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 style="it">
            <s xml:id="echoid-s14914" xml:space="preserve">
              <pb o="218" file="0238" n="238" rhead="GNOMONICES"/>
            ſi ita collocetur, vt omnes eius partes inuertantur, vt diximus, eaſdem omnino res nobis indicet per vm-
              <lb/>
              <note position="left" xlink:label="note-0238-01" xlink:href="note-0238-01a" xml:space="preserve">Horizontalis li
                <lb/>
              nea in omni ho
                <lb/>
              rologio aufert
                <lb/>
              portionem ſupe
                <lb/>
              tiorem, quæ ex
                <lb/>
              hibet horolo-
                <lb/>
              giũ in facie ho-
                <lb/>
              rologli oppoſi-
                <lb/>
              ta collocandũ,
                <lb/>
              ſi prius ſupe-
                <lb/>
              r
                <unsure/>
              ior pars fiat in
                <lb/>
              ferior, & quæ
                <lb/>
              poſt hanc inuer
                <lb/>
              ſionẽ nobis ad
                <lb/>
              horologium cõ
                <lb/>
              uerſis dextra
                <lb/>
              eſt, fiat ſiniſtra,
                <lb/>
              & contra.</note>
            bram ſtyli, quas in altera facie, in qua horologium deſcriptum fuit à principio, nobis monſtrat altera ho-
              <lb/>
            rologij portio infra horizontalem lineam comprehenſa; </s>
            <s xml:id="echoid-s14915" xml:space="preserve">adeo vt ſegmenta linearum ſupra lineam hori-
              <lb/>
            zontalem exiſtentia ſint eorundem maximorum circulorum ſectiones communes cum plano horologii in
              <lb/>
            facie oppoſita collocandi, ſi illa partium inuerſio fiat, de qua loquuti ſumus, quorum communes ſectiones
              <lb/>
            cum plano horologii, quod ab initio in altera facie deſcriptum est, ſunt ſegmenta earundem linearum in-
              <lb/>
            fra horizontalem lineam poſita, ſiue illi circuli ſint horarii à meridie, vel media nocte, ſiue Verticales, ſi-
              <lb/>
            ue Meridiani, ſiue domorum cœleſtium, ſiue Zodiacum repreſentãtes, quatenus varias obtinet poſitiones,
              <lb/>
            dum ſigna cœlestia oriuntur, ſiue horarum ab ortu, vel occaſu, ſiue denique inæqualium horarum indices.
              <lb/>
            </s>
            <s xml:id="echoid-s14916" xml:space="preserve">Hoc autem ita demonſtrabimus.</s>
            <s xml:id="echoid-s14917" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">10</note>
          <p style="it">
            <s xml:id="echoid-s14918" xml:space="preserve">SINT duo horologia, vnum australe, & </s>
            <s xml:id="echoid-s14919" xml:space="preserve">boreale alterum, ſi plana ipſorum ad Horizontem recta
              <lb/>
            ſunt; </s>
            <s xml:id="echoid-s14920" xml:space="preserve">vel vnum ſuperius, & </s>
            <s xml:id="echoid-s14921" xml:space="preserve">alterum inferius, ſi plana eorum ad Horizontem non ſunt recta; </s>
            <s xml:id="echoid-s14922" xml:space="preserve">in quibus
              <lb/>
            ſtyli A B, C D, æquales, & </s>
            <s xml:id="echoid-s14923" xml:space="preserve">ad plana horologiorum recti. </s>
            <s xml:id="echoid-s14924" xml:space="preserve">Intelligantur autem ambo horologia in propria
              <lb/>
            poſitione, ita vt Auſtrale ad auſtrum, & </s>
            <s xml:id="echoid-s14925" xml:space="preserve">boreale ad Boream vergat, vel ſuperius ſpectet ad Zenith, & </s>
            <s xml:id="echoid-s14926" xml:space="preserve">in-
              <lb/>
              <figure xlink:label="fig-0238-01" xlink:href="fig-0238-01a" number="165">
                <image file="0238-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0238-01"/>
              </figure>
              <note position="left" xlink:label="note-0238-03" xlink:href="note-0238-03a" xml:space="preserve">20</note>
            ferius ad Nadir; </s>
