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-div717" type="section" level="1" n="178">
          <p style="it">
            <s xml:id="echoid-s14328" xml:space="preserve">
              <pb o="209" file="0229" n="229" rhead="LIBER SECVNDVS."/>
            ductus cadit in oppoſitam partem; </s>
            <s xml:id="echoid-s14329" xml:space="preserve">hoc eſt, ea lege & </s>
            <s xml:id="echoid-s14330" xml:space="preserve">conditione, vt conuerſo ad nos horologio auſtrali,
              <lb/>
            exiſtenteq́, puncto F, ad ſiniſtram, & </s>
            <s xml:id="echoid-s14331" xml:space="preserve">K, ad dexteram, lineę horar ie in facie oppoſita, & </s>
            <s xml:id="echoid-s14332" xml:space="preserve">boreali ducan-
              <lb/>
            tur omnino reſpondentes horarijs lineis auſtralis horologij per centrum H, eductis; </s>
            <s xml:id="echoid-s14333" xml:space="preserve">adeò vt nobis faciem
              <lb/>
            plani borealem aſpicientibus punctum F, poſitum ſit ad dexterarn, & </s>
            <s xml:id="echoid-s14334" xml:space="preserve">K, ad ſiniſtram; </s>
            <s xml:id="echoid-s14335" xml:space="preserve">contra ſcilicet,
              <lb/>
            quàm in auſtr ali contingit; </s>
            <s xml:id="echoid-s14336" xml:space="preserve">vel quod idem eſt, F, vergat in occaſum, & </s>
            <s xml:id="echoid-s14337" xml:space="preserve">K, in ortum, vt in auſtrali.</s>
            <s xml:id="echoid-s14338" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s14339" xml:space="preserve">ERIT autem horologium boreale arte proxime tradita delineatum omnino ęquale, & </s>
            <s xml:id="echoid-s14340" xml:space="preserve">ſimile au-
              <lb/>
            ſtrali ob ęqualitatem axium H A, H D; </s>
            <s xml:id="echoid-s14341" xml:space="preserve">gnomonum C A, G D; </s>
            <s xml:id="echoid-s14342" xml:space="preserve">communium ſectionum Aequatoris, & </s>
            <s xml:id="echoid-s14343" xml:space="preserve">
              <lb/>
            Meridiani A B, D I; </s>
            <s xml:id="echoid-s14344" xml:space="preserve">& </s>
            <s xml:id="echoid-s14345" xml:space="preserve">portionum meridianę lineę H B, H I, inter centrum horologii, & </s>
            <s xml:id="echoid-s14346" xml:space="preserve">lineas ęquino
              <lb/>
            ctiales poſitarum. </s>
            <s xml:id="echoid-s14347" xml:space="preserve">Hinc enim efficitur, triangulum H B L, in boreali horologio, cuius later a ſunt linea me
              <lb/>
            ridiana H B, ęquinoctialis B L, & </s>
            <s xml:id="echoid-s14348" xml:space="preserve">linea horę quintę H L, ęquale eſſe, & </s>
            <s xml:id="echoid-s14349" xml:space="preserve">ſimile prorſus triangulo H I K,
              <lb/>
              <note position="left" xlink:label="note-0229-01" xlink:href="note-0229-01a" xml:space="preserve">10</note>
              <note position="right" xlink:label="note-0229-02" xlink:href="note-0229-02a" xml:space="preserve">26. primi.</note>
            in horologio auſtrali, cuius etiam latera ſunt meridiana linea H I, ęquinoctialis I K, & </s>
            <s xml:id="echoid-s14350" xml:space="preserve">linea horę 5.
