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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            <s xml:id="echoid-s20533" xml:space="preserve">
              <pb o="305" file="0321" n="321" rhead="LIBER TERTIVS."/>
            deorſum aut em in eo, quod à Septentrione deflectit, in quo numer ata altitudine poli, initio facto à re cta
              <lb/>
            A B, ducatur ex β, ad finem ſupputationis recta ſecans C E, in C, puncto, quod centrum erit horologii,
              <lb/>
            in quo omnes lineę horarię conuenient. </s>
            <s xml:id="echoid-s20534" xml:space="preserve">Ducta autem ex C, per K, locum ſtyli recta C K, pro linea styli,
              <lb/>
            quam recta ex α, ducta ſecet ad angulos rectos in G; </s>
            <s xml:id="echoid-s20535" xml:space="preserve">erit recta α G, linea æquinoctialis. </s>
            <s xml:id="echoid-s20536" xml:space="preserve">Post hæc excite
              <lb/>
            tur ex K, recta K I, ad C K, perpendicularis, & </s>
            <s xml:id="echoid-s20537" xml:space="preserve">ſtylo K F, æqualis, iungantur rectę C I, G I, quæ in
              <lb/>
            I, angulum rectum continebunt, vt demonstrabimus. </s>
            <s xml:id="echoid-s20538" xml:space="preserve">Vnde ducta recta C I, ſi ad eam excitemus per-
              <lb/>
            pendicularem I G, inueniemus in linea ſtyli C K, punctum G, per quod ex α, ducenda eſt ęquinoctialis li-
              <lb/>
            nea α G, ad C K, perpendicularis. </s>
            <s xml:id="echoid-s20539" xml:space="preserve">Erit autem C I, axis mundi. </s>
            <s xml:id="echoid-s20540" xml:space="preserve">Iam vero in linea ſtyli C K, ſumpta
              <lb/>
            recta G L, ipſi G I, ęquali, deſcribatur ex L, circulus cuiuſuis magnitudinis, qui in partes 24. </s>
            <s xml:id="echoid-s20541" xml:space="preserve">ęquales
              <lb/>
            diſtribuatur, initio facto à recta L M, quæ ex L, ducitur per punctum M, vbi ęquinoctialis linea meridia-
              <lb/>
              <note position="left" xlink:label="note-0321-01" xlink:href="note-0321-01a" xml:space="preserve">10</note>
            nam interſecat, quæ quidem recta L M, neceſſario ductam rectam L α, ad angulos rectos ſecabit, ſi non
              <lb/>
            fuerit erratum. </s>
            <s xml:id="echoid-s20542" xml:space="preserve">Reliqua denique perficiantur, vt in principio huius propoſ. </s>
            <s xml:id="echoid-s20543" xml:space="preserve">traditum eſt.</s>
            <s xml:id="echoid-s20544" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s20545" xml:space="preserve">HANC constructionem ita demonſtrabim{us}. </s>
            <s xml:id="echoid-s20546" xml:space="preserve">Intelligatur per rectam A B, & </s>
            <s xml:id="echoid-s20547" xml:space="preserve">ſtylum K F, qui
              <lb/>
              <note position="right" xlink:label="note-0321-02" xlink:href="note-0321-02a" xml:space="preserve">Demonſtratio
                <lb/>
              huius
                <unsure/>
              conſtru-
                <lb/>
              ctionis.</note>
            rectus ſit ad planum horologii in puncto K, duci Horizon, ita vt A B, communis ſectio ſit Horizontis
              <lb/>
            ac plani horologij declinantis, nempe linea horizontalis. </s>
            <s xml:id="echoid-s20548" xml:space="preserve">Per polum quoque plani declinantis, & </s>
            <s xml:id="echoid-s20549" xml:space="preserve">polum
              <lb/>
            Horizontis concipiatur duci circulus maxim{us}, qui per propoſ. </s>
            <s xml:id="echoid-s20550" xml:space="preserve">15 lib. </s>
            <s xml:id="echoid-s20551" xml:space="preserve">1. </s>
            <s xml:id="echoid-s20552" xml:space="preserve">Theod. </s>
            <s xml:id="echoid-s20553" xml:space="preserve">& </s>
            <s xml:id="echoid-s20554" xml:space="preserve">ad planum declinãs,
              <lb/>
            & </s>
            <s xml:id="echoid-s20555" xml:space="preserve">ad Horizontem rectus erit, ac proinde cum per centrum mundi, id eſt, per verticem ſtyli F, tran-
              <lb/>
