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-s42144" xml:space="preserve">
              <pb o="642" file="0658" n="658" rhead="GNOMONICES"/>
            diſtantis, tranſibit hic, ex ſcholio propoſ. </s>
            <s xml:id="echoid-s42145" xml:space="preserve">15. </s>
            <s xml:id="echoid-s42146" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s42147" xml:space="preserve">1. </s>
            <s xml:id="echoid-s42148" xml:space="preserve">Theod. </s>
            <s xml:id="echoid-s42149" xml:space="preserve">viciſſim per illius polũ. </s>
            <s xml:id="echoid-s42150" xml:space="preserve">Vnde ſi eadem
              <lb/>
              <note position="left" xlink:label="note-0658-01" xlink:href="note-0658-01a" xml:space="preserve">Tacilis inuen-
                <lb/>
              tio polorum, ex
                <lb/>
              quibus circuli
                <lb/>
              horatum in-
                <lb/>
              æqualium de-
                <lb/>
              ſcribuntur.</note>
            circini apertura manente, vnus pes ſtatuatur in quolibet puncto tropici ♋, vel ♑, & </s>
            <s xml:id="echoid-s42151" xml:space="preserve">alter pona-
              <lb/>
            tur in circulo illius horæ à mer. </s>
            <s xml:id="echoid-s42152" xml:space="preserve">vel med. </s>
            <s xml:id="echoid-s42153" xml:space="preserve">noc. </s>
            <s xml:id="echoid-s42154" xml:space="preserve">occulte producti, qui ſex horis in Aequatore ab-
              <lb/>
            eſt à puncto, quod puncto accepto in tropico reſpondet, habebitur polus illius circuli horarum
              <lb/>
            inæqualium. </s>
            <s xml:id="echoid-s42155" xml:space="preserve">Verbi gratia. </s>
            <s xml:id="echoid-s42156" xml:space="preserve">Quoniam circulus horæ 1. </s>
            <s xml:id="echoid-s42157" xml:space="preserve">inæqualis ducendus eſt per primum pun-
              <lb/>
            ctum Aequatoris infra D, & </s>
            <s xml:id="echoid-s42158" xml:space="preserve">per prima puncta tropicorum infra I, & </s>
            <s xml:id="echoid-s42159" xml:space="preserve">M; </s>
            <s xml:id="echoid-s42160" xml:space="preserve">abeſt autem circulus ho-
              <lb/>
            ræ 1. </s>
            <s xml:id="echoid-s42161" xml:space="preserve">à mer. </s>
            <s xml:id="echoid-s42162" xml:space="preserve">in Aequatore ſex horis à primo puncto infra D. </s>
            <s xml:id="echoid-s42163" xml:space="preserve">Igitur ſi vnus pes circini ſtatuatur in
              <lb/>
            primo puncto tropici infra I, vel M, & </s>
            <s xml:id="echoid-s42164" xml:space="preserve">alter extendatur vſque ad circulum horæ 1. </s>
            <s xml:id="echoid-s42165" xml:space="preserve">à mei
              <unsure/>
            . </s>
            <s xml:id="echoid-s42166" xml:space="preserve">occultè
              <lb/>
            productum, habebitur in hoc circulo polus illius circuli, & </s>
            <s xml:id="echoid-s42167" xml:space="preserve">ſic de cæteris.</s>
            <s xml:id="echoid-s42168" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s42169" xml:space="preserve">STYLVS horas indicans erit axis mundi æqualis ſemidiametro hemiſphærij, qui ita in F,
              <lb/>
              <note position="left" xlink:label="note-0658-02" xlink:href="note-0658-02a" xml:space="preserve">Stylus horas
                <lb/>
              monſtrans.</note>
              <note position="left" xlink:label="note-0658-03" xlink:href="note-0658-03a" xml:space="preserve">10</note>
            polo figendus eſt, vt eius punctum extremum centrum hemiſphærij occupet. </s>
            <s xml:id="echoid-s42170" xml:space="preserve">quod tum demum
              <lb/>
            factum erit, cum extenſis in orificio hemiſphærii duobus filis ab A, in C, & </s>
