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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        <div xml:id="echoid-div1024" type="section" level="1" n="254">
          <p>
            <s xml:id="echoid-s20024" xml:space="preserve">
              <pb o="297" file="0313" n="313" rhead="LIBER TERTIVS."/>
            quòd hæc communis ſectio parallela eſt rectæ C G, in plano horologii. </s>
            <s xml:id="echoid-s20025" xml:space="preserve">Manifeſtum eſt autem
              <lb/>
              <note position="right" xlink:label="note-0313-01" xlink:href="note-0313-01a" xml:space="preserve">16. vndec.</note>
            hunc angulum in Meridiano proprio plani declinantis conſ
              <unsure/>
            titutum in centro mundi inſiſtere ar-
              <lb/>
            cui altitudinis poli ſupra illum circulum maximum, cui horologium æquidiſtat.</s>
            <s xml:id="echoid-s20026" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s20027" xml:space="preserve">RECTAM autem G H, ad lineam ſtyli C G, perpendicularem, communem eſſe ſectionem
              <lb/>
            Aequatoris, & </s>
            <s xml:id="echoid-s20028" xml:space="preserve">plani horologii declinantis, vt in conſtructione aſſumpſimus, ita faciemus perſpi-
              <lb/>
            cuum. </s>
            <s xml:id="echoid-s20029" xml:space="preserve">Quoniam axis mundi C H, rectus eſt, per propoſ. </s>
            <s xml:id="echoid-s20030" xml:space="preserve">10. </s>
            <s xml:id="echoid-s20031" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s20032" xml:space="preserve">1. </s>
            <s xml:id="echoid-s20033" xml:space="preserve">Theodoſii, ad Aequatoris pla-
              <lb/>
            num, tranſitq́ue per eius centrum, atque adeo, per defin. </s>
            <s xml:id="echoid-s20034" xml:space="preserve">3. </s>
            <s xml:id="echoid-s20035" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s20036" xml:space="preserve">11. </s>
            <s xml:id="echoid-s20037" xml:space="preserve">Euclidis, perpendicularis eſt
              <lb/>
            ad communem ſectionem Aequatoris, & </s>
            <s xml:id="echoid-s20038" xml:space="preserve">plani per axem mundi C H, & </s>
            <s xml:id="echoid-s20039" xml:space="preserve">rectam G H, ducti, quod
              <lb/>
            quidem ad planum horologii declinantis rectum eſt, tanquam nouus quidam, & </s>
            <s xml:id="echoid-s20040" xml:space="preserve">proprius Meri-
              <lb/>
              <note position="right" xlink:label="note-0313-02" xlink:href="note-0313-02a" xml:space="preserve">18. vndec.</note>
            dianus ipſius, quòd & </s>
            <s xml:id="echoid-s20041" xml:space="preserve">linea G H, per quam ducitur, ad idem recta ſit facta, propter motum trian-
              <lb/>
              <note position="left" xlink:label="note-0313-03" xlink:href="note-0313-03a" xml:space="preserve">10</note>
            guli C G H, circa rectam C G, vt proxime dictum eſt; </s>
            <s xml:id="echoid-s20042" xml:space="preserve">efficitur rectam I G, ſi punctum I, pro cen-
              <lb/>
            tro mundi, Aequatorisve accipiatur, (poteſt autem quodlibet punctum axis pro centro ſumi, cum
              <lb/>
            inſenſibilis ſit, ac planè imperceptibilis eius diſtantia in plano horologii declinãtis à centro mun
              <lb/>
            di, ſi cum diſtantia ipſius à Sole conferatur, vt in ſphæra docuimus) communem ſectionem eſſe
              <lb/>
            Aequatoris, & </s>
            <s xml:id="echoid-s20043" xml:space="preserve">plani per axem C I, & </s>
            <s xml:id="echoid-s20044" xml:space="preserve">rectam I G, ducti; </s>
