Clavius, Christoph, Gnomonices libri octo, in quibus non solum horologiorum solariu[m], sed aliarum quo[quam] rerum, quae ex gnomonis umbra cognosci possunt, descriptiones geometricè demonstrantur

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            <s xml:id="echoid-s3064" xml:space="preserve">
              <pb o="46" file="0066" n="66" rhead="GNOMONICES"/>
            neis rectis in centro mundi ſe ſecantibus, per præcedentem propoſ. </s>
            <s xml:id="echoid-s3065" xml:space="preserve">ſit vt communes eorum, & </s>
            <s xml:id="echoid-s3066" xml:space="preserve">
              <lb/>
            plani horologij ſectiones, id eſt, lineæ eorum horariæ, ſecent communes ſectiones illarum ſuper-
              <lb/>
            ficierum conicarum, & </s>
            <s xml:id="echoid-s3067" xml:space="preserve">plani horologii, in illis punctis, in quibus lineæ illæ rectæ, quibus circuli
              <lb/>
            horarij ſuperficies conicas ſecant, plano horologij, & </s>
            <s xml:id="echoid-s3068" xml:space="preserve">conicis ſectionibus occurrunt; </s>
            <s xml:id="echoid-s3069" xml:space="preserve">quandoqui-
              <lb/>
            dem lineæ huiuſmodi horariæ, communes ſcilicet ſectiones circulorum horariorum, & </s>
            <s xml:id="echoid-s3070" xml:space="preserve">plani ho-
              <lb/>
            rologij, exiſtunt in planis horariorum circulorum, qui ſuperficies conicas, atque adeo & </s>
            <s xml:id="echoid-s3071" xml:space="preserve">ſectiones
              <lb/>
            conicas in plano horologij exiſtentes ibidem ſecant. </s>
            <s xml:id="echoid-s3072" xml:space="preserve">Hinc enim fit, vt cum planum horologij, & </s>
            <s xml:id="echoid-s3073" xml:space="preserve">
              <lb/>
            plana circulorum horariorum in illis punctis ſe interſecent, & </s>
            <s xml:id="echoid-s3074" xml:space="preserve">tam illud quàm hæc plana intra
              <lb/>
            conum, atque adeo & </s>
            <s xml:id="echoid-s3075" xml:space="preserve">intra conicas ſectiones tendant, earum communes ſectiones, nempe lineæ
              <lb/>
            horariæ, cadant quoque ab illis punctis intra conum, ac proinde & </s>
            <s xml:id="echoid-s3076" xml:space="preserve">intra ſectiones conicas, cum
              <lb/>
              <note position="left" xlink:label="note-0066-01" xlink:href="note-0066-01a" xml:space="preserve">10</note>
            poſt illa puncta neque à plano horologij, neque à planis dictorum circulorum recedant, ſed in
              <lb/>
            vtriſque perpetuo exiſtant. </s>
            <s xml:id="echoid-s3077" xml:space="preserve">Conſtat ergo id, quod primo loco propoſitum eſt.</s>
            <s xml:id="echoid-s3078" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3079" xml:space="preserve">Q V I A vero circuli horarum ab ortu, vel occaſu tangunt eaſdem ſuperficies conicas, per
              <lb/>
            candem propoſ. </s>
            <s xml:id="echoid-s3080" xml:space="preserve">antecedentem, in lineis illis, quibus eas ſecant circuli horarum à meridie, vel me-
              <lb/>
            dia nocte; </s>
            <s xml:id="echoid-s3081" xml:space="preserve">efficitur, vt communes illorum, & </s>
            <s xml:id="echoid-s3082" xml:space="preserve">plani horologij ſectiones, hoc eſt, lineæ eorum ho-
              <lb/>
            rariæ, tangant ſectiones conicas, quas facit horologij planum, in illis punctis, in quibus lineæ il-
              <lb/>
            lę rectæ, quibus circuli horarii ſuperficies conicas tangunt, plano horologij, & </s>
            <s xml:id="echoid-s3083" xml:space="preserve">conicis ſectionibus
              <lb/>
            occurrunt, in ijs nimirum, in quibus lineæ horarum à meridie, vel media nocte, ſectiones coni-
              <lb/>
            cas ſecant; </s>
            <s xml:id="echoid-s3084" xml:space="preserve">quandoquidem lineæ horariæ ab ortu, vel occaſu, communes videlicet ſectiones cir-