            <s xml:id="echoid-s42171" xml:space="preserve">á B, in D, extremum
              <lb/>
            punctum in communi interſectione filorum collocatum erit. </s>
            <s xml:id="echoid-s42172" xml:space="preserve">Poteſt idem ſtylus in quouis pun-
              <lb/>
            cto figi, ſed tunc non erit axis mundi. </s>
            <s xml:id="echoid-s42173" xml:space="preserve">Accommodandum quoque erit inſtrumentum in circulo
              <lb/>
            Meridiano vna cum acu Magnete illita, ita tamen, vt planum inſtrumenti Horizonti æquidiſtet.</s>
            <s xml:id="echoid-s42174" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s42175" xml:space="preserve">SI LVBET, poterunt quoque in hoc hemiſphærio deſcribi omnia illa, quæ in planis ho-
              <lb/>
              <note position="left" xlink:label="note-0658-04" xlink:href="note-0658-04a" xml:space="preserve">Deſcriptio pa@
                <lb/>
              rallelorum lon
                <lb/>
              gitudinum die-
                <lb/>
              rum, & latitu-
                <lb/>
              dinum ciui-
                <lb/>
              tatum, Ve@tica
                <lb/>
              lium circulorũ,
                <lb/>
              & parallelorum
                <lb/>
              Horizon is; Me
                <lb/>
              ridianorũ; Do-
                <lb/>
              morum cæle
                <lb/>
              ſtium, & aſcen-
                <lb/>
              dentium ſigno-
                <lb/>
              rum in hemi-
                <lb/>
              ſphærio conca-
                <lb/>
              uo.</note>
            rologiis lib. </s>
            <s xml:id="echoid-s42176" xml:space="preserve">2. </s>
            <s xml:id="echoid-s42177" xml:space="preserve">& </s>
            <s xml:id="echoid-s42178" xml:space="preserve">3. </s>
            <s xml:id="echoid-s42179" xml:space="preserve">deſcripſimus. </s>
            <s xml:id="echoid-s42180" xml:space="preserve">Nam paralleli longitudinum dierum, & </s>
            <s xml:id="echoid-s42181" xml:space="preserve">latitudinum ciuita-
              <lb/>
            tum delineabuntur ex polo F, vt paralleli ſignorum, ſi eorum declinationes à G, ſupputentur in
              <lb/>
            Meridiano, verſus H, quidem, ſi fuerint boreales, at verſus L, ſi auſtrales. </s>
            <s xml:id="echoid-s42182" xml:space="preserve">Verticales autem cir-
              <lb/>
            culi deſcribentur per E, ex ſingulis gradibus Horizontis A B C D, qui per eorum polos tranſit,
              <lb/>
              <note position="left" xlink:label="note-0658-05" xlink:href="note-0658-05a" xml:space="preserve">20</note>
            ex ſcholio propoſ. </s>
            <s xml:id="echoid-s42183" xml:space="preserve">15. </s>
            <s xml:id="echoid-s42184" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s42185" xml:space="preserve">1. </s>
            <s xml:id="echoid-s42186" xml:space="preserve">Theod. </s>
            <s xml:id="echoid-s42187" xml:space="preserve">cum viciſſim Verticales per Horizontis polum E, tranſeant.
              <lb/>
            </s>
            <s xml:id="echoid-s42188" xml:space="preserve">Paralleli vero Horizontis deſcribentur ex E, polo Horizõtis per ſingulos gradus Meridiani A C,
              <lb/>
            vel Verticalis B D. </s>
            <s xml:id="echoid-s42189" xml:space="preserve">Meridiani, hoc eſt, circuli longitudinum ciuitatum, ducentur per ſingulos
              <lb/>
            gradus Aequatoris, veluti circuli horarum à mer. </s>
            <s xml:id="echoid-s42190" xml:space="preserve">& </s>
            <s xml:id="echoid-s42191" xml:space="preserve">med. </s>
            <s xml:id="echoid-s42192" xml:space="preserve">noc. </s>
            <s xml:id="echoid-s42193" xml:space="preserve">ſi diuiſio Aequatoris in gradus ini-
