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-s19919" xml:space="preserve">
              <pb o="295" file="0311" n="311" rhead="LIBER TERTIVS."/>
            niſ
              <unsure/>
            tram, (commodius tamen fuerit, ſi ſumatur ad partes oppoſitas lineæ declinationis E F; </s>
            <s xml:id="echoid-s19920" xml:space="preserve">vt ſi
              <lb/>
            E F, fuerit ad ſiniſtram rectæ C D, punctum β, accipiatur ad dextram eiuſdem rectæ C D, &</s>
            <s xml:id="echoid-s19921" xml:space="preserve">c.
              <lb/>
            </s>
            <s xml:id="echoid-s19922" xml:space="preserve">quoniam in ea parte, quæ rectæ E F, opponitur, pauciores lineæ horariæ,
              <unsure/>
            ducentur, vt mox planũ
              <lb/>
            fiet. </s>
            <s xml:id="echoid-s19923" xml:space="preserve">Quò etiam remotius fuerit punctum β, à puncto E, eò maius efficietur horologium) con-
              <lb/>
            ſtituatur ad rectam E β, in puncto β, angulus altitudinis poli E β C, ſupra quidem rectam A B,
              <lb/>
            ſi planum à meridie declinat,
              <unsure/>
            infra verò eandem rectam A B, ſi planum declinat à Borea, & </s>
            <s xml:id="echoid-s19924" xml:space="preserve">ſem-
              <lb/>
              <note position="right" xlink:label="note-0311-01" xlink:href="note-0311-01a" xml:space="preserve">Centrum ho-
                <lb/>
              rologu.</note>
            per verſus rectam C D, ita vt recta β C, ſecet rectam C D, in C, puncto, quod erit centrum horo-
              <lb/>
            gii, per quod omnes horariæ lineæ ducendæ ſunt, vt demonſtrabimus.</s>
            <s xml:id="echoid-s19925" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s19926" xml:space="preserve">RVRSVS in linea declinationis E F, ſumpta recta E F, ipſi E β, æquali, ducatur ex F, ad A B,
              <lb/>
            perpendicularis F G, & </s>
            <s xml:id="echoid-s19927" xml:space="preserve">ex centro horologii C, per G, recta ducatur C G, quæ linea ſtyli, vel indi-
              <lb/>
              <note position="left" xlink:label="note-0311-02" xlink:href="note-0311-02a" xml:space="preserve">10</note>
              <note position="right" xlink:label="note-0311-03" xlink:href="note-0311-03a" xml:space="preserve">Linea ſty li.</note>
            cis vocetur; </s>
            <s xml:id="echoid-s19928" xml:space="preserve">quoniam in ea figendus erit ſtylus angulos rectos faciens cum plano horologij. </s>
            <s xml:id="echoid-s19929" xml:space="preserve">Ad
              <lb/>
            hanc autem lineam Indicis C G, ex G, educatur in vtramque partem perpendicularis G H; </s>
            <s xml:id="echoid-s19930" xml:space="preserve">erit
              <lb/>
            hæc, linea æquinoctialis; </s>
            <s xml:id="echoid-s19931" xml:space="preserve">in qua accepta recta G H, ſiue ad dextram puncti G, ſiue ad ſiniſtram, ipſi
              <lb/>
              <note position="right" xlink:label="note-0311-04" xlink:href="note-0311-04a" xml:space="preserve">Linea ęquino-
                <lb/>
              ctialis.</note>
            F G, æquali, ductaq́ue recta C H, ducatur ad eam perpendicularis G I; </s>
            <s xml:id="echoid-s19932" xml:space="preserve">& </s>
            <s xml:id="echoid-s19933" xml:space="preserve">ex I, ad lineam indicis
              <lb/>
            C G, perpendicularis I K. </s>
            <s xml:id="echoid-s19934" xml:space="preserve">Erit C H, axis mundi, & </s>
            <s xml:id="echoid-s19935" xml:space="preserve">I K, longitudo ſtyli, eiusq́ue locus K, in linea
              <lb/>
              <note position="right" xlink:label="note-0311-05" xlink:href="note-0311-05a" xml:space="preserve">Axis mundi.