            ſeat, omnia autem plana ducta per ſtylum K F, qui rectus eſt ad planum declinans, recta ſint ad idem pla
              <lb/>
              <note position="right" xlink:label="note-0321-03" xlink:href="note-0321-03a" xml:space="preserve">18. vndec.</note>
            num declinans, tranſibit dictus circulus maximus per ſtylum F K, planum{q́ue} horologij declinantis ſecabit
              <lb/>
            in K. </s>
            <s xml:id="echoid-s20556" xml:space="preserve">Quoniam igitur tam planum horologij, quam planum huius circuli maximi rectum eſt ad Horizon-
              <lb/>
              <note position="left" xlink:label="note-0321-04" xlink:href="note-0321-04a" xml:space="preserve">20</note>
            tem, erit quoque communis eorum ſectio ad eundem, at que adeo, per defin. </s>
            <s xml:id="echoid-s20557" xml:space="preserve">3. </s>
            <s xml:id="echoid-s20558" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s20559" xml:space="preserve">11. </s>
            <s xml:id="echoid-s20560" xml:space="preserve">Eucl. </s>
            <s xml:id="echoid-s20561" xml:space="preserve">& </s>
            <s xml:id="echoid-s20562" xml:space="preserve">ad rect am
              <lb/>
              <note position="right" xlink:label="note-0321-05" xlink:href="note-0321-05a" xml:space="preserve">19. vndec.</note>
            A B, in Horizonte exiſtentem, perpendicularis erit. </s>
            <s xml:id="echoid-s20563" xml:space="preserve">Quare recta F D, quam per K, duximus ad A B,
              <lb/>
            perpendicularem, communis ſectio erit dicti maximi circuli, & </s>
            <s xml:id="echoid-s20564" xml:space="preserve">plani horologij declinantis, ac proinde
              <lb/>
            ad Horizontem perpendicularis. </s>
            <s xml:id="echoid-s20565" xml:space="preserve">Quod ſi primo loco ducatur recta F D, ad Horizontem perpendicula-
              <lb/>
            ris, intelligatur per rectam F D, & </s>
            <s xml:id="echoid-s20566" xml:space="preserve">per ſtylum F K, qui rectus ſit ad planum horologij declinantis, duci
              <lb/>
            planum, quod rectum erit & </s>
            <s xml:id="echoid-s20567" xml:space="preserve">ad Horizontem, & </s>
            <s xml:id="echoid-s20568" xml:space="preserve">ad planum horologij declinantis. </s>
            <s xml:id="echoid-s20569" xml:space="preserve">Quoniam igitur tam
              <lb/>
              <note position="right" xlink:label="note-0321-06" xlink:href="note-0321-06a" xml:space="preserve">18. vndec.</note>
            planum horologij, quam planum Horizontis rectum eſt ad planum per rectam F D, & </s>
            <s xml:id="echoid-s20570" xml:space="preserve">ſtylum F K, du-
              <lb/>
            ctum, erit quoque ad idem planum recta communis illorum ſectio, atque adeo, per defin. </s>
            <s xml:id="echoid-s20571" xml:space="preserve">3. </s>
            <s xml:id="echoid-s20572" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s20573" xml:space="preserve">11. </s>
            <s xml:id="echoid-s20574" xml:space="preserve">Eucl. </s>
            <s xml:id="echoid-s20575" xml:space="preserve">ad
              <lb/>
              <note position="right" xlink:label="note-0321-07" xlink:href="note-0321-07a" xml:space="preserve">19. vndec.</note>
            rectam F D, in dicto plano exiſtentem perpendicularis, in puncto K, per quod Horizon ducitur, cum per
              <lb/>
            ſtylum F K, ducatur. </s>
            <s xml:id="echoid-s20576" xml:space="preserve">Recta igitur A B, quam ad F D, duximus perpendicularem, communis ſectio e-
              <lb/>
              <note position="left" xlink:label="note-0321-08" xlink:href="note-0321-08a" xml:space="preserve">30</note>
            rit plani horologij & </s>
            <s xml:id="echoid-s20577" xml:space="preserve">Horizontis, hoc e st, linea horizontalis.</s>
            <s xml:id="echoid-s20578" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s20579" xml:space="preserve">DEINDE quia E F k, angulus eſt declinationis plani horologij à Verticali, erit F E K, angu-
              <lb/>
            lus complementi eiuſdem declinationis, qualem nimirum Meridianus cum plano declinante conſtituit.
