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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    <echo version="1.0RC">
      <text xml:lang="it" type="free">
        <div xml:id="echoid-div2086" type="section" level="1" n="530">
          <p>
            <s xml:id="echoid-s41984" xml:space="preserve">
              <pb o="641" file="0657" n="657" rhead="LIBER OCTAVVS."/>
            & </s>
            <s xml:id="echoid-s41985" xml:space="preserve">ad inter@allum F L, portio tropici ♋, infra Horizontem. </s>
            <s xml:id="echoid-s41986" xml:space="preserve">Et quoniam, Sole exiſtente ſupra Ho
              <lb/>
            rizontem in principio ♋, eius radius per centrum ſphæræ tranſiens cadit in parallelum oppoſitũ,
              <lb/>
            nempe in tropicum ♑, ſub Horizonte; </s>
            <s xml:id="echoid-s41987" xml:space="preserve">in tropicum vero ♋, ſub Horizonte, eodem exiſtente in
              <lb/>
            principio ♑, ſupra Horizontem, appellabitur K H I, tropicus ♋, & </s>
            <s xml:id="echoid-s41988" xml:space="preserve">N L M, tropicus ♑, quòd
              <lb/>
            vmbra centri ſphæræ in eos cadat, Sole in dictis tropicis exiſtente. </s>
            <s xml:id="echoid-s41989" xml:space="preserve">Eodemq́ue modo alii paralleli
              <lb/>
            inter duos tropicos deſcribentur ex polo F, ſi eorum declinationes à G, in vtramque partem
              <lb/>
            ſupputentur.</s>
            <s xml:id="echoid-s41990" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s41991" xml:space="preserve">IAM vero diuiſo vtroque quadrante Aequatoris G B, G D, in ſex partes æquales, vel etiam
              <lb/>
            in plures, ſi horarum partes deſiderentur, (Eſſe autem G B, G D, quadrantes, ita planum fiet.
              <lb/>
            </s>
            <s xml:id="echoid-s41992" xml:space="preserve">Quoniam Meridianus A C, per polos Verticalis A, C, & </s>
            <s xml:id="echoid-s41993" xml:space="preserve">per F, polum Aequatoris ductus ſecat,
              <lb/>
              <note position="left" xlink:label="note-0657-01" xlink:href="note-0657-01a" xml:space="preserve">10</note>
            per propoſ. </s>
            <s xml:id="echoid-s41994" xml:space="preserve">9. </s>
            <s xml:id="echoid-s41995" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s41996" xml:space="preserve">2. </s>
            <s xml:id="echoid-s41997" xml:space="preserve">Theod. </s>
            <s xml:id="echoid-s41998" xml:space="preserve">ſegmenta Verticalis, & </s>
            <s xml:id="echoid-s41999" xml:space="preserve">Aequatoris B E D, B G D, quæ quidem, per
              <lb/>
            propoſ. </s>
            <s xml:id="echoid-s42000" xml:space="preserve">11. </s>
            <s xml:id="echoid-s42001" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s42002" xml:space="preserve">1. </s>
            <s xml:id="echoid-s42003" xml:space="preserve">Theod. </s>
            <s xml:id="echoid-s42004" xml:space="preserve">ſemicirculi ſunt, bifariam, erunt ſegmenta E B, E D, G B, G D, quadran
              <lb/>
            tes) deſcribemus horas æquales tam à mer. </s>
            <s xml:id="echoid-s42005" xml:space="preserve">& </s>
            <s xml:id="echoid-s42006" xml:space="preserve">med. </s>
            <s xml:id="echoid-s42007" xml:space="preserve">noc. </s>
            <s xml:id="echoid-s42008" xml:space="preserve">quàm ab or. </s>
            <s xml:id="echoid-s42009" xml:space="preserve">& </s>
            <s xml:id="echoid-s42010" xml:space="preserve">occ. </s>
            <s xml:id="echoid-s42011" xml:space="preserve">vnica apertura cir-
              <lb/>
              <note position="right" xlink:label="note-0657-02" xlink:href="note-0657-02a" xml:space="preserve">Deſcripiio ho-
                <lb/>
              rarum à mer.