            <s xml:id="echoid-s20045" xml:space="preserve">quandoquidem recta I G, in plano hoc
              <lb/>
            exiſtens perpendicularis eſt ad axem. </s>
            <s xml:id="echoid-s20046" xml:space="preserve">Si enim Aequator non tranſiret per rectam I G, ſed per aliã
              <lb/>
            quampiam ex puncto I, quod accepimus pro centro, per quod neceſſario Aequator incedit, du-
              <lb/>
            ctam, eſſet axis C I, ad hanc
              <unsure/>
            etiam perpendicularis, per defin. </s>
            <s xml:id="echoid-s20047" xml:space="preserve">3. </s>
            <s xml:id="echoid-s20048" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s20049" xml:space="preserve">11. </s>
            <s xml:id="echoid-s20050" xml:space="preserve">Euclidis, quòd rectus ſit ad
              <lb/>
            Aequatoris planum, in quo hæc recta exiſteret. </s>
            <s xml:id="echoid-s20051" xml:space="preserve">Quare in plano per axem C I, & </s>
            <s xml:id="echoid-s20052" xml:space="preserve">rectam I G, ducto
              <lb/>
            duæ perpendiculares ad axem in puncto I, ducerentur, quod eſt abſurdum. </s>
            <s xml:id="echoid-s20053" xml:space="preserve">Occurret igitur Ae-
              <lb/>
              <note position="left" xlink:label="note-0313-04" xlink:href="note-0313-04a" xml:space="preserve">20</note>
            quatoris planum per rectam I G, ductum plano horologii declinantis in G, puncto lineæ indicis;
              <lb/>
            </s>
            <s xml:id="echoid-s20054" xml:space="preserve">ac proinde per punctum G, ducenda erit linea æquinoctialis, communis nimirum ſectio Aequa-
              <lb/>
            toris, & </s>
            <s xml:id="echoid-s20055" xml:space="preserve">plani horologii declinantis. </s>
            <s xml:id="echoid-s20056" xml:space="preserve">Quoniam verò planum trianguli C G I, rectum eſt ad Aequa-
              <lb/>
              <note position="right" xlink:label="note-0313-05" xlink:href="note-0313-05a" xml:space="preserve">18. vndec.</note>
            torem, propterea quòd recta C I, per quam ducitur dictum triangulum, perpendicularis eſt ad
              <lb/>
            eundem, vt dictum eſt; </s>
            <s xml:id="echoid-s20057" xml:space="preserve">vel certe per propoſ. </s>
            <s xml:id="echoid-s20058" xml:space="preserve">15. </s>
            <s xml:id="echoid-s20059" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s20060" xml:space="preserve">1. </s>
            <s xml:id="echoid-s20061" xml:space="preserve">Theodoſii, propterea quòd planum trian-
              <lb/>
            guli C G I, per axem C I, atque adeò per polos mundi ſeu Aequatoris ductum ſit; </s>
            <s xml:id="echoid-s20062" xml:space="preserve">erit viciſſim & </s>
            <s xml:id="echoid-s20063" xml:space="preserve">
              <lb/>
            Aequator ad planum trianguli C G I, rectus: </s>
            <s xml:id="echoid-s20064" xml:space="preserve">Eſt autem & </s>
            <s xml:id="echoid-s20065" xml:space="preserve">planum horologii declinantis rectum
              <lb/>
            ad idem planum@trianguli C G I, quòd hoc ad illud nuper oſtenſum ſit rectum. </s>
            <s xml:id="echoid-s20066" xml:space="preserve">Igitur communis
              <lb/>
            ſectio Aequatoris, & </s>
            <s xml:id="echoid-s20067" xml:space="preserve">plani horologii declinantis ad idem planum trianguli C G I, recta erit, atque
              <lb/>
              <note position="right" xlink:label="note-0313-06" xlink:href="note-0313-06a" xml:space="preserve">19. vndec.</note>
            adeò & </s>
