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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          <pb o="58" file="0078" n="78" rhead="GNOMONICES"/>
          <p style="it">
            <s xml:id="echoid-s3693" xml:space="preserve">PRIM Aindicat, quænam duæ lineę horarię, quarũ altera ſumitur ab ortu, vel occaſu, altera verò à
              <lb/>
            meridie, vel media nocte, ſecent in eodem puncto lineam horę 24. </s>
            <s xml:id="echoid-s3694" xml:space="preserve">ab ortu, vel occaſu. </s>
            <s xml:id="echoid-s3695" xml:space="preserve">Secunda, quænam
              <lb/>
            duæ lineæ horariæ, quarum altera quoque ab ortu, uel occaſu, altera verò à meridie, vel media nocte
              <lb/>
            ſumitur, ſecent lineam horæ 12. </s>
            <s xml:id="echoid-s3696" xml:space="preserve">ab ortu, vel occaſu, in eodem puncto. </s>
            <s xml:id="echoid-s3697" xml:space="preserve">Tertia, quænam duæ lineæ hora-
              <lb/>
            riæ ab ortu, vel occaſu, ſecent in vno, eodemq́, puncto lineam horę 6. </s>
            <s xml:id="echoid-s3698" xml:space="preserve">à meridie, vel media nocte. </s>
            <s xml:id="echoid-s3699" xml:space="preserve">Quar-
              <lb/>
            ta denique, quænam duæ lineæ horarię ab ortu, vel occaſu lineam horæ 12. </s>
            <s xml:id="echoid-s3700" xml:space="preserve">à meridie, vel media nocte, in
              <lb/>
            vno eodem{q́ue} puncto interſecent. </s>
            <s xml:id="echoid-s3701" xml:space="preserve">Quæ omnia facile ex hac propoſitione colligi poſſunt. </s>
            <s xml:id="echoid-s3702" xml:space="preserve">Nam ſi rectè con-
              <lb/>
            ſiderentur hæ tabulæ, & </s>
            <s xml:id="echoid-s3703" xml:space="preserve">figur a propoſ. </s>
            <s xml:id="echoid-s3704" xml:space="preserve">9. </s>
            <s xml:id="echoid-s3705" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s3706" xml:space="preserve">comperientur in prioribus duabus tabulis hora ab
              <lb/>
            ortu, vel occaſu in titulis poſita, & </s>
            <s xml:id="echoid-s3707" xml:space="preserve">hora quælibet ab ortu, vel occaſu in ipſis tabulis deſcripta, æqualiter
              <lb/>
            diſtare ab hora collater ali à meridie, vel media nocte. </s>
            <s xml:id="echoid-s3708" xml:space="preserve">Quare illarum lineæ ſecabunt huius lineam in
              <lb/>
              <note position="left" xlink:label="note-0078-01" xlink:href="note-0078-01a" xml:space="preserve">10</note>
            codem puncto, vt in hac propoſitione eſt oſtenſum; </s>
            <s xml:id="echoid-s3709" xml:space="preserve">atque adeò & </s>
            <s xml:id="echoid-s3710" xml:space="preserve">lineæ quarumuis duarum horarum in
              <lb/>
            tabulis poſitarum, in vno eodem{q́ue} puncto lineam horæ in titulis poſitæ interſecabunt. </s>
            <s xml:id="echoid-s3711" xml:space="preserve">In poſterioribus
              <lb/>
            autem duabus tabulis deprehendentur quælibet duæ horæ ab ortu, vel occaſu in tabulis poſitæ ab hora
              <lb/>
            à meridie, vel media nocte, in titulis deſcripta distare æqualiter. </s>
            <s xml:id="echoid-s3712" xml:space="preserve">Quare per hanc eandem propeſitio-
              <lb/>
            nem lineæ illarum lineam huius in vno puncto interſecabunt. </s>
            <s xml:id="echoid-s3713" xml:space="preserve">Itaque ſi cognitum fuerit punctum, in quo
              <lb/>
            lineam horæ 24. </s>
            <s xml:id="echoid-s3714" xml:space="preserve">vel 12. </s>
            <s xml:id="echoid-s3715" xml:space="preserve">ab ortu, vel occaſu, vel horæ 6. </s>
            <s xml:id="echoid-s3716" xml:space="preserve">vel 12. </s>
            <s xml:id="echoid-s3717" xml:space="preserve">à meridie, vel media nocte ſecet altera
              <lb/>
            horarum in tabulis poſitarum, ſciemus, per idem illud punctum duci debere reliquam horam in tabulis
              <lb/>
            deſcriptam, &</s>