                <lb/>
              Longitudo ſty-
                <lb/>
              li, e iu@q; locus.</note>
            ſtyli, ſiue indicis: </s>
            <s xml:id="echoid-s19936" xml:space="preserve">Angulus autem G C H, erit angulus altitudinis poli ſupra planum declinans,
              <lb/>
            vt demonſtrabimus.</s>
            <s xml:id="echoid-s19937" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">Altitudo poli
            <lb/>
          ſupra planum
            <lb/>
          declinans.</note>
          <p>
            <s xml:id="echoid-s19938" xml:space="preserve">POSTREMO in linea indicis C G, ſumpta recta G L, ſiue ſupra G, ſiue infra, ipſi G I, æqua-
              <lb/>
            li, deſcribatur ex L, circulus cuiuſuis magnitudinis, qui in partes 24. </s>
            <s xml:id="echoid-s19939" xml:space="preserve">æquales diſtribuatur, initio
              <lb/>
            facto à recta L M, quæ ex L, centro circuli per punctum M, vbi æquinoctialis linea rectam D, in-
              <lb/>
              <note position="left" xlink:label="note-0311-07" xlink:href="note-0311-07a" xml:space="preserve">20</note>
            terſecat. </s>
            <s xml:id="echoid-s19940" xml:space="preserve">Si enim per hæc puncta diuiſionum, & </s>
            <s xml:id="echoid-s19941" xml:space="preserve">centrum L, rectæ occultæ egrediantur, ſecabitur
              <lb/>
            linea æquinoctialis G H, in punctis, per quæ rectæ emiſſæ ex C, centro horologii dabunt horas à
              <lb/>
            meridie, vel media nocte, eundem ordinem ſeruantes, quem in Verticali horologio habent. </s>
            <s xml:id="echoid-s19942" xml:space="preserve">In
              <lb/>
            horologio enim, quod à meridie declinat ſiue in ortum, ſiue in occaſum, portio rectæ C D, inci-
              <lb/>
              <note position="right" xlink:label="note-0311-08" xlink:href="note-0311-08a" xml:space="preserve">Ordo horarum
                <lb/>
              in horologio
                <lb/>
              declinante à
                <lb/>
              Verticali.</note>
            piens à C, verſusq́ue æquinoctialem lineam extenſa, monſtrat horam 12. </s>
            <s xml:id="echoid-s19943" xml:space="preserve">meridiei: </s>
            <s xml:id="echoid-s19944" xml:space="preserve">lineæ verò
              <lb/>
            æquinoctialem lineam ſecantes ad partem ſiniſtram ipſius C D, hoc eſt, ad partes A, occidenta-
              <lb/>
            lesve, indicant horas à media nocte; </s>
            <s xml:id="echoid-s19945" xml:space="preserve">lineę denique ſecantes æquinoctialem lineam ad partem dex-
              <lb/>
            tram, id eſt, ad partes B, ſeu orientales, pertinent ad horas à meridie; </s>
            <s xml:id="echoid-s19946" xml:space="preserve">ita vt proxima linea ad ſini-
              <lb/>
            ſtram ipſius C D, ſignificet horam 11. </s>
            <s xml:id="echoid-s19947" xml:space="preserve">à media nocte, proxima verò ad dexteram eiuſdem oſten-
              <lb/>
            dat horam 1. </s>
            <s xml:id="echoid-s19948" xml:space="preserve">à meridie, &</s>
            <s xml:id="echoid-s19949" xml:space="preserve">c. </s>
            <s xml:id="echoid-s19950" xml:space="preserve">In horologio verò, quod à ſeptentrione in ortũ, occaſumve deflectit,
              <lb/>
              <note position="left" xlink:label="note-0311-09" xlink:href="note-0311-09a" xml:space="preserve">30</note>
            contrarium intelligatur. </s>
            <s xml:id="echoid-s19951" xml:space="preserve">Nam portio rectæ C D, à C, verſus ęquinoctialem lineam protenſa da-
              <lb/>