              <lb/>
            tium ſumat ab eo puncto, quod terminat longitudinem loci à G, verſus B, computatam. </s>
            <s xml:id="echoid-s42194" xml:space="preserve">Circuli
              <lb/>
            domorum cæleſtium ſecundum ſententiam loan. </s>
            <s xml:id="echoid-s42195" xml:space="preserve">Regiom. </s>
            <s xml:id="echoid-s42196" xml:space="preserve">deſcribentur per diuiſiones Aequa-
              <lb/>
            toris, ſtatuendo pro polis ipſorum pedem circini immobilem in Verticali B D, ita vt omnes tran-
              <lb/>
            ſeant per puncta A, C, vbi Meridianus Horizontem interſecat: </s>
            <s xml:id="echoid-s42197" xml:space="preserve">Ex ſententia vero Campani per
              <lb/>
            diuiſiones Verticalis, ſtatuendo quoque pro polis ipſorum pedem circini immobilem in Vertica-
              <lb/>
            li circulo, ita vt rurſus tranſeant per puncta A, C. </s>
            <s xml:id="echoid-s42198" xml:space="preserve">Hi enim circuli ſecundum Ioan. </s>
            <s xml:id="echoid-s42199" xml:space="preserve">Regiom. </s>
            <s xml:id="echoid-s42200" xml:space="preserve">di-
              <lb/>
              <note position="left" xlink:label="note-0658-06" xlink:href="note-0658-06a" xml:space="preserve">30</note>
            uidunt Aequatorem in 12. </s>
            <s xml:id="echoid-s42201" xml:space="preserve">partes æquales, ſecundum vero Campanum Verticalis circulus ab eiſ-
              <lb/>
            dem in 12. </s>
            <s xml:id="echoid-s42202" xml:space="preserve">æquales partes ſecatur. </s>
            <s xml:id="echoid-s42203" xml:space="preserve">Signa denique aſcendentia, id eſt, Eclipticæ poſitiones variæ,
              <lb/>
            initijs ſignorum orientibus, depingentur hac ratione. </s>
            <s xml:id="echoid-s42204" xml:space="preserve">Ex tabulis 3. </s>
            <s xml:id="echoid-s42205" xml:space="preserve">& </s>
            <s xml:id="echoid-s42206" xml:space="preserve">4. </s>
            <s xml:id="echoid-s42207" xml:space="preserve">poſitis in propoſ. </s>
            <s xml:id="echoid-s42208" xml:space="preserve">9. </s>
            <s xml:id="echoid-s42209" xml:space="preserve">lib.
              <lb/>
            </s>
            <s xml:id="echoid-s42210" xml:space="preserve">2. </s>
            <s xml:id="echoid-s42211" xml:space="preserve">aut aliis ſimilibus ex doctrina dictæ propoſ. </s>
            <s xml:id="echoid-s42212" xml:space="preserve">ad datam loci latitudinem ſupputatis, accipiatur
              <lb/>
            hora, qua quoduis ſignum oritur, Sole exiſtente in principio ♋, vel ♑, prout illa hora in tropico
              <lb/>
            ♋, aut ♑, continebitur in hemiſphærio concauo, eaq́ue in Aequatore numeretur à G, verſus qui-
              <lb/>
            dem D, ſi antemeridiana eſt, ſi vero pomeridiana, verſus B: </s>
            <s xml:id="echoid-s42213" xml:space="preserve">& </s>
            <s xml:id="echoid-s42214" xml:space="preserve">per finem numerationis (poſito
              <lb/>
            pede circini immobili in puncto Aequatoris, quod quadrante abeſt à fine numerationis) deſcriba-
              <lb/>
            tur circulus maximus occultus ſecans tropicum ♋, aut ♑, (prout hora ſumpta eſt, Sole in ♋, exi-
              <lb/>
            ſtente, aut in ♑.) </s>
            <s xml:id="echoid-s42215" xml:space="preserve">in puncto, per quod ad interuallum quadrantis in illo circulo occulto acceptũ
              <lb/>
              <note position="left" xlink:label="note-0658-07" xlink:href="note-0658-07a" xml:space="preserve">40</note>
            circulus maximus deſcribatur, referet is Eclipticæ ſitum, dum propoſitum ſignum
              <unsure/>
            oritur, adeo
              <lb/>
            vt, extremitate vmbræ in hunc circulum cadente, ſignum illud ſupra Horizontem incipiat oriri.