            <s xml:id="echoid-s3718" xml:space="preserve">c. </s>
            <s xml:id="echoid-s3719" xml:space="preserve">Vt in prima tabula, per quod punctum lineæ 24. </s>
            <s xml:id="echoid-s3720" xml:space="preserve">ab ortu, vel occaſu tranſierit linea
              <lb/>
            horæ {1/2} à meridie, vel media nocte, per idem ducenda erit linea horę primæ ab ortu, vel occaſu, & </s>
            <s xml:id="echoid-s3721" xml:space="preserve">ſic
              <lb/>
            de cæteris.</s>
            <s xml:id="echoid-s3722" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">20</note>
          <p style="it">
            <s xml:id="echoid-s3723" xml:space="preserve">EADEM via, ac ratione inueſtigabimus per hanc propoſitionem, quænam lineæ horarię ab ortu,
              <lb/>
              <note position="left" xlink:label="note-0078-03" xlink:href="note-0078-03a" xml:space="preserve">Quænam lineæ
                <lb/>
              horarum ab or.
                <lb/>
              u@l occ. & à
                <lb/>
              mer. uel med.
                <lb/>
              noc. ſe mutuo
                <lb/>
              in eodem pun-
                <lb/>
              cto interſecen@.</note>
            vel occaſu, propoſitam aliam quamcunque lineam horariam à meridie, vel media nocte, in vno eodemq́,
              <lb/>
            puncto interſecent. </s>
            <s xml:id="echoid-s3724" xml:space="preserve">Item quamnam lineam horariam ab ortu, vel occaſu, duę quæcunque lineę hora-
              <lb/>
            rię, altera quidem ab ortu, vel occaſu, altera verò à meridie, vel media nocte, ſecent in vno, & </s>
            <s xml:id="echoid-s3725" xml:space="preserve">eo-
              <lb/>
            dem puncto, &</s>
            <s xml:id="echoid-s3726" xml:space="preserve">c. </s>
            <s xml:id="echoid-s3727" xml:space="preserve">Nam ſi accipiantur in figura propoſ. </s>
            <s xml:id="echoid-s3728" xml:space="preserve">9. </s>
            <s xml:id="echoid-s3729" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s3730" xml:space="preserve">tres horæ, vna quidem à meridie,
              <lb/>
            vel media nocte quęcunque, reliquę verò ab ortu, vel occaſu quotæcunque, remotę tamen hinc inde ab
              <lb/>
            hora à meridie, vel media nocte ęqualiter, ſecabunt lineam cuiuslibet illarum trium lineæ reliquarum
              <lb/>
            duarum in vno, & </s>
            <s xml:id="echoid-s3731" xml:space="preserve">eodem puncto: </s>
            <s xml:id="echoid-s3732" xml:space="preserve">Vt lineam horæ 23. </s>
            <s xml:id="echoid-s3733" xml:space="preserve">ab ortu, vel occaſu, in vno puncto interſecant
              <lb/>
            duę lineæ, quarum altera horam 13. </s>
            <s xml:id="echoid-s3734" xml:space="preserve">ab ortu, vel occaſu, altera vero horam ſextam à meridie, vel me-
              <lb/>
            dia nocte indicat: </s>
            <s xml:id="echoid-s3735" xml:space="preserve">quia in figura propoſ. </s>
            <s xml:id="echoid-s3736" xml:space="preserve">9. </s>
            <s xml:id="echoid-s3737" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s3738" xml:space="preserve">hora ſexta à merid. </s>
            <s xml:id="echoid-s3739" xml:space="preserve">vel med. </s>
            <s xml:id="echoid-s3740" xml:space="preserve">noc. </s>
            <s xml:id="echoid-s3741" xml:space="preserve">æqualiter ab
              <lb/>
              <note position="left" xlink:label="note-0078-04" xlink:href="note-0078-04a" xml:space="preserve">30</note>
            hora 23. </s>
            <s xml:id="echoid-s3742" xml:space="preserve">& </s>
            <s xml:id="echoid-s3743" xml:space="preserve">13. </s>
            <s xml:id="echoid-s3744" xml:space="preserve">ab or. </s>
            <s xml:id="echoid-s3745" xml:space="preserve">vel occ. </s>
            <s xml:id="echoid-s3746" xml:space="preserve">abeſt. </s>
            <s xml:id="echoid-s3747" xml:space="preserve">Eodem @odo lineam horæ ſextę à meridie, vel media nocte ſe-
              <lb/>