              <lb/>
            culorum horariorum, & </s>
            <s xml:id="echoid-s3085" xml:space="preserve">plani horologij, exiſtunt in planis circulorum horariorum, qui ibidem
              <lb/>
              <note position="left" xlink:label="note-0066-02" xlink:href="note-0066-02a" xml:space="preserve">20</note>
            ſuperficies conicas, atque adeò & </s>
            <s xml:id="echoid-s3086" xml:space="preserve">conicas ſectiones in plano horologij exiſtentes tangunt. </s>
            <s xml:id="echoid-s3087" xml:space="preserve">Hinc
              <lb/>
            enim efficitur, vt cum planum horologij, & </s>
            <s xml:id="echoid-s3088" xml:space="preserve">plana circulorum horariorum in illis punctis ſe in-
              <lb/>
            terſecent, & </s>
            <s xml:id="echoid-s3089" xml:space="preserve">illud quidem intra conum, atque adeo intra conicas ſectiones extendatur, hæc ve-
              <lb/>
            ro plana extra conum, & </s>
            <s xml:id="echoid-s3090" xml:space="preserve">ideo extra ſectiones conicas protendantur, earum communes ſectiones,
              <lb/>
            hoc eſt, horariæ lineæ, cadant ab illis punctis totæ extra conum, ac proinde & </s>
            <s xml:id="echoid-s3091" xml:space="preserve">extra ſectiones coni-
              <lb/>
            cas; </s>
            <s xml:id="echoid-s3092" xml:space="preserve">cum poſt illa puncta neque à plan o horologij, nec à planis dictorum circulorum recedant,
              <lb/>
            ſed in vtriſque perpetuo exiſtant, quorum hæc tota extra conum, & </s>
            <s xml:id="echoid-s3093" xml:space="preserve">conicas ſectiones reperiuntur.
              <lb/>
            </s>
            <s xml:id="echoid-s3094" xml:space="preserve">Patet igitur & </s>
            <s xml:id="echoid-s3095" xml:space="preserve">id, quod ſecundo loco fuit propoſitum. </s>
            <s xml:id="echoid-s3096" xml:space="preserve">Lineæ ergo horarum à meridie, vel media
              <lb/>
            nocte ſecant, &</s>
            <s xml:id="echoid-s3097" xml:space="preserve">c. </s>
            <s xml:id="echoid-s3098" xml:space="preserve">Quod oſten dendum erat.</s>
            <s xml:id="echoid-s3099" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">30</note>
        </div>
        <div xml:id="echoid-div175" type="section" level="1" n="51">
          <head xml:id="echoid-head54" style="it" xml:space="preserve">SCHOLIVM.</head>
          <p style="it">
            <s xml:id="echoid-s3100" xml:space="preserve">QVOD ſi planum horologij æquidiſtet alicui circulo horæ à meridie, vel media nocte, non ſecabit
              <lb/>
            hic cir culus conicam ſectionem à plano horologij factam, cum nec ipſum planum horologij ſecet, vt con-
              <lb/>
            ſtat. </s>
            <s xml:id="echoid-s3101" xml:space="preserve">Vnde neque linea horaria illius eandem conicam ſectionem ſecabit, at que adeo lineæ horariæ ab or-
              <lb/>
            tu, vel occaſu, quarum circuli tangunt conicas ſuperficie
              <unsure/>
            s in lineis, in quibus à circulo illo horario à meri-
              <lb/>
            die, vel media nocte ſccatur, non tangent conicas ſectiones, vt propoſ. </s>
            <s xml:id="echoid-s3102" xml:space="preserve">ſequenti demonſlrabitur.</s>
            <s xml:id="echoid-s3103" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div176" type="section" level="1" n="52">
          <head xml:id="echoid-head55" xml:space="preserve">THEOREMA 13. PROPOSITIO 15.</head>
          <note position="left" xml:space="preserve">40</note>
          <p>
            <s xml:id="echoid-s3104" xml:space="preserve">SI circulus cuiuſuis horæ à meridie, vel media nocte plano horolo-
              <lb/>
              <note position="left" xlink:label="note-0066-05" xlink:href="note-0066-05a" xml:space="preserve">Lineæ horarum
                <lb/>
              ab or. vel occ.