              <lb/>
            </s>
            <s xml:id="echoid-s42216" xml:space="preserve">Quoniam enim, vmbra cadente in illud punctum notatum in tropico ♋, vel ♑, monſtratur ho-
              <lb/>
            ra, qua datum ſignum oritur, exiſtit autem radius Solis per centrum tranſiens in plano Eclipticæ,
              <lb/>
            tranſibit neceſſario Ecliptica per illud punctum tropici ♋, vel ♑; </s>
            <s xml:id="echoid-s42217" xml:space="preserve">atque adeo in eo puncto tropi-
              <lb/>
            cum tanget, quemadmodum & </s>
            <s xml:id="echoid-s42218" xml:space="preserve">in cælo. </s>
            <s xml:id="echoid-s42219" xml:space="preserve">Cum ergo, per propoſ. </s>
            <s xml:id="echoid-s42220" xml:space="preserve">3. </s>
            <s xml:id="echoid-s42221" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s42222" xml:space="preserve">2. </s>
            <s xml:id="echoid-s42223" xml:space="preserve">Theod. </s>
            <s xml:id="echoid-s42224" xml:space="preserve">circulus vltimo
              <lb/>
            deſcriptus tropicum in eo puncto tangat, propterea quòd tam ipſe, quàm tropicus eo in puncto
              <lb/>
            ſecet circulum illum maximum occultum, in quo vtriuſque polus exiſtit, erit omnino circulus
              <lb/>
            hic Ecliptica. </s>
            <s xml:id="echoid-s42225" xml:space="preserve">Hoc artificio omia ſigna aſcendentia deſcribentur. </s>
            <s xml:id="echoid-s42226" xml:space="preserve">Signum ♈, tanget tropicum
              <lb/>
            ♑, in L, habebitq́ue polum in Meridiano diſtantem quadrante à puncto L. </s>
            <s xml:id="echoid-s42227" xml:space="preserve">Signum vero ♎, tro-
              <lb/>
              <note position="left" xlink:label="note-0658-08" xlink:href="note-0658-08a" xml:space="preserve">50</note>
            picum ♋, tanget in H, & </s>
            <s xml:id="echoid-s42228" xml:space="preserve">vtrumque per puncta B, & </s>
            <s xml:id="echoid-s42229" xml:space="preserve">D, tranſibit. </s>
            <s xml:id="echoid-s42230" xml:space="preserve">Signum autem ♋, tanget tropi-
              <lb/>
            cum ♋, in I, & </s>
            <s xml:id="echoid-s42231" xml:space="preserve">tropicum ♑, in N. </s>
            <s xml:id="echoid-s42232" xml:space="preserve">Signum denique ♑, tropicum ♋, tanget in K, & </s>
            <s xml:id="echoid-s42233" xml:space="preserve">tropicum ♑,
              <lb/>
            in M, vt ex dictis tabellis colligitur.</s>
            <s xml:id="echoid-s42234" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s42235" xml:space="preserve">ITAQVE, vt vides, facili negotio omnia illa, quæ in horologiis planis lib. </s>
            <s xml:id="echoid-s42236" xml:space="preserve">2. </s>
            <s xml:id="echoid-s42237" xml:space="preserve">& </s>
            <s xml:id="echoid-s42238" xml:space="preserve">3. </s>
            <s xml:id="echoid-s42239" xml:space="preserve">deſcripſi-
              <lb/>
            mus, in hemiſphærio cõcauo delineantur. </s>
            <s xml:id="echoid-s42240" xml:space="preserve">Vnde ſi in aliqua tabula plana hemiſphæriũ concauũ,
              <lb/>
              <note position="left" xlink:label="note-0658-09" xlink:href="note-0658-09a" xml:space="preserve">Quomedo be-
                <lb/>
              neficio horolo-
                <lb/>
              gii hemiſphæri-
                <lb/>
              ci@concaui ex
                <lb/>
              vmbra in quo-
                <lb/>
              uis plano hoto
                <lb/>
              logia deſcriban
                <lb/>
              tur.</note>
            in quo omnia ſint deſcripta, affigatur, ducaturq́ue in ea linea meridiana, reſpondens Meridiano
              <lb/>
            hemiſphærii, (quod facile fiet, ſi tabula Soli expoſita vna cum hemiſphærio circumuertatur, do-
              <lb/>
            nec vmbra ſtyli in Meridianum circulum cadat. </s>
            <s xml:id="echoid-s42241" xml:space="preserve">Si enim tunc obſeruetur in tabula vmbra alicuius
              <lb/>
            ſtyli ad angulos rectos in fixi, in cuius medio duo puncta notentur, erit recta per hæc puncta du-
              <lb/>
            cta linea meridiana) deſcribetur ex vmbra ſtyli horologium quodcunque (ſi habeatur ratio ſitus
              <lb/>
            eius proprij, quod ad inclinationem ad Horizontem, & </s>
            <s xml:id="echoid-s42242" xml:space="preserve">ad declinationem à Verticali attinet, </s>
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