                <lb/>
              & med. noc. in
                <lb/>
              hemiſphærio
                <lb/>
              concauo.</note>
            cini hoc modo. </s>
            <s xml:id="echoid-s42012" xml:space="preserve">Quoniam circuli horarij à mer. </s>
            <s xml:id="echoid-s42013" xml:space="preserve">& </s>
            <s xml:id="echoid-s42014" xml:space="preserve">med.</s>
            <s xml:id="echoid-s42015" xml:space="preserve">noc.</s>
            <s xml:id="echoid-s42016" xml:space="preserve">per F, polum Aequatoris ducuntur,
              <lb/>
            vt propoſ. </s>
            <s xml:id="echoid-s42017" xml:space="preserve">9. </s>
            <s xml:id="echoid-s42018" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s42019" xml:space="preserve">1. </s>
            <s xml:id="echoid-s42020" xml:space="preserve">demonſtrauimus, tranſibit viciſſim, ex ſcholio propoſ. </s>
            <s xml:id="echoid-s42021" xml:space="preserve">15. </s>
            <s xml:id="echoid-s42022" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s42023" xml:space="preserve">1. </s>
            <s xml:id="echoid-s42024" xml:space="preserve">Theod.
              <lb/>
            </s>
            <s xml:id="echoid-s42025" xml:space="preserve">Aequator per eorum polos. </s>
            <s xml:id="echoid-s42026" xml:space="preserve">Omnes ergo polos habent in Aequatore. </s>
            <s xml:id="echoid-s42027" xml:space="preserve">Quare diſtentis circini
              <lb/>
            cruribus ad interuallum quadrantis A B, vel G B, vel F G, circuli maximi, ſi alter pes ſtatuatur in
              <lb/>
            ſingulis punctis diuiſionum Aequatoris B G D, & </s>
            <s xml:id="echoid-s42028" xml:space="preserve">alter in Aequatote firmetur, nem pe in punctis,
              <lb/>
            quæ ſex horis, vel quadrante à prioribus abſunt, deſcribentur omnes circuli horarii ab hora 6. </s>
            <s xml:id="echoid-s42029" xml:space="preserve">à
              <lb/>
            med. </s>
            <s xml:id="echoid-s42030" xml:space="preserve">noc. </s>
            <s xml:id="echoid-s42031" xml:space="preserve">vſque ad horam 6. </s>
            <s xml:id="echoid-s42032" xml:space="preserve">à mer. </s>
            <s xml:id="echoid-s42033" xml:space="preserve">inter tropicos contenti. </s>
            <s xml:id="echoid-s42034" xml:space="preserve">Inter hos enim circuli horarii dun-
              <lb/>
              <note position="left" xlink:label="note-0657-03" xlink:href="note-0657-03a" xml:space="preserve">20</note>
            taxat erunt delineandi: </s>
            <s xml:id="echoid-s42035" xml:space="preserve">Si tamen producerentur, tranſirent omnes per polum F. </s>
            <s xml:id="echoid-s42036" xml:space="preserve">Exempli gra-
              <lb/>
            tia, ex G, tanquam polo, ad interuallum G D, vel G B, vel G F, (quod interuallum mutari non de-
              <lb/>
            bet, donec omnes horarii circuli, vel quicunque alii maximi deſcripti ſint) deſcribentur arcus cir
              <lb/>
            culi horæ 6. </s>
            <s xml:id="echoid-s42037" xml:space="preserve">à med. </s>
            <s xml:id="echoid-s42038" xml:space="preserve">noc & </s>
            <s xml:id="echoid-s42039" xml:space="preserve">mer. </s>
            <s xml:id="echoid-s42040" xml:space="preserve">terminati inter Aequatorem, & </s>
            <s xml:id="echoid-s42041" xml:space="preserve">tropicum ♋. </s>
            <s xml:id="echoid-s42042" xml:space="preserve">Ponendo poſtea cir
              <lb/>
            cini pedem vnum in proximo puncto Aequatoris à G, verſus B, deſcribentur altero pede arcus cir
              <lb/>
            culi horæ 7. </s>
            <s xml:id="echoid-s42043" xml:space="preserve">à med. </s>
            <s xml:id="echoid-s42044" xml:space="preserve">noc. </s>
            <s xml:id="echoid-s42045" xml:space="preserve">& </s>
            <s xml:id="echoid-s42046" xml:space="preserve">à mer. </s>
            <s xml:id="echoid-s42047" xml:space="preserve">quorum prior tranſibit per proximum punctum Aequatoris in-
              <lb/>
            fra D, poſterior vero tranſiret per proximum punctum Aequatoris ſupra B, ſi integra ſphæra eſſet.
