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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          <p>
            <s xml:id="echoid-s20349" xml:space="preserve">
              <pb o="302" file="0318" n="318" rhead="GNOMONICES"/>
            ſupputandus erit dictus arcus ad ſiniſtram verſus A: </s>
            <s xml:id="echoid-s20350" xml:space="preserve">quia, vt diximus, Meridianus Horizontis
              <lb/>
              <note position="left" xlink:label="note-0318-01" xlink:href="note-0318-01a" xml:space="preserve">Quam in partẽ
                <lb/>
              numerãdus ſit
                <lb/>
              arcus plani de-
                <lb/>
              clinantis inter
                <lb/>
              Meridianũ pro
                <lb/>
              prium, & Meri
                <lb/>
              dianum Hori-
                <lb/>
              zontis interie-
                <lb/>
              ctus.</note>
            tunc occidentalior eſt Meridiano ipſius plani declinantis. </s>
            <s xml:id="echoid-s20351" xml:space="preserve">Vnde horologio in propria poſitione
              <lb/>
            collocato, erit linea meridiana C D, orientalior, quàm recta C P, communis ſectio plani horolo-
              <lb/>
            gij, & </s>
            <s xml:id="echoid-s20352" xml:space="preserve">Meridiani proprij ipſius plani declinantis, cum in plano horologij radius Solis in quocun-
              <lb/>
            que circulo exiſtentis proiiciatur ſemper in contrariam partem. </s>
            <s xml:id="echoid-s20353" xml:space="preserve">Perſpicuũ autem eſt, rectam C D,
              <lb/>
            eſſe orientaliorem recta C P, ſi horologium proprium ſitum habeat. </s>
            <s xml:id="echoid-s20354" xml:space="preserve">Si verò planum à meridie in
              <lb/>
            occaſum vergat, numerandus erit arcus D P, ad dextram verſus B: </s>
            <s xml:id="echoid-s20355" xml:space="preserve">quoniam tunc orientalior eſt
              <lb/>
            Meridianus Horizontis Meridiano plani declinantis, vt diximus, atque adeo in horologio occi-
              <lb/>
            dentalior eſſe debet meridiana linea C D, quàm recta C P.</s>
            <s xml:id="echoid-s20356" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s20357" xml:space="preserve">IN quam aut partem dictus arcus numerandus ſit in horologio boreali, non tradimus, pro-
              <lb/>
              <note position="left" xlink:label="note-0318-02" xlink:href="note-0318-02a" xml:space="preserve">10</note>
            pter cauſas paulo ante explicatas, ne videlicet ingenium Lectoris obruatur multitudine præcepto-
              <lb/>
            rum, maximè cum ſatis ſit, ſi auſtrale horologiũ deſcribatur. </s>
            <s xml:id="echoid-s20358" xml:space="preserve">Ex hoc enim boreale deducetur ſine
              <lb/>
            vllo labore, vt ex ſcholio ſequenti manifeſtum erit. </s>
            <s xml:id="echoid-s20359" xml:space="preserve">Adde quòd res ipſa difficilis non eſt, ſi conſide
              <lb/>
            retur, an Meridianus proprius plani declinantis in hemiſphærio infero ſit orientalior Meridiano
              <lb/>
            Horizontis, occidentaliorve. </s>
            <s xml:id="echoid-s20360" xml:space="preserve">Nam arcus prædictus ſemper numerandus erit in horologio in con-
              <lb/>
            trariam partem, &</s>
            <s xml:id="echoid-s20361" xml:space="preserve">c. </s>
            <s xml:id="echoid-s20362" xml:space="preserve">hac tamen lege, vt in boreali horologio punctum C, ſit infra arcum D P.</s>
            <s xml:id="echoid-s20363" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s20364" xml:space="preserve">POST hæc ex quocunque puncto rectæ C P, vt ex G, ducatur ad ipſam perpendicularis G H,
              <lb/>
            quæ erit linea æquinoctialis. </s>
            <s xml:id="echoid-s20365" xml:space="preserve">Nam recta C P, eſt linea indicis, vt mox oſtendemus, ad quam ne-
              <lb/>
            ceſſario linea æquinoctialis eſt perpendicularis, vt ſupra demonſtrauimus. </s>
            <s xml:id="echoid-s20366" xml:space="preserve">Inuenta autem, per
              <lb/>
            propoſ. </s>
            <s xml:id="echoid-s20367" xml:space="preserve">29. </s>
            <s xml:id="echoid-s20368" xml:space="preserve">primi libri, altitudine poli ſupra planum declinans, conſtituatur in C, ad rectam C P,
              <lb/>
              <note position="left" xlink:label="note-0318-03" xlink:href="note-0318-03a" xml:space="preserve">20</note>