              <lb/>
            </s>
            <s xml:id="echoid-s14351" xml:space="preserve">H K; </s>
            <s xml:id="echoid-s14352" xml:space="preserve">propterea quod duo anguli illius B H L, H B L, duobus angulis huius I H K, H I K, ęquales ſunt,
              <lb/>
            (Nam anguli ad H, æquales ſunt, cum ſint ad verticem, & </s>
            <s xml:id="echoid-s14353" xml:space="preserve">anguli ad B, I, recti.) </s>
            <s xml:id="echoid-s14354" xml:space="preserve">& </s>
            <s xml:id="echoid-s14355" xml:space="preserve">latus H B, lateri
              <lb/>
              <note position="right" xlink:label="note-0229-03" xlink:href="note-0229-03a" xml:space="preserve">15. primi.</note>
            H I, ęquale, vt oſtenſum eſt, & </s>
            <s xml:id="echoid-s14356" xml:space="preserve">c. </s>
            <s xml:id="echoid-s14357" xml:space="preserve">Eadem ratio eſt de cęteris triangulis, quorum baſes ſunt lineę horarię
              <lb/>
            inter centrum H, & </s>
            <s xml:id="echoid-s14358" xml:space="preserve">lineas ęquinoctales poſitę, ſubtenſęque angulis rectis ad B, I, comprehenſis ſub me-
              <lb/>
            ridiana linea, & </s>
            <s xml:id="echoid-s14359" xml:space="preserve">lineis ęquinoctialibus. </s>
            <s xml:id="echoid-s14360" xml:space="preserve">Totum ergo horologium boreale toti auſtrali ęquale erit, & </s>
            <s xml:id="echoid-s14361" xml:space="preserve">ſimi
              <lb/>
            le, cum ſingulę partes ſingulis partibus ęquales ſint & </s>
            <s xml:id="echoid-s14362" xml:space="preserve">ſimiles.</s>
            <s xml:id="echoid-s14363" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">Si lineamenta
            <lb/>
          auſtialis horo-
            <lb/>
          logu deicriban
            <lb/>
          tur in facie pla
            <lb/>
          ni oppoſita, ita
            <lb/>
          vt ad vnguem-
            <lb/>
          reſpondeant li-
            <lb/>
          neamentis ho-
            <lb/>
          rologii auſtra-
            <lb/>
          lis, & poſt hanc
            <lb/>
          deſcriptionem
            <lb/>
          pars ſuperior
            <lb/>
          mutetur in in-
            <lb/>
          feriorem, deſcri
            <lb/>
          ptum crit horo
            <lb/>
          gium boreale.</note>
          <p style="it">
            <s xml:id="echoid-s14364" xml:space="preserve">VNDE ſi in parte oppoſita plani horologii deſcribantur lineę reſpondentes ad vnguem lineis in ho-
              <lb/>
            rologio auſtrali, & </s>
            <s xml:id="echoid-s14365" xml:space="preserve">deinde pars ſuperior mutetur in inferiorem, ac proinde & </s>
            <s xml:id="echoid-s14366" xml:space="preserve">illa, quę poſt deſcriptionẽ
              <lb/>
            illam dextra eſt, fiat ſiniſtra, et contra, deſcriptum erit horologium boreale in facie plani horologii borea-
              <lb/>
              <note position="left" xlink:label="note-0229-05" xlink:href="note-0229-05a" xml:space="preserve">20</note>
            li. </s>
            <s xml:id="echoid-s14367" xml:space="preserve">Quia hac ratione punctum K, quod in auſtrali horologio nobis eſt ad dexteram, & </s>
            <s xml:id="echoid-s14368" xml:space="preserve">in boreali poſt illam
              <lb/>
            deſcriptionem ad ſiniſtram, fit nobis iterum ad dexteram, ſi ſuperior pars in inſeriorem mutetur, vt con-
              <lb/>
            ſtat. </s>
            <s xml:id="echoid-s14369" xml:space="preserve">Sed hac de re plura in propoſ. </s>
            <s xml:id="echoid-s14370" xml:space="preserve">ſequenti ſcribemus.</s>
            <s xml:id="echoid-s14371" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s14372" xml:space="preserve">EX his omnibus (vt ad id, quod propoſitum eſt, veniamus) perſpicuum eſſe arbitror, horologium au
              <lb/>
            ſtrale indicare horas in facie plani V erticalis boreali, ſi omnia immut entur, vt dictum eſt, hoc eſt, ſi ſu-
              <lb/>
            perior pars mutetur in inferiorem, & </s>
            <s xml:id="echoid-s14373" xml:space="preserve">quæ poſt hanc mutationem nobis ad horologium conuerſis dextra
              <lb/>
            eſt, fiat ſiniſtra, & </s>
            <s xml:id="echoid-s14374" xml:space="preserve">contra. </s>
            <s xml:id="echoid-s14375" xml:space="preserve">Nam auſtrale horologium H R K, ſi inuertatur, vt punctum I, ſurſum ver-
              <lb/>
            ſus, & </s>
            <s xml:id="echoid-s14376" xml:space="preserve">H, deorſum verſus ponatur, punctum{q́ue} R, quod in eo ſitu nobis ad horologium conuerſis eſt ad
              <lb/>
            dextram, in ſiniſtram partem, & </s>
            <s xml:id="echoid-s14377" xml:space="preserve">K, in dextram cadat, acquiret omnino eundem ſitum, quem habet bo-
              <lb/>
            reale horologium L H B, in facie oppoſita delineatum, vbi punctum L, nobis ad horologium conuerſis
              <lb/>
              <note position="left" xlink:label="note-0229-06" xlink:href="note-0229-06a" xml:space="preserve">30</note>
            poſitum eſt ad dextram, & </s>
            <s xml:id="echoid-s14378" xml:space="preserve">B, ad ſinistram, vt manifestum eſt. </s>
            <s xml:id="echoid-s14379" xml:space="preserve">Similiter ex ijs, quæ in ſcbolio propoſ. </s>
            <s xml:id="echoid-s14380" xml:space="preserve">1.