            <s xml:id="echoid-s14927" xml:space="preserve">ipſa{q́ue} inter ſe ſint parallela, ac vertices ſtylorum B, D, coniungantur in centro mundi,
              <lb/>
              <note position="left" xlink:label="note-0238-04" xlink:href="note-0238-04a" xml:space="preserve">30</note>
            ipſismet ſtylis lineam vnam rectam constituentibus, nempe axem illius circuli maximi, cui vtrumque ho-
              <lb/>
            rologium æquidiſt at, ita vt horologia ſe mutuo aſpiciant. </s>
            <s xml:id="echoid-s14928" xml:space="preserve">Præterea intelligatur circulus maximus duci
              <lb/>
            per polos plani vtriuſque horologii, & </s>
            <s xml:id="echoid-s14929" xml:space="preserve">per polos Horizontis. </s>
            <s xml:id="echoid-s14930" xml:space="preserve">Erit hic circulus ad planum vtriuſque ho
              <lb/>
            rologii, & </s>
            <s xml:id="echoid-s14931" xml:space="preserve">ad Horizontem, per propoſ. </s>
            <s xml:id="echoid-s14932" xml:space="preserve">15. </s>
            <s xml:id="echoid-s14933" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s14934" xml:space="preserve">1. </s>
            <s xml:id="echoid-s14935" xml:space="preserve">Theod. </s>
            <s xml:id="echoid-s14936" xml:space="preserve">rectus, tranſibit{q́ue}, per ſtylos A B, C D, hoc eſt,
              <lb/>
            per axem plani vtriuſque horologii, cum per eiuſdem polos ducatur, vt diximus. </s>
            <s xml:id="echoid-s14937" xml:space="preserve">Faciat autem dictus cir-
              <lb/>
            culus maximus cum horologiorum planis communes ſectiones rectas A E, C F, quæ parallelæ inter ſe
              <lb/>
              <note position="left" xlink:label="note-0238-05" xlink:href="note-0238-05a" xml:space="preserve">10. vndec.</note>
            erunt. </s>
            <s xml:id="echoid-s14938" xml:space="preserve">Huiuſmodi circulus in horologio Verticali, polari, æquinoctiali, & </s>
            <s xml:id="echoid-s14939" xml:space="preserve">ad Horizontem inclinato erit
              <lb/>
            Meridianus ipſe; </s>
            <s xml:id="echoid-s14940" xml:space="preserve">propterea quòd cùm in Meridiano exiſtant & </s>
            <s xml:id="echoid-s14941" xml:space="preserve">poli plani vtriuſque horologii Vertica-
              <lb/>
            lis, polaris, æquinoctialis, atque ad Horizontem inclinati, & </s>
            <s xml:id="echoid-s14942" xml:space="preserve">poli Horizontis, (vt conſtat, ſi attentius
              <lb/>
            poſitio maximorum circulorum, cui eiuſmodi horologia æquidiſtant, perpendatur) Meridianus per dictos
              <lb/>
              <note position="left" xlink:label="note-0238-06" xlink:href="note-0238-06a" xml:space="preserve">40</note>
            polos neceſſariò tranſeat, atque adeo ad plana illorum horologiorum, & </s>
            <s xml:id="echoid-s14943" xml:space="preserve">ad Horizontem rectus ſit, per
              <lb/>
            propoſ. </s>
            <s xml:id="echoid-s14944" xml:space="preserve">15. </s>
            <s xml:id="echoid-s14945" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s14946" xml:space="preserve">1. </s>
            <s xml:id="echoid-s14947" xml:space="preserve">Theod. </s>
            <s xml:id="echoid-s14948" xml:space="preserve">Ex quo efficitur, rectas A E, C F, eſſe in nominatis horologiis lineas meridia-
              <lb/>
            nas, In aliis autem horologiis maximus ille circulus non poteſt eſſe Meridianus; </s>
            <s xml:id="echoid-s14949" xml:space="preserve">quia Meridianus ad eo-
              <lb/>
            rum plana rectus non eſt, cum per eorum polos minimè tranſeat, vt patet: </s>
            <s xml:id="echoid-s14950" xml:space="preserve">Sed in Meridiano quidem ho-
              <lb/>
            rologio, & </s>
            <s xml:id="echoid-s14951" xml:space="preserve">declinante ab Horizonte, is circulus erit proprie dictus Verticalis, cum tranſeat & </s>
            <s xml:id="echoid-s14952" xml:space="preserve">per polos
              <lb/>
            Meridiani horologii, declinantis{q́ue} ab Horizonte, & </s>