            <s xml:id="echoid-s20068" xml:space="preserve">perpendicularis erit, per defin. </s>
            <s xml:id="echoid-s20069" xml:space="preserve">3. </s>
            <s xml:id="echoid-s20070" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s20071" xml:space="preserve">11. </s>
            <s xml:id="echoid-s20072" xml:space="preserve">Euclidis, ad lineam indicis C G, in eo plano exi-
              <lb/>
              <note position="left" xlink:label="note-0313-07" xlink:href="note-0313-07a" xml:space="preserve">30</note>
            ſtentem. </s>
            <s xml:id="echoid-s20073" xml:space="preserve">Quare cum dicta communis ſectio ducenda ſit per punctum G, vt proximè oſtendimus,
              <lb/>
            erit G H, perpendicularis ducta ad C G, communis ſectio Aquatoris, & </s>
            <s xml:id="echoid-s20074" xml:space="preserve">plani horologii declinan-
              <lb/>
            tis, id eſt, linea æquinoctialis.</s>
            <s xml:id="echoid-s20075" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s20076" xml:space="preserve">ET quia punctum I, pro centro mundi acceptum eſt, ex quo cadit recta I K, ad planum horo
              <lb/>
            logii declinantis, per defin. </s>
            <s xml:id="echoid-s20077" xml:space="preserve">4. </s>
            <s xml:id="echoid-s20078" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s20079" xml:space="preserve">11. </s>
            <s xml:id="echoid-s20080" xml:space="preserve">Euclidis, perpendicularis, quòd perpendicularis ducta ſit ad
              <lb/>
            C G, communem ſectionem plani horologii, & </s>
            <s xml:id="echoid-s20081" xml:space="preserve">trianguli C G I, quod ad illud rectum eſt; </s>
            <s xml:id="echoid-s20082" xml:space="preserve">erit re-
              <lb/>
            cta I K, ſtylus, eiusq́ue locus in K, puncto lineæ indicis; </s>
            <s xml:id="echoid-s20083" xml:space="preserve">quia nulla alia linea ad planum horolo-
              <lb/>
            gii recta, præter K I, in centrum mundi I, cadere poteſt, vt patet.</s>
            <s xml:id="echoid-s20084" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s20085" xml:space="preserve">IAM verò ſi circulus ex centro L, deſcriptus circumduci intelligatur circa æquinoctialem li-
              <lb/>
            neam G H, donec centrum eius L, cum centro mundi I, coniungatur, (coniungetur autem neceſſa
              <lb/>
              <note position="left" xlink:label="note-0313-08" xlink:href="note-0313-08a" xml:space="preserve">40</note>
            rio cum eo; </s>
            <s xml:id="echoid-s20086" xml:space="preserve">quia rectæ G I, G L, æquales ſunr, & </s>
            <s xml:id="echoid-s20087" xml:space="preserve">vtraque ad lineam æquinoctialem perpendicula-
              <lb/>
            ris eſt, ſi triangulum C G I, intelligatur eſſe rectum ad planum horologii) erunt rectæ per centrũ
              <lb/>
            L, quod tunc idem eſt, quod centrum Aequatoris, & </s>
            <s xml:id="echoid-s20088" xml:space="preserve">per diuiſiones circuli emiſſæ, communes ſe-
              <lb/>
            ctiones Aequatoris, & </s>
            <s xml:id="echoid-s20089" xml:space="preserve">horariorum circulorum à meridie, vel media nocte, quemadmodum in ho
              <lb/>
            rologio horizontali demonſtrauimus propoſ. </s>
            <s xml:id="echoid-s20090" xml:space="preserve">1. </s>
            <s xml:id="echoid-s20091" xml:space="preserve">ſuperioris lib. </s>
            <s xml:id="echoid-s20092" xml:space="preserve">Nam in illa poſitione circulus hic
              <lb/>
            idem centrum cum Aequatore habens exiſtit in plano Aequatoris. </s>