              <lb/>
            </s>
            <s xml:id="echoid-s14381" xml:space="preserve">huius libri tradidimus, manifeſtum eſt, portionem illam lineę meridianæ, quæ in horologio Auſtrali indi-
              <lb/>
            cabat horam 12. </s>
            <s xml:id="echoid-s14382" xml:space="preserve">meridiei, in boreali monstrare horam 12. </s>
            <s xml:id="echoid-s14383" xml:space="preserve">mediæ noctis; </s>
            <s xml:id="echoid-s14384" xml:space="preserve">& </s>
            <s xml:id="echoid-s14385" xml:space="preserve">horas, quæ ibi à meridie nu-
              <lb/>
            merabantur, hic à media nocte, et quæibi à media nocte, hic à meridie computandas eſſe: </s>
            <s xml:id="echoid-s14386" xml:space="preserve">quoniam vide-
              <lb/>
            licet, vt proxime demonstratum eſt, horæ Auſtralis horologij vltra centrum horologij dant in facie bo-
              <lb/>
            reali eaſdem numero horas; </s>
            <s xml:id="echoid-s14387" xml:space="preserve">& </s>
            <s xml:id="echoid-s14388" xml:space="preserve">vt ex dicto ſcholio conſtat, horę antemeridianæ vltra centrum horolo-
              <lb/>
            gij productæ faciunt pomeridianas, & </s>
            <s xml:id="echoid-s14389" xml:space="preserve">pomeridianæ antemeridianas. </s>
            <s xml:id="echoid-s14390" xml:space="preserve">Quod etiam facile intelligetur, ſi
              <lb/>
            in facie boreali concipiantur per axem H A, ducti circuli horarij. </s>
            <s xml:id="echoid-s14391" xml:space="preserve">Nam vmbra axis, vel ſtyli, dummodo
              <lb/>
            Sol faciem borealem illuſtret, proijcietur in meridianam lineam H B, Sole exiſtente in ſemicirculo Meri-
              <lb/>
            diani ſub terra, in lineas verò horarias verſus punctum L, quod nobis in boreali horologio eſt ad dexte-
              <lb/>
              <note position="left" xlink:label="note-0229-07" xlink:href="note-0229-07a" xml:space="preserve">40</note>
            ram, Sole exiſtente in ſemicirculis horarijs poſt mediã noctem, hoc eſt, in ſemicir culis, qui opponuntur il-
              <lb/>
            lis, in quibus Sol exiſtit, cum vmbra axis, vel ſtyli in Auſtrali horologio proijcitur in horarias lineas ver
              <lb/>
            ſus K, & </s>
            <s xml:id="echoid-s14392" xml:space="preserve">c. </s>
            <s xml:id="echoid-s14393" xml:space="preserve">vt perſpicuum eſt, ſi & </s>
            <s xml:id="echoid-s14394" xml:space="preserve">horologium boreale L H B, & </s>
            <s xml:id="echoid-s14395" xml:space="preserve">axis H A, & </s>
            <s xml:id="echoid-s14396" xml:space="preserve">circuli horarij in propria
              <lb/>
            poſitione concipiantur. </s>
            <s xml:id="echoid-s14397" xml:space="preserve">Hæc omnia planiora fient, ſi horologium boreale L H B, in facie oppoſita, vt di-
              <lb/>
            ctum eſt, delineatum confer atur cum boreali horologio, quod ante deſcripſimus. </s>
            <s xml:id="echoid-s14398" xml:space="preserve">Deprehendemus enim
              <lb/>
            hoc illi omnino ſimile eſſe, & </s>
            <s xml:id="echoid-s14399" xml:space="preserve">æquale.</s>
            <s xml:id="echoid-s14400" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s14401" xml:space="preserve">EADEM hæc demonſtratio in horologia tam à V erticali circulo, quàm ab Horizonte declinan-
              <lb/>