            angulus huius altitudinis poli inuentæ G C H. </s>
            <s xml:id="echoid-s20369" xml:space="preserve">Eritenim G H, axis mundi, ad quem ex G, per-
              <lb/>
            pendicularis excitetur G I, & </s>
            <s xml:id="echoid-s20370" xml:space="preserve">reliqua fiant, vt in prima deſcriptione huius horologij declinantis;
              <lb/>
            </s>
            <s xml:id="echoid-s20371" xml:space="preserve">hoc eſt, rectæ G I, ſumatur æqualis G L, & </s>
            <s xml:id="echoid-s20372" xml:space="preserve">circulus ex L, deſcriptus ſecetur in partes 24. </s>
            <s xml:id="echoid-s20373" xml:space="preserve">ęquales,
              <lb/>
            principio ſumpto à recta L M, &</s>
            <s xml:id="echoid-s20374" xml:space="preserve">c. </s>
            <s xml:id="echoid-s20375" xml:space="preserve">Gnomon erit I K, perpendicularis ducta ex I, ad C P, vt prius.</s>
            <s xml:id="echoid-s20376" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s20377" xml:space="preserve">QVOD autem recta C P, ſit ſectio communis plani horologij declinantis, & </s>
            <s xml:id="echoid-s20378" xml:space="preserve">proprij Meri-
              <lb/>
            diani eiuſdem plani, hac ratione oſtendemus. </s>
            <s xml:id="echoid-s20379" xml:space="preserve">Quoniam Meridianus Horizontis, & </s>
            <s xml:id="echoid-s20380" xml:space="preserve">Meridianus
              <lb/>
            plani declinantis, hoc eſt, circulus maximus per polos mundi, & </s>
            <s xml:id="echoid-s20381" xml:space="preserve">per polos plani declinantis du-
              <lb/>
            ctus, per axem mundi ducuntur, occurruntq́ue circulo maximo, cui horologium æquidiſtat, in
              <lb/>
            centro mundi, nempe in I, vertice ſtyli; </s>
            <s xml:id="echoid-s20382" xml:space="preserve">fit vt cum hoc circulo maximo faciant communes ſectio-
              <lb/>
            nes, rectas lineas, quæ in mundi centro angulum conſtituant, cui ſubtenditur arcus eiuſdem circu
              <lb/>
              <note position="left" xlink:label="note-0318-04" xlink:href="note-0318-04a" xml:space="preserve">30</note>
            li maximi, qui inter illos Meridianos interijcitur. </s>
            <s xml:id="echoid-s20383" xml:space="preserve">Quoniam verò ijdem Meridiani occurrunt
              <lb/>
            plano horologij in C, puncto, vbi axis eidem plano occurrere ponitur, faciuntq́ue cum eo ſectio-
              <lb/>
            nes communes lineas rectas, quæ illis in circulo maximo æquidiſtant, eò quod eidem circulo ma
              <lb/>
              <note position="left" xlink:label="note-0318-05" xlink:href="note-0318-05a" xml:space="preserve">16. vndec.</note>
            ximo planum horologij parallelum eſt, comprchendent huiuſmodi lineæ in plano horologij an-
              <lb/>
            gulum æqualem illi angulo, quem in circulo maximo priores illæ lineæ efficiunt. </s>
            <s xml:id="echoid-s20384" xml:space="preserve">Quare cum an-
              <lb/>
              <note position="left" xlink:label="note-0318-06" xlink:href="note-0318-06a" xml:space="preserve">10. vndec.</note>
            gulus D C P, ſit illi æqualis, vt in ſcholio propoſ. </s>
            <s xml:id="echoid-s20385" xml:space="preserve">33. </s>
            <s xml:id="echoid-s20386" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s20387" xml:space="preserve">6. </s>
            <s xml:id="echoid-s20388" xml:space="preserve">Eucl. </s>
            <s xml:id="echoid-s20389" xml:space="preserve">oſtendimus, quòd arcus D P, ſi-
              <lb/>
            milis ſit arcui illius circuli inter duos Meridianos interiecto, quia totidem gradus, ac Minuta con
              <lb/>
            tinet; </s>
            <s xml:id="echoid-s20390" xml:space="preserve">ponatur autem C D, linea meridiana, id eſt, communis ſectio Meridiani Horizontis, & </s>
            <s xml:id="echoid-s20391" xml:space="preserve">pla-
              <lb/>
            ni horologij, erit C P, communis ſectio plani horologij declinantis, & </s>
            <s xml:id="echoid-s20392" xml:space="preserve">Meridiani eiuſdem plani,
              <lb/>
            id eſt, circuli maximi per polos mundi, & </s>
            <s xml:id="echoid-s20393" xml:space="preserve">polos ipſius plani tranſeuntis: </s>
            <s xml:id="echoid-s20394" xml:space="preserve">ac proinde in ea ſtylus
              <lb/>
              <note position="left" xlink:label="note-0318-07" xlink:href="note-0318-07a" xml:space="preserve">40</note>