              <lb/>
            </s>
            <s xml:id="echoid-s42048" xml:space="preserve">Sic etiam ſtatuendo vnum pedem circini in ſecundo puncto à G, verſus B, deſcribetur altero ho-
              <lb/>
            ra 8. </s>
            <s xml:id="echoid-s42049" xml:space="preserve">à med. </s>
            <s xml:id="echoid-s42050" xml:space="preserve">noc. </s>
            <s xml:id="echoid-s42051" xml:space="preserve">tranſiens per ſecundum punctum infra D, & </s>
            <s xml:id="echoid-s42052" xml:space="preserve">ita deinceps, ſtatuendo polos circu-
              <lb/>
            lorum per puncta quadrantis G D, tranſeuntium in quadrante G B, aliorum autem in quadrante
              <lb/>
              <note position="left" xlink:label="note-0657-04" xlink:href="note-0657-04a" xml:space="preserve">30</note>
            G D, ita vt deſcribantur eadem circini apertura etiam arcus inter Horizontem, & </s>
            <s xml:id="echoid-s42053" xml:space="preserve">tropicum ♋,
              <lb/>
            licet Aequatorem non ſecent in hemiſphærio, vt contingit in hora 5. </s>
            <s xml:id="echoid-s42054" xml:space="preserve">à med. </s>
            <s xml:id="echoid-s42055" xml:space="preserve">noc. </s>
            <s xml:id="echoid-s42056" xml:space="preserve">& </s>
            <s xml:id="echoid-s42057" xml:space="preserve">7. </s>
            <s xml:id="echoid-s42058" xml:space="preserve">à mer. </s>
            <s xml:id="echoid-s42059" xml:space="preserve">&</s>
            <s xml:id="echoid-s42060" xml:space="preserve">c.</s>
            <s xml:id="echoid-s42061" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">Deſeript@@ h@-
            <lb/>
          rarum ab occ.
            <lb/>
          & or. in h@mi@
            <lb/>
          ſphærio conca-
            <lb/>
          uo.</note>
          <p>
            <s xml:id="echoid-s42062" xml:space="preserve">RVRSVS quia circuli horarum ab occ. </s>
            <s xml:id="echoid-s42063" xml:space="preserve">& </s>
            <s xml:id="echoid-s42064" xml:space="preserve">or. </s>
            <s xml:id="echoid-s42065" xml:space="preserve">polos habent in parallelo R S Q, per verticem
              <lb/>
            loci ducto, vt propoſ. </s>
            <s xml:id="echoid-s42066" xml:space="preserve">10. </s>
            <s xml:id="echoid-s42067" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s42068" xml:space="preserve">1. </s>
            <s xml:id="echoid-s42069" xml:space="preserve">demonſtrauimus, atque adeo & </s>
            <s xml:id="echoid-s42070" xml:space="preserve">in parallelo O E P, oppoſito, cum
              <lb/>
            huius puncta ſingula ſingulis punctis illius opponantur; </s>
            <s xml:id="echoid-s42071" xml:space="preserve">ſi eadem circini apertura manente, vnus
              <lb/>
            pes in ſingulis punctis Aequatoris ſtatuatur, & </s>
            <s xml:id="echoid-s42072" xml:space="preserve">alter pes in parallelo O E P, vel in R S Q , quando
              <lb/>
            non poteſt ſtatui in O E P, deſcribentur per puncta Aequatoris arcus circulorum horarum ab occ.