              <lb/>
            </s>
            <s xml:id="echoid-s20580" xml:space="preserve">Quare ſi triangulum E F K, circa E K, moueatur, donec rectum ſit ad planum horologij in proprio ſitu
              <lb/>
            poſitum, erit F E, communis ſectio Horizontis ac Meridiani per F, verticem ſtyli ducti; </s>
            <s xml:id="echoid-s20581" xml:space="preserve">ac propte-
              <lb/>
            rea, vt in prima deſcriptione huius propoſ. </s>
            <s xml:id="echoid-s20582" xml:space="preserve">demonstrauimus, erit C M, linea meridiana, communis vi-
              <lb/>
            delicet ſectio Meridiani ac plani horologii. </s>
            <s xml:id="echoid-s20583" xml:space="preserve">Et quoniam arc{us} H N, quadrans eſt, erit angulus E F α, re-
              <lb/>
            ctus; </s>
            <s xml:id="echoid-s20584" xml:space="preserve">ac proinde recta F α, communis ſectio Verticalis at que Horizontis. </s>
            <s xml:id="echoid-s20585" xml:space="preserve">Cum enim tam Horizon, quàm
              <lb/>
            Verticalis ad Meridianum rectus ſit, erit & </s>
            <s xml:id="echoid-s20586" xml:space="preserve">eorum ſectio communis ad eundem recta, ac proinde, per
              <lb/>
              <note position="right" xlink:label="note-0321-09" xlink:href="note-0321-09a" xml:space="preserve">19. vndec.</note>
            defin. </s>
            <s xml:id="echoid-s20587" xml:space="preserve">3. </s>
            <s xml:id="echoid-s20588" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s20589" xml:space="preserve">11. </s>
            <s xml:id="echoid-s20590" xml:space="preserve">Eucl. </s>
            <s xml:id="echoid-s20591" xml:space="preserve">ad rectam F E, in Meridiano exiſtentem perpendicularis in F, centro mundi. </s>
            <s xml:id="echoid-s20592" xml:space="preserve">Qua-
              <lb/>
              <note position="left" xlink:label="note-0321-10" xlink:href="note-0321-10a" xml:space="preserve">40</note>
            re F α, quæ ad F E, perpendicularis eſt, communis ſectio est Verticalis atque Horizontis. </s>
            <s xml:id="echoid-s20593" xml:space="preserve">Habet autẽ
              <lb/>
            Aequator eandem communem ſectionem cum Horizonte ac Verticali, nempe axem Meridiani, cum om-
              <lb/>
            nes hi tres circuli per polos Meridiani tranſeant, per propoſ. </s>
            <s xml:id="echoid-s20594" xml:space="preserve">13. </s>
            <s xml:id="echoid-s20595" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s20596" xml:space="preserve">1. </s>
            <s xml:id="echoid-s20597" xml:space="preserve">Theod. </s>
            <s xml:id="echoid-s20598" xml:space="preserve">proptcrea quòd ad Meri-
              <lb/>
            dianum recti ſunt. </s>
            <s xml:id="echoid-s20599" xml:space="preserve">Igitur Aequator per rectam F α, ducitur, occurrit{q́ue} plano horologii declinantis in
              <lb/>
            puncto α; </s>
            <s xml:id="echoid-s20600" xml:space="preserve">at que adeo per α, ducenda erit linea æquinoctialis.</s>
            <s xml:id="echoid-s20601" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s20602" xml:space="preserve">MANENTE adhuc triangulo E F K, ad planum horologij recto, ita vt angulus C E F, rectus
              <lb/>
            ſit, (Quòd enim rect{us} ſit, it a ostendemus. </s>
            <s xml:id="echoid-s20603" xml:space="preserve">Quoniam tam planum horologij, quàm planum Meridiani re-
              <lb/>
            ctum est ad Horizontem, erit quoque communis eorum ſectio C E, ad eundem, atque adeo, per defin. </s>
            <s xml:id="echoid-s20604" xml:space="preserve">3.
