtãtię ab oculo ad
              <lb/>
            quo dlibet punctum ſiue interualla inter duo puncta, vbicunq; </s>
            <s xml:id="echoid-s5922" xml:space="preserve">exiſtant: </s>
            <s xml:id="echoid-s5923" xml:space="preserve">dum-
              <lb/>
            modo vtrumq; </s>
            <s xml:id="echoid-s5924" xml:space="preserve">extremum longitudinis dimetiendæ videri poſsit à menſore, v-
              <lb/>
            bicun que etiam ipſe exiſtat. </s>
            <s xml:id="echoid-s5925" xml:space="preserve">Nam ſi per problema 15. </s>
            <s xml:id="echoid-s5926" xml:space="preserve">præſertim per ea, quæ Nu.
              <lb/>
            </s>
            <s xml:id="echoid-s5927" xml:space="preserve">5. </s>
            <s xml:id="echoid-s5928" xml:space="preserve">eius problematis ſcripſimus, diſtantiæ à menſore vſque ad duo extrema lon-
              <lb/>
            gitu dinis explorentur, inueſtigato prius angulo, quem duæ illæ diſtantiæ, ſiue
              <lb/>
            hypotenuſæ effi ciunt, vt in ſcholio probl. </s>
            <s xml:id="echoid-s5929" xml:space="preserve">7. </s>
            <s xml:id="echoid-s5930" xml:space="preserve">Num. </s>
            <s xml:id="echoid-s5931" xml:space="preserve">2. </s>
            <s xml:id="echoid-s5932" xml:space="preserve">docuimus; </s>
            <s xml:id="echoid-s5933" xml:space="preserve">&</s>
            <s xml:id="echoid-s5934" xml:space="preserve">c. </s>
            <s xml:id="echoid-s5935" xml:space="preserve">factum e-
              <lb/>
            rit, quod proponitur. </s>
            <s xml:id="echoid-s5936" xml:space="preserve">Itaque ſi diligenter ea, quæ in problem. </s>
            <s xml:id="echoid-s5937" xml:space="preserve">15. </s>
            <s xml:id="echoid-s5938" xml:space="preserve">ac 16. </s>
            <s xml:id="echoid-s5939" xml:space="preserve"/>
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