            cabunt in vno puncto lineæ horarum 23. </s>
            <s xml:id="echoid-s3748" xml:space="preserve">& </s>
            <s xml:id="echoid-s3749" xml:space="preserve">13. </s>
            <s xml:id="echoid-s3750" xml:space="preserve">ab ortu, vel occaſu. </s>
            <s xml:id="echoid-s3751" xml:space="preserve">Sic etiam lineam horę tertiæ à
              <lb/>
            meridie, vel media nocte, ſecabunt lineæ horarum 14. </s>
            <s xml:id="echoid-s3752" xml:space="preserve">& </s>
            <s xml:id="echoid-s3753" xml:space="preserve">16. </s>
            <s xml:id="echoid-s3754" xml:space="preserve">ab ortu, vel occaſu. </s>
            <s xml:id="echoid-s3755" xml:space="preserve">Et ſic de reliquis.</s>
            <s xml:id="echoid-s3756" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s3757" xml:space="preserve">EX his facili negotio alias tabulas præcedentibus ſimiles conficiemus, ſingulas nimirum pro ſingu-
              <lb/>
              <note position="left" xlink:label="note-0078-05" xlink:href="note-0078-05a" xml:space="preserve">Compoſitio a-
                <lb/>
              liarum tabula-
                <lb/>
              rum præceden-
                <lb/>
              tibus ſimilium,
                <lb/>
              pro ſingulis li-
                <lb/>
              neis horarũ ab
                <lb/>
              or. vel occ & à
                <lb/>
              mer. vel med.
                <lb/>
              noc@</note>
            lis lineis horarijs tam ab ortu, vel occaſu, quàm à meridie, vel media nocte; </s>
            <s xml:id="echoid-s3758" xml:space="preserve">quales ſunt ſequentes tri-
              <lb/>
            ginta duæ tabulæ. </s>
            <s xml:id="echoid-s3759" xml:space="preserve">Sed quia ad deſcribendas lineas horarias ab ortu, vel occaſu, in quocunque plano, de-
              <lb/>
            ſcriptis prius lineis horarijs à meridie, vel media nocte, (In hunc etenim vſum prædictas tabulas con-
              <lb/>
            ſtruximus) ſufficiunt prædictę quinque tabulæ, vt ſuo loco oſtendemus, propterea eas ab alijs triginta
              <lb/>
            duabus, quæ paulo infra ponentur, ſeiunximus, vt nimirum ſemper in promptu haberi poſſint, cum earum
              <lb/>
            vſus neceſſarius erit.</s>
            <s xml:id="echoid-s3760" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">40</note>
          <p style="it">
            <s xml:id="echoid-s3761" xml:space="preserve">PORRO Franciſcus Maurolycus Abbas Meſſanenſis primus est, quod ego ſciam, inuentor harum
              <lb/>
            interſectionum, quas inter ſe faciunt mutuo lineæ hor ariæ ab ortu, vel occaſu, & </s>
            <s xml:id="echoid-s3762" xml:space="preserve">à meridie, vel media
              <lb/>
            nocte. </s>
            <s xml:id="echoid-s3763" xml:space="preserve">Primum enim eas obſeruaui in ipſius libello de lineis borarijs deſcribendis, quem ipſe Meſſana
              <lb/>
            propria manu conſcriptum Romam ad me miſit: </s>
            <s xml:id="echoid-s3764" xml:space="preserve">nondum enim in lucem eum ediderat. </s>
            <s xml:id="echoid-s3765" xml:space="preserve">Et quoniam
              <lb/>
            conſideratio hæc interſectionum & </s>
            <s xml:id="echoid-s3766" xml:space="preserve">iucundiſſima eſt, & </s>
            <s xml:id="echoid-s3767" xml:space="preserve">ad lineas horarias ab ortu, vel occaſu deſcriben-
              <lb/>
            das vtiliſſima, faciendum mihi omnino putaui, vt ad communem ftudioſorum vtilitatem demonſtratio-
              <lb/>
            nibus Geometricis (quod quidem in pręcedentibus propoſitionibus præſtitimus) eam confirmarem. </s>
            <s xml:id="echoid-s3768" xml:space="preserve">Nam
              <lb/>
            ſine demonſtrationibus huiuſmodi ſectiones linearum horariarum allatæ mibi fuerunt ex Sicilia, neque
              <lb/>
            earum demonſtrationem apud vllum potui comperire. </s>
            <s xml:id="echoid-s3769" xml:space="preserve">Vnde paſſi non ſumus, eam diutius deſiderari.