            bit horam 12. </s>
            <s xml:id="echoid-s19952" xml:space="preserve">mediæ noctis, quæ verò ei ſunt ad ſiniſtram in æquinoctiali linea, horas à meridie,
              <lb/>
            quæ autem ad dextram, horas à media nocte, vt in vtroque Verticali horologio.</s>
            <s xml:id="echoid-s19953" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">Quando linea
            <lb/>
          horatia per cen
            <lb/>
          trnm horologii
            <lb/>
          C, ducenda ſit
            <lb/>
          æquinoctiali li-
            <lb/>
          neæ pa rallela.</note>
          <p>
            <s xml:id="echoid-s19954" xml:space="preserve">QVOD ſi quando recta per aliquod punctum diuiſionis circuli ex L, deſcripti, & </s>
            <s xml:id="echoid-s19955" xml:space="preserve">per cen-
              <lb/>
            trum L, ducta parallela ſit æquinoctiali lineæ, tum ducta per C, linea recta æquinoctiali lineæ pa-
              <lb/>
            rallela dabit illam horam, quæcunque fuerit, non aliter, qnàm in horologio horizontali contin-
              <lb/>
            git, vbi hora 6. </s>
            <s xml:id="echoid-s19956" xml:space="preserve">ducitur per centrum horologii lineæ æquinoctiali æquidiſtans, quia recta in cir-
              <lb/>
            culo ex E, ibi deſcripto ducta per punctum horæ 6. </s>
            <s xml:id="echoid-s19957" xml:space="preserve">& </s>
            <s xml:id="echoid-s19958" xml:space="preserve">centrum E, æquinoctiali lineæ æquidiſtat.</s>
            <s xml:id="echoid-s19959" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s19960" xml:space="preserve">HANC autem conſtructionem hoc modo demonſtrabimus. </s>
            <s xml:id="echoid-s19961" xml:space="preserve">Intelligatur in plano horologij
              <lb/>
              <note position="right" xlink:label="note-0311-11" xlink:href="note-0311-11a" xml:space="preserve">Demonſtratio
                <lb/>
              conſtructionis
                <lb/>
              horolo gii de cli
                <lb/>
              nantis à
                <unsure/>
              Verti-
                <lb/>
              cali.</note>
            recta A B, æquidiſtare Horizonti, ita vt ſit communis ſectio plani horologii horizontalis, & </s>
            <s xml:id="echoid-s19962" xml:space="preserve">pla-
              <lb/>
              <note position="left" xlink:label="note-0311-12" xlink:href="note-0311-12a" xml:space="preserve">40</note>
            ni horologii declinantis; </s>
            <s xml:id="echoid-s19963" xml:space="preserve">& </s>
            <s xml:id="echoid-s19964" xml:space="preserve">planum per rectas A B, E F, E D, ductum concipiatur animo moueri
              <lb/>
            circa rectam A B, donec Horizonti æquidiſtet, atque adeò cum plano horologii horizontalis con-
              <lb/>
            iungatur. </s>
            <s xml:id="echoid-s19965" xml:space="preserve">His poſitis, cum D E F, ſit angulus declinationis plani horologii à Verticali, erit A E F,
              <lb/>
            angulus complementi dictæ declinationis, qualem nimirum Meridianus cum plano declinante
              <lb/>
            comprehendit. </s>
            <s xml:id="echoid-s19966" xml:space="preserve">Quare recta E F, communis ſectio erit Meridiani, & </s>
            <s xml:id="echoid-s19967" xml:space="preserve">plani horologii horizonta-
              <lb/>
            lis, proptereaq́ue Meridianus planum horologii declinantis in puncto E, ſecabit. </s>
            <s xml:id="echoid-s19968" xml:space="preserve">Quoniam verò
              <lb/>
            tam planum Meridiani, quàm planum horologii declinantis ad planum horologii horizontalis