            collocandus erit ad angulos rectos, cum hac ratione à plano huius Meridiani non recedat, ſed ad
              <lb/>
            ipſum axem mundi in eo exiſtentem pertingat. </s>
            <s xml:id="echoid-s20395" xml:space="preserve">Quare C P, linea erit Indicis, ſeu ſtyli. </s>
            <s xml:id="echoid-s20396" xml:space="preserve">Vnde reli-
              <lb/>
            qua conſtructio horologij demonſtrabitur, vt prima conſtructio ad initium huius propoſ. </s>
            <s xml:id="echoid-s20397" xml:space="preserve">Horo-
              <lb/>
            logium igitur Aſtronomicum à Verticali circulo declinans, hoc eſt, lineas horarum, &</s>
            <s xml:id="echoid-s20398" xml:space="preserve">c. </s>
            <s xml:id="echoid-s20399" xml:space="preserve">deſcri-
              <lb/>
            pſimus. </s>
            <s xml:id="echoid-s20400" xml:space="preserve">Quod faciendum erat.</s>
            <s xml:id="echoid-s20401" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1046" type="section" level="1" n="255">
          <head xml:id="echoid-head264" style="it" xml:space="preserve">SCHOLIVM.</head>
          <p style="it">
            <s xml:id="echoid-s20402" xml:space="preserve">SED videtur hoc loco ſcrupulus quidam ex animo Lectoris euellendus, qui illum fortaſſis non parũ
              <lb/>
              <note position="left" xlink:label="note-0318-08" xlink:href="note-0318-08a" xml:space="preserve">Dubitatio ad-
                <lb/>
              uerſus ea, quæ
                <lb/>
              proxime dicta
                <lb/>
              ſunt.</note>
            angere ac torquere poſſet. </s>
            <s xml:id="echoid-s20403" xml:space="preserve">Qui enim fieri poteſt, dicet aliquis, vt angulus in plano horologii à ſectioni-
              <lb/>
              <note position="left" xlink:label="note-0318-09" xlink:href="note-0318-09a" xml:space="preserve">50</note>
            bus illorum Meridianorum conſtitutus æqualis ſit angulo in circulo maximo, cui planum horologii æquidi
              <lb/>
            ſtat, ab eorundem Meridianorum ſectionibus conſtituto, cum illi Meridiani circulum à plano horologii
              <lb/>
            in ſphæra factum, & </s>
            <s xml:id="echoid-s20404" xml:space="preserve">circulum muximum, cui horologium æquidiſtat, non ſecent in arcus ſimiles? </s>
            <s xml:id="echoid-s20405" xml:space="preserve">Si enini
              <lb/>
            in arcus ſimiles ipſos ſecarent, tranſirent per propoſ. </s>
            <s xml:id="echoid-s20406" xml:space="preserve">16. </s>
            <s xml:id="echoid-s20407" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s20408" xml:space="preserve">2. </s>
            <s xml:id="echoid-s20409" xml:space="preserve">Theodoſii, vel per eorum polos, vel eun-
              <lb/>
            dem vnum parallelum tangerent, quorum neutrum hic fieri poteſt. </s>
            <s xml:id="echoid-s20410" xml:space="preserve">Nam cum per polos mundi ducantur
              <lb/>
            ambo, qui pol{us} ipſorum eſſe non poteſt, (ſiquidem polus ipſorum in Horizonte exiſtit) non poterunt
              <lb/>
            tranſire per illorum polos. </s>
            <s xml:id="echoid-s20411" xml:space="preserve">Præterea cum Meridianus plani declinantis per cius polos tranſeat, ſecabit
              <lb/>
            omnes ipſius parallelos bifarium, per propoſ. </s>
            <s xml:id="echoid-s20412" xml:space="preserve">15. </s>
            <s xml:id="echoid-s20413" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s20414" xml:space="preserve">1. </s>
            <s xml:id="echoid-s20415" xml:space="preserve">Theodoſii, ac proinde nullum tanget. </s>
            <s xml:id="echoid-s20416" xml:space="preserve">Quare am-
              <lb/>
            bo illi Meridiani eundem vnum parallelum tangere non poſſunt. </s>
            <s xml:id="echoid-s20417" xml:space="preserve">Non ergo ſimiles ſunt illi arcus, quos
              <lb/>
            prædicti anguli æquales auferunt. </s>
            <s xml:id="echoid-s20418" xml:space="preserve">Hoc idem ad ſenſum patet in ſphæra materiali, vbi manifeſtè cernitu
              <unsure/>
            r,
              <lb/>
            Meridianum, & </s>
            <s xml:id="echoid-s20419" xml:space="preserve">vtrumuis Colurum non poſſe diuidere Horizontem, & </s>
            <s xml:id="echoid-s20420" xml:space="preserve">circulum ſub Horizonte ei </s>
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