              <note position="right" xlink:label="note-0229-08" xlink:href="note-0229-08a" xml:space="preserve">Ea, quæ proxi-
                <lb/>
              me dicta ſunt
                <lb/>
              de inuerſione
                <lb/>
              omnium parti@
                <lb/>
              horologii, intel
                <lb/>
              ligenda quoque
                <lb/>
              ſunt in horolo-
                <lb/>
              giis declinanti-
                <lb/>
              bus, & inclina-
                <lb/>
              tis.</note>
            tia: </s>
            <s xml:id="echoid-s14402" xml:space="preserve">Item in inclinata ad Horizontem, & </s>
            <s xml:id="echoid-s14403" xml:space="preserve">in ea, quæ & </s>
            <s xml:id="echoid-s14404" xml:space="preserve">à Verticali circulo declinant, & </s>
            <s xml:id="echoid-s14405" xml:space="preserve">ad Horizontem
              <lb/>
            ſunt inclinata, de quibus libro inſequenti dicemus, quadrat omni ex parte; </s>
            <s xml:id="echoid-s14406" xml:space="preserve">ſi modo in illis rectam B I, nõ
              <lb/>
            intelligamus eſſe meridianam, ſed lineam ſtyli, ſiue indicis, & </s>
            <s xml:id="echoid-s14407" xml:space="preserve">pro Meridiano circulo per axem A D, & </s>
            <s xml:id="echoid-s14408" xml:space="preserve">
              <lb/>
              <note position="left" xlink:label="note-0229-09" xlink:href="note-0229-09a" xml:space="preserve">50</note>
            meridianam lineam B I, ducto ſumamus circulum alium maximum, qui per axem A D, & </s>
            <s xml:id="echoid-s14409" xml:space="preserve">lineam ſtyli
              <lb/>
            B I, ducitur, inſtar noui cuiuſdam Meridiani in illorum horologiorum planis, vt ſuis locis monebimus.
              <lb/>
            </s>
            <s xml:id="echoid-s14410" xml:space="preserve">Quodcunque enim horologium eiuſmodi in vna facie plani deſcriptum, vt v. </s>
            <s xml:id="echoid-s14411" xml:space="preserve">g. </s>
            <s xml:id="echoid-s14412" xml:space="preserve">in ea, quæ à meridie decli-
              <lb/>
            nat, ſi planum ad Horizontem fuerit rectum, vel in ſuperiori facie, ſi planum ad Horizontem fuerit incli-
              <lb/>
            natum, erit quoque horologium in facie plani eiuſdem oppoſita deſcribendum, vt in ea, quę à Septentrio-
              <lb/>
            ne declinat, vel in facie inferiori; </s>
            <s xml:id="echoid-s14413" xml:space="preserve">ſi tamen omnes partes inuertantur, vt diximus, hoc eſt, ſuperior primũ
              <lb/>
            mutetur in inferiorem, & </s>
            <s xml:id="echoid-s14414" xml:space="preserve">quæ poſt hanc mutationem primam dextra eſt, euadat ſiniſtra, & </s>
            <s xml:id="echoid-s14415" xml:space="preserve">contra. </s>
            <s xml:id="echoid-s14416" xml:space="preserve">Quæ
              <lb/>
            omnia ſuo loco perſpicua erunt.</s>
            <s xml:id="echoid-s14417" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s14418" xml:space="preserve">HACTENVS conſtruximus V erticale horologium in plana ſuperficie quacunque, vt illud po-
              <lb/>
            ſtea in murum, vel planum, quod ad Horizontem rectum eſt, & </s>
            <s xml:id="echoid-s14419" xml:space="preserve">directò ad meridiem, Septentrionemve
              <lb/>
            ſpectat, transferri poſſit, ita vt H E, meridiana linea ad Horizontem ſit perpendicularis, </s>
          </p>
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