              <lb/>
            </s>
            <s xml:id="echoid-s20605" xml:space="preserve">
              <note position="right" xlink:label="note-0321-11" xlink:href="note-0321-11a" xml:space="preserve">19. vndec.</note>
            lib. </s>
            <s xml:id="echoid-s20606" xml:space="preserve">11. </s>
            <s xml:id="echoid-s20607" xml:space="preserve">Eucl. </s>
            <s xml:id="echoid-s20608" xml:space="preserve">& </s>
            <s xml:id="echoid-s20609" xml:space="preserve">ad rectam F E, in Horizonte existentem in illo ſitu, perpendicularis) intelligatur trian-
              <lb/>
            gulum β E C, moueri circa rectam C E, donec recta β E, rectæ F E, & </s>
            <s xml:id="echoid-s20610" xml:space="preserve">punctum β, puncto F, congruat
              <lb/>
              <note position="left" xlink:label="note-0321-12" xlink:href="note-0321-12a" xml:space="preserve">50</note>
            propter angulos rectos β E C, F E C, & </s>
            <s xml:id="echoid-s20611" xml:space="preserve">æqualitatem rectarum E β, E F. </s>
            <s xml:id="echoid-s20612" xml:space="preserve">Quo facto, erit β C, axis mun
              <lb/>
            di; </s>
            <s xml:id="echoid-s20613" xml:space="preserve">quandoquidem in plano Meridiani, qui per rectas F E, E C, ducitur, cum meridiana linea Horizon-
              <lb/>
            tis E F, in centro mundi F, angulum conſtituit E β C, altitudinis poli ſupra Horizontem. </s>
            <s xml:id="echoid-s20614" xml:space="preserve">Igitur per co
              <lb/>
            roll. </s>
            <s xml:id="echoid-s20615" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s20616" xml:space="preserve">21. </s>
            <s xml:id="echoid-s20617" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s20618" xml:space="preserve">1. </s>
            <s xml:id="echoid-s20619" xml:space="preserve">punctum C, in quod axis cadit, centrum erit horologij. </s>
            <s xml:id="echoid-s20620" xml:space="preserve">Hinc efficitur, rectam C K,
              <lb/>
            eſſe lineam styli, hoc eſt, communem ſectionem plani horologii declinantis, & </s>
            <s xml:id="echoid-s20621" xml:space="preserve">Meridiani proprij ipſi{us}
              <lb/>
            plani declinantis, qui per axem & </s>
            <s xml:id="echoid-s20622" xml:space="preserve">ſtylum ducitur, instar propriæ lineę meridianæ horologij declinantis:
              <lb/>
            </s>
            <s xml:id="echoid-s20623" xml:space="preserve">quemadmodum & </s>
            <s xml:id="echoid-s20624" xml:space="preserve">in prima deſcriptione hui{us} propoſ. </s>
            <s xml:id="echoid-s20625" xml:space="preserve">linea styli C G, ducta eſt ex centro horologii C,
              <lb/>
            per K, locum ſtyli. </s>
            <s xml:id="echoid-s20626" xml:space="preserve">Pari ratione efficitur, rectam α G, quæ ad lineam styli perpendicularis est, eſſe li-
              <lb/>
            neam ęquinoctialem, quandoquidem per punctum α, ducenda eſt, vt nuper oſtendim{us}, & </s>
            <s xml:id="echoid-s20627" xml:space="preserve">angulos rectos
              <lb/>
            facit cum linea styli, vt in prima deſcriptione hui{us} propoſ. </s>
            <s xml:id="echoid-s20628" xml:space="preserve">demonstratum eſt.</s>
            <s xml:id="echoid-s20629" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s20630" xml:space="preserve">RECTAM autem C I, eſſe axem mundi, perſpicuum eſt. </s>
            <s xml:id="echoid-s20631" xml:space="preserve">Si enim triangulum C I K, circa C </s>
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