            <s xml:id="echoid-s14953" xml:space="preserve">per polos Horizontis: </s>
            <s xml:id="echoid-s14954" xml:space="preserve">In declinantibus autem à Ver
              <lb/>
            ticali erit idem circulus vnus ex Verticalibus tantum à Meridiano declinans, quantum planum horolo-
              <lb/>
            gij declinantis abeſt à Verticali circulo; </s>
            <s xml:id="echoid-s14955" xml:space="preserve">atque adeo in horologijs inclinatis metietur inclinationem pla-
              <lb/>
            ni horologij ad Horizontem, cùm per polos horologii, & </s>
            <s xml:id="echoid-s14956" xml:space="preserve">per polos Horizontis ducatur.</s>
            <s xml:id="echoid-s14957" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s14958" xml:space="preserve">RVRSVS concipiatur duci alius circulus maximus per polos plani vtriuſque horologii, & </s>
            <s xml:id="echoid-s14959" xml:space="preserve">per po
              <lb/>
              <note position="left" xlink:label="note-0238-07" xlink:href="note-0238-07a" xml:space="preserve">50</note>
            los prioris circuli maximi per rectas A E, C F, ducti. </s>
            <s xml:id="echoid-s14960" xml:space="preserve">Erit hic circulus ad planum quoque vtriuſque ho
              <lb/>
            rologii, & </s>
            <s xml:id="echoid-s14961" xml:space="preserve">ad priorem illum circulum maximum, per propoſ. </s>
            <s xml:id="echoid-s14962" xml:space="preserve">15. </s>
            <s xml:id="echoid-s14963" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s14964" xml:space="preserve">1. </s>
            <s xml:id="echoid-s14965" xml:space="preserve">Theodoſii, rectus, tranſibit{q́ue} per
              <lb/>
            ſtylos A B, C D, nempe per axem plani vtriuſque horologii, cum per eiuſdem polos ducatur, vt dictum
              <lb/>
            eſt. </s>
            <s xml:id="echoid-s14966" xml:space="preserve">Faciat autem dictus circulus maximus cum planis horologiorum communes ſectiones rectas A G,
              <lb/>
            C H, quæ etiam inter ſe parallelæ erunt. </s>
            <s xml:id="echoid-s14967" xml:space="preserve">Eædem quoque ad rec
              <unsure/>
            tas A E, C F, erunt perpendiculares. </s>
            <s xml:id="echoid-s14968" xml:space="preserve">Cũ
              <lb/>
              <note position="left" xlink:label="note-0238-08" xlink:href="note-0238-08a" xml:space="preserve">16. vndec.</note>
            enim & </s>
            <s xml:id="echoid-s14969" xml:space="preserve">planum horologii, cuius ſtylus A B, & </s>
            <s xml:id="echoid-s14970" xml:space="preserve">planum circuli huius poſterioris per rectam A G, ducti
              <lb/>
            rectum ſit ad planum prioris illius circuli per rectam A E, ducti, ex conſtructione; </s>
            <s xml:id="echoid-s14971" xml:space="preserve">erit & </s>
            <s xml:id="echoid-s14972" xml:space="preserve">communis
              <lb/>
            illorum ſectio A G, ad planum eiuſdem circuli per A E, ducti, atque adeò per defin. </s>
            <s xml:id="echoid-s14973" xml:space="preserve">3. </s>
            <s xml:id="echoid-s14974" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s14975" xml:space="preserve">11. </s>
            <s xml:id="echoid-s14976" xml:space="preserve">Euclidis,
              <lb/>
              <note position="left" xlink:label="note-0238-09" xlink:href="note-0238-09a" xml:space="preserve">19. vndec.</note>
            ad rectam quoque A E, in dicto circulo exiſtentem perpendicularis: </s>
            <s xml:id="echoid-s14977" xml:space="preserve">Eadem ratione erit C H, ad C F,
              <lb/>
            perpendicularis. </s>
            <s xml:id="echoid-s14978" xml:space="preserve">Poſterior autem hic circulus in Verticali horologio, Meridiano, & </s>
            <s xml:id="echoid-s14979" xml:space="preserve">declinante à Ver-
              <lb/>
            ticali eſt ipſemet Horizon. </s>
            <s xml:id="echoid-s14980" xml:space="preserve">Cum enim horum horologiorum plana ad Horizontem recta ſint, erit </s>
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