              <lb/>
            </s>
            <s xml:id="echoid-s42073" xml:space="preserve">& </s>
            <s xml:id="echoid-s42074" xml:space="preserve">or. </s>
            <s xml:id="echoid-s42075" xml:space="preserve">Diuident autem poli horum circulorum parallelos O E P, Q S R, in partes æquales, exi-
              <lb/>
            ſtentq́ue in illis punctis, vbi à circulis horarum à mer. </s>
            <s xml:id="echoid-s42076" xml:space="preserve">& </s>
            <s xml:id="echoid-s42077" xml:space="preserve">med. </s>
            <s xml:id="echoid-s42078" xml:space="preserve">noc. </s>
            <s xml:id="echoid-s42079" xml:space="preserve">diuiduntur in ſpatia horaria
              <lb/>
            æqualia, vt propoſ. </s>
            <s xml:id="echoid-s42080" xml:space="preserve">10. </s>
            <s xml:id="echoid-s42081" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s42082" xml:space="preserve">1. </s>
            <s xml:id="echoid-s42083" xml:space="preserve">oſtendimus: </s>
            <s xml:id="echoid-s42084" xml:space="preserve">propterea quòd cum circuli horarum ab or. </s>
            <s xml:id="echoid-s42085" xml:space="preserve">vel occ. </s>
            <s xml:id="echoid-s42086" xml:space="preserve">
              <lb/>
              <note position="left" xlink:label="note-0657-06" xlink:href="note-0657-06a" xml:space="preserve">40</note>
            tranſeant in Aequatore per polos circulorum horarum à mer. </s>
            <s xml:id="echoid-s42087" xml:space="preserve">& </s>
            <s xml:id="echoid-s42088" xml:space="preserve">med. </s>
            <s xml:id="echoid-s42089" xml:space="preserve">noc. </s>
            <s xml:id="echoid-s42090" xml:space="preserve">hi viciſſim per illo-
              <lb/>
            rum polos ducantur, ex ſcholio propoſ. </s>
            <s xml:id="echoid-s42091" xml:space="preserve">15. </s>
            <s xml:id="echoid-s42092" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s42093" xml:space="preserve">1. </s>
            <s xml:id="echoid-s42094" xml:space="preserve">Theod. </s>
            <s xml:id="echoid-s42095" xml:space="preserve">Cum ergo illorum poli in parallelis
              <lb/>
            O E P, Q S R, exiſtant, erunt omnino poli illa puncta, vbi dicti paralleli à circulis horarum à
              <lb/>
            mer. </s>
            <s xml:id="echoid-s42096" xml:space="preserve">& </s>
            <s xml:id="echoid-s42097" xml:space="preserve">med. </s>
            <s xml:id="echoid-s42098" xml:space="preserve">noc. </s>
            <s xml:id="echoid-s42099" xml:space="preserve">ſecantur, ita vt polus cuiuslibet circuli horarii ab or. </s>
            <s xml:id="echoid-s42100" xml:space="preserve">vel occ. </s>
            <s xml:id="echoid-s42101" xml:space="preserve">ſit in eo puncto
              <lb/>
            paralleli O E P, vel Q S R, per quod circulus horarius à mer. </s>
            <s xml:id="echoid-s42102" xml:space="preserve">vel med. </s>
            <s xml:id="echoid-s42103" xml:space="preserve">noc. </s>
            <s xml:id="echoid-s42104" xml:space="preserve">ab illo ſex horis in
              <lb/>
            Aequatore diſtans tranſit. </s>
            <s xml:id="echoid-s42105" xml:space="preserve">Vnde vt hi poli expedite habeantur, producendi erunt circuli hora-
              <lb/>
            rum à mer. </s>
            <s xml:id="echoid-s42106" xml:space="preserve">& </s>
            <s xml:id="echoid-s42107" xml:space="preserve">med. </s>
            <s xml:id="echoid-s42108" xml:space="preserve">noc. </s>
            <s xml:id="echoid-s42109" xml:space="preserve">vſque ad parallelos O E P, Q S R, occultè tamen. </s>
            <s xml:id="echoid-s42110" xml:space="preserve">Vel certe ex G, ad in-
              <lb/>
            teruallum quadrantis G F, arcus circuli horæ 6@ à mer. </s>
            <s xml:id="echoid-s42111" xml:space="preserve">& </s>
            <s xml:id="echoid-s42112" xml:space="preserve">med. </s>