            <s xml:id="echoid-s20093" xml:space="preserve">Principium autem diuiſionis
              <lb/>
            circuli ſumitur à recta L M, quæ per centrum L, & </s>
            <s xml:id="echoid-s20094" xml:space="preserve">punctum M, vbi linea horæ 12. </s>
            <s xml:id="echoid-s20095" xml:space="preserve">& </s>
            <s xml:id="echoid-s20096" xml:space="preserve">linea æqui-
              <lb/>
            noctialis ſe mutuo interſecant, duo
              <unsure/>
            itur; </s>
            <s xml:id="echoid-s20097" xml:space="preserve">quia ea linea communis ſectio eſt Aequatoris, & </s>
            <s xml:id="echoid-s20098" xml:space="preserve">Meridia-
              <lb/>
            ni, ſeu circuli horæ 12. </s>
            <s xml:id="echoid-s20099" xml:space="preserve">cum plano horologii occurrat in puncto M, per quod linea meridiana, & </s>
            <s xml:id="echoid-s20100" xml:space="preserve">
              <lb/>
            linea æquinoctialis tranſeunt: </s>
            <s xml:id="echoid-s20101" xml:space="preserve">hinc enim fit, vmbram ſtyli in punctum M, cadere, cum Sol in com
              <lb/>
              <note position="left" xlink:label="note-0313-09" xlink:href="note-0313-09a" xml:space="preserve">50</note>
            muni ſectione Meridiani, & </s>
            <s xml:id="echoid-s20102" xml:space="preserve">Aequatoris exiſtit, vt colligi vel facile poteſt ex propoſ. </s>
            <s xml:id="echoid-s20103" xml:space="preserve">11. </s>
            <s xml:id="echoid-s20104" xml:space="preserve">primi lib.
              <lb/>
            </s>
            <s xml:id="echoid-s20105" xml:space="preserve">Quoniam enim, Sole exiſtente in vtrolibet illorum circulorum, vmbra ſtyli cadit, per dictam pro-
              <lb/>
            poſ. </s>
            <s xml:id="echoid-s20106" xml:space="preserve">in communem ſectionem ipſius, & </s>
            <s xml:id="echoid-s20107" xml:space="preserve">plani horologii, fit vt, Sole exiſtente in puncto, vbi ſe mu
              <lb/>
            tuo dicti circuli ſecant, vmbra ſtyli cadat in punctum, vbi communes ſectiones ipſorum, & </s>
            <s xml:id="echoid-s20108" xml:space="preserve">plani
              <lb/>
            horologii ſe interſecant, cuiuſmodi eſt punctum M; </s>
            <s xml:id="echoid-s20109" xml:space="preserve">alias non caderet in vtramque lineam, vt pa-
              <lb/>
            tet. </s>
            <s xml:id="echoid-s20110" xml:space="preserve">Quæ
              <unsure/>
            cum ita ſint, ſecabunt circuli horarij planum horologii declinantis in ijſdem punctis, in
              <lb/>
            quibus rectæ per centrum L, & </s>
            <s xml:id="echoid-s20111" xml:space="preserve">per diuiſiones circuli eductæ, tanquam communes ſectiones di-
              <lb/>
            ctorum circulorum & </s>
            <s xml:id="echoid-s20112" xml:space="preserve">Aequatoris, lineæ æquinoctiali G H, occurrunt; </s>
            <s xml:id="echoid-s20113" xml:space="preserve">atque adeo communes ſe-
              <lb/>
            ctiones eorundem circulorum, ac plani horologii declinantis, hoc eſt, lineæ horariæ, per eadem
              <lb/>
            puncta ducendæ erunt. </s>
            <s xml:id="echoid-s20114" xml:space="preserve">Cum ergo eædem, ex coroll. </s>
            <s xml:id="echoid-s20115" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s20116" xml:space="preserve">21. </s>
            <s xml:id="echoid-s20117" xml:space="preserve">primi libri ſe mutuo ſecent in C,
              <lb/>
            centro horologij, erunt rectæ ex C, per puncta æquinoctialis lineæ ductæ, lineæ horarum à </s>
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