              <lb/>
            </s>
            <s xml:id="echoid-s3770" xml:space="preserve">Solus Ioan. </s>
            <s xml:id="echoid-s3771" xml:space="preserve">Baptiſta Benedictus cap. </s>
            <s xml:id="echoid-s3772" xml:space="preserve">65. </s>
            <s xml:id="echoid-s3773" xml:space="preserve">ſuæ Gnomonices mutuam hanc interſectionem in linea ſola horæ
              <lb/>
              <note position="left" xlink:label="note-0078-07" xlink:href="note-0078-07a" xml:space="preserve">50</note>
            12. </s>
            <s xml:id="echoid-s3774" xml:space="preserve">ab or. </s>
            <s xml:id="echoid-s3775" xml:space="preserve">vel occ. </s>
            <s xml:id="echoid-s3776" xml:space="preserve">demonſtrare eſt aggreſſus.</s>
            <s xml:id="echoid-s3777" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s3778" xml:space="preserve">VT autem clarior adbuc reddatur mutua hæc interſectio horariarum linearum, libet alio modo de-
              <lb/>
            monſtrare hoc loco, quaratione prædictę tabulæ ſint conſtruendæ. </s>
            <s xml:id="echoid-s3779" xml:space="preserve">Atque vt à tabula Aequinoctia-
              <lb/>
            lis lineę incipiamus, quam in ſcholio propoſ. </s>
            <s xml:id="echoid-s3780" xml:space="preserve">19. </s>
            <s xml:id="echoid-s3781" xml:space="preserve">huius libri deſcripſimus; </s>
            <s xml:id="echoid-s3782" xml:space="preserve">Sit Aequator A B, & </s>
            <s xml:id="echoid-s3783" xml:space="preserve">paral-
              <lb/>
            lelus ſemper apparentium maximus C D, polusq́, parallelorum, ſiue mundi, E. </s>
            <s xml:id="echoid-s3784" xml:space="preserve">Tangant autem paralle-
              <lb/>
            lum C D, in punctis oppoſitis C, D, duo circuli horarum ab ortu, vel occaſu C F, D F, & </s>
            <s xml:id="echoid-s3785" xml:space="preserve">eundem ſecet
              <lb/>
            per polum E, circulus alicuius horæ à meridie, vel media nocte in puncto G, quod ęqualibus ſpatijs, nem-
              <lb/>
            pe ſex horis, abſit à punctis C, & </s>
            <s xml:id="echoid-s3786" xml:space="preserve">D, ita vt C G, D G, quadrantes ſint. </s>
            <s xml:id="echoid-s3787" xml:space="preserve">Dicotres circulos C F, D F, E G,
              <lb/>
            ſe mutuo ſecare in Aequatore A B, vt in puncto F. </s>
            <s xml:id="echoid-s3788" xml:space="preserve">Deſcribatur enim per E, polum parallelorum, & </s>
            <s xml:id="echoid-s3789" xml:space="preserve">per
              <lb/>
            C, punctum contactus, circulus maximus E C, ſecans Aequatorem in A, & </s>
            <s xml:id="echoid-s3790" xml:space="preserve">B, qui quoniam per polos
              <lb/>
            paralleli C D, tranſiens eum ſecat, per propoſ. </s>
            <s xml:id="echoid-s3791" xml:space="preserve">15. </s>
            <s xml:id="echoid-s3792" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s3793" xml:space="preserve">1. </s>
            <s xml:id="echoid-s3794" xml:space="preserve">Theodoſii, bifariam, tranſibit quoque per </s>
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