            <s xml:id="echoid-s42113" xml:space="preserve">noc. </s>
            <s xml:id="echoid-s42114" xml:space="preserve">deſcribendus, atque vterq;
              <lb/>
            </s>
            <s xml:id="echoid-s42115" xml:space="preserve">quadrans E T, E V, in ſex partes æquales diuidendus pro polis circulorum horarum ab or. </s>
            <s xml:id="echoid-s42116" xml:space="preserve">& </s>
            <s xml:id="echoid-s42117" xml:space="preserve">occ. </s>
            <s xml:id="echoid-s42118" xml:space="preserve">
              <lb/>
            ac denique hæc puncta beneficio circini ex E, accepta transferenda in parallelum Q S R, ex S,
              <lb/>
              <note position="left" xlink:label="note-0657-07" xlink:href="note-0657-07a" xml:space="preserve">50</note>
            pro polis aliorum circulorum, qui polos non habent in portione O E P. </s>
            <s xml:id="echoid-s42119" xml:space="preserve">Exempli gratia, E, polus
              <lb/>
            eſt Horizontis, ſiue circuli horæ 24. </s>
            <s xml:id="echoid-s42120" xml:space="preserve">ab or. </s>
            <s xml:id="echoid-s42121" xml:space="preserve">vel occ. </s>
            <s xml:id="echoid-s42122" xml:space="preserve">proximum deinde punctũ in parallelo O E P,
              <lb/>
            ab E, verſus O, polus eſt circuli horæ 23. </s>
            <s xml:id="echoid-s42123" xml:space="preserve">ab occ. </s>
            <s xml:id="echoid-s42124" xml:space="preserve">proximum vero punctum ab E, verſus P, polus
              <lb/>
            eſt circuli horæ 1. </s>
            <s xml:id="echoid-s42125" xml:space="preserve">ab or. </s>
            <s xml:id="echoid-s42126" xml:space="preserve">& </s>
            <s xml:id="echoid-s42127" xml:space="preserve">ita de cæteris. </s>
            <s xml:id="echoid-s42128" xml:space="preserve">In exemplo deſcriptæ ſunt tantum horæ à mer. </s>
            <s xml:id="echoid-s42129" xml:space="preserve">& </s>
            <s xml:id="echoid-s42130" xml:space="preserve">med.
              <lb/>
            </s>
            <s xml:id="echoid-s42131" xml:space="preserve">noc. </s>
            <s xml:id="echoid-s42132" xml:space="preserve">atque horæ ab occ.</s>
            <s xml:id="echoid-s42133" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">Deſcriptio ho-
            <lb/>
          rarum inæqua-
            <lb/>
          lium in hemi-
            <lb/>
          ſphærio couca-
            <lb/>
          uo.</note>
          <p>
            <s xml:id="echoid-s42134" xml:space="preserve">PRO deſcriptione denique horarum inæqualium, diuidendæ ſunt ſingulæ portiones tropi-
              <lb/>
            corum H I, H K, L M, L N, in ſenas partes æquales, & </s>
            <s xml:id="echoid-s42135" xml:space="preserve">per terna puncta, (quorum vnum eſt in tro
              <lb/>
            pico ♋, alterum in Aequatore, & </s>
            <s xml:id="echoid-s42136" xml:space="preserve">tertium in tropico ♑,) æqualiter à Meridiano remota circuli
              <lb/>
            horarum inæqualium deſcribendi. </s>
            <s xml:id="echoid-s42137" xml:space="preserve">Erit autem polus cuiuslibet circuli in circulo horario à mer.
              <lb/>
            </s>
            <s xml:id="echoid-s42138" xml:space="preserve">vel med. </s>
            <s xml:id="echoid-s42139" xml:space="preserve">noc. </s>
            <s xml:id="echoid-s42140" xml:space="preserve">qui ſex horis ab eo abeſt in Aequatore. </s>
            <s xml:id="echoid-s42141" xml:space="preserve">Quoniam enim quilibet circulus horarum
              <lb/>
            inæqualium tranſit in Aequatore per polum circuli horarii à mer. </s>
            <s xml:id="echoid-s42142" xml:space="preserve">vel med. </s>
            <s xml:id="echoid-s42143" xml:space="preserve">noc. </s>
            <s xml:id="echoid-s42144" xml:space="preserve">ſex horis ab </s>
          </p>
        </div>
      </text>
    </echo>
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