              <lb/>
              <note position="right" xlink:label="note-0311-13" xlink:href="note-0311-13a" xml:space="preserve">19. vndec.</note>
            rectum eſt, erit quoque communis eorum ſectio ad idem perpendicularis, ac proinde & </s>
            <s xml:id="echoid-s19969" xml:space="preserve">ad rectã
              <lb/>
            A B, in dicto plano perpendicularis erit, ex defin. </s>
            <s xml:id="echoid-s19970" xml:space="preserve">3. </s>
            <s xml:id="echoid-s19971" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s19972" xml:space="preserve">11. </s>
            <s xml:id="echoid-s19973" xml:space="preserve">Euclidis. </s>
            <s xml:id="echoid-s19974" xml:space="preserve">Cum ergo communis hæc
              <lb/>
            ſectio per E, tranſeat, & </s>
            <s xml:id="echoid-s19975" xml:space="preserve">recta C D, perpendicularis ſit, per conſtructionem, ad A B; </s>
            <s xml:id="echoid-s19976" xml:space="preserve">erit C D, ſectio
              <lb/>
              <note position="left" xlink:label="note-0311-14" xlink:href="note-0311-14a" xml:space="preserve">50</note>
            communis Meridiani, & </s>
            <s xml:id="echoid-s19977" xml:space="preserve">plani horologii declinantis, hoc eſt, linea meridiana horologii declinan
              <lb/>
            tis. </s>
            <s xml:id="echoid-s19978" xml:space="preserve">Rurſus quia tam planum Meridiani, quàm planum horologii declinantis rectum eſt ad pla-
              <lb/>
            num horologii horizontalis, erit eorum communis ſectio C E, ad idem perpendicularis, atque
              <lb/>
              <note position="right" xlink:label="note-0311-15" xlink:href="note-0311-15a" xml:space="preserve">19. vndec.</note>
            adeò, per defin. </s>
            <s xml:id="echoid-s19979" xml:space="preserve">3. </s>
            <s xml:id="echoid-s19980" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s19981" xml:space="preserve">11. </s>
            <s xml:id="echoid-s19982" xml:space="preserve">Euclidis, & </s>
            <s xml:id="echoid-s19983" xml:space="preserve">ad rectam E F, in plano horologii horizontalis exiſtentem.
              <lb/>
            </s>
            <s xml:id="echoid-s19984" xml:space="preserve">Si igitur triangulum β E C, intelligatur moueri circa C E, donec cum plano Meridiani per re-
              <lb/>
            ctas C E, E F, ducti coniungatur, congruet angulus rectus β E C, recto angulo C E F, & </s>
            <s xml:id="echoid-s19985" xml:space="preserve">punctum
              <lb/>
            β, puncto F, propter æqualitatem rectarum E β, E F. </s>
            <s xml:id="echoid-s19986" xml:space="preserve">Quare recta β C, conſtituens in eo ſitu cum
              <lb/>
            meridiana linea E F, horologii horizontalis angulum altitudinis poli E β C, porrectaq́ue verſus
              <lb/>
            partes ſeptentrionales ex parte ſuperiori rectæ E F, erit axis mundi occurrens plano horologii de-
              <lb/>
            clinantis in C, puncto; </s>
            <s xml:id="echoid-s19987" xml:space="preserve">ac proinde ex coroll. </s>
            <s xml:id="echoid-s19988" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s19989" xml:space="preserve">21. </s>
            <s xml:id="echoid-s19990" xml:space="preserve">primi lib. </s>
            <s xml:id="echoid-s19991" xml:space="preserve">punctum C, centrum erit ho-
              <lb/>
            rologii declinantis. </s>
            <s xml:id="echoid-s19992" xml:space="preserve">Axis enim cum meridiana linea horologii horizontalis conſtituit </s>
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