                <lb/>
              quarum circuli
                <lb/>
              tangunt paralle
                <lb/>
              lum ſemper ap-
                <lb/>
              parentium ma-
                <lb/>
              ximum in eiſ-
                <lb/>
              dem punctis, in
                <lb/>
              quibus a circu-
                <lb/>
              lo alicuius horę
                <lb/>
              à mer. uel med.
                <lb/>
              noc qui horolo
                <lb/>
              gio æquidiſter,
                <lb/>
              ſecatur, non cõ-
                <lb/>
              ueniunt cum ſe
                <lb/>
              ctionibus coni-
                <lb/>
              cis, quas in ſu-
                <lb/>
              perficiebus coni
                <lb/>
              cis, quarum ba-
                <lb/>
              ſes ſunt maxi-
                <lb/>
              mi parallelorũ
                <lb/>
              ſemper apparé-
                <lb/>
              tium & laten-
                <lb/>
              tium, facit horo
                <lb/>
              logit planum:
                <lb/>
              ſemper tamen
                <lb/>
              longius produ-
                <lb/>
              ctæ propinquio
                <lb/>
              res fiunt coni-
                <lb/>
              cis ſectionibus.</note>
            gij æquidiſtet, tangant autem maximum parallelorum ſemper apparen-
              <lb/>
            tium duo circuli horarum ab ortu, vel occaſu in eiſdem punctis, in qui-
              <lb/>
            bus à circulo illo horæ à meridie, vel media nocte ſecatur; </s>
            <s xml:id="echoid-s3105" xml:space="preserve">erunt duæ
              <lb/>
            illæ lineæ horarum ab ortu, vel occaſu ἀσύμπτοτοι, hoc eſt, non conue-
              <lb/>
            nientes cum conicis ſectionibus, quas planum horologij facitin ſu-
              <lb/>
            perficiebus conicis, quarum baſes ſunt maximi parallelorum ſemper ap-
              <lb/>
              <note position="left" xlink:label="note-0066-06" xlink:href="note-0066-06a" xml:space="preserve">50</note>
            parentium, & </s>
            <s xml:id="echoid-s3106" xml:space="preserve">deliteſcentium, ſemperq́; </s>
            <s xml:id="echoid-s3107" xml:space="preserve">longius productæ fient coni-
              <lb/>
            cis ſectionibus propinquiores.</s>
            <s xml:id="echoid-s3108" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3109" xml:space="preserve">SECET ſuperficies conicas A B C, A D E, ad centrum A, coniunctas, quarum baſes ſint pa-
              <lb/>
            rallelus D E, ſemper apparentium maximus, & </s>
            <s xml:id="echoid-s3110" xml:space="preserve">B C, parallelus maximus ſemper latentium ſub
              <lb/>
            Horizonte, circulus aliquis horarius à meridie, vel media nocte F G, per axem F G, rectis H I,
              <lb/>
            K L, faciensq́, diametros parallelorum H K, L I, (cum eos, per propoſ. </s>
            <s xml:id="echoid-s3111" xml:space="preserve">15. </s>
            <s xml:id="echoid-s3112" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s3113" xml:space="preserve">1. </s>
            <s xml:id="echoid-s3114" xml:space="preserve">Theod. </s>
            <s xml:id="echoid-s3115" xml:space="preserve">ſecet
              <lb/>
            bifariam, atque adeo per eorum diametros) & </s>
            <s xml:id="echoid-s3116" xml:space="preserve">æquidiſtans plano horologij M N, quod per pro-
              <lb/>
            poſ. </s>
            <s xml:id="echoid-s3117" xml:space="preserve">6. </s>
            <s xml:id="echoid-s3118" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s3119" xml:space="preserve">faciet duas hyperbolas oppoſitas, & </s>
            <s xml:id="echoid-s3120" xml:space="preserve">æquales O P Q, R S T. </s>
            <s xml:id="echoid-s3121" xml:space="preserve">Et quoniam plana
              <lb/>
            F G, M N, parallela ponuntur, erunt eorum communes ſectiones factæ à parallelo D E, </s>
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