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

Table of Notes

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          <p>
            <s xml:id="echoid-s14154" xml:space="preserve">
              <pb o="207" file="0227" n="227" rhead="LIBER SECVNDVS."/>
            ex centro E, egredientes, communes ſectiones Aequatoris, & </s>
            <s xml:id="echoid-s14155" xml:space="preserve">circulorum horariorum à meridie,
              <lb/>
            vel media nocte, nempe N M, communis ſectio Aequatoris, et circuli horæ 12. </s>
            <s xml:id="echoid-s14156" xml:space="preserve">O P, communis ſe-
              <lb/>
            ctio Aequatoris, et circuli horæ primæ à meridie, vel media nocte; </s>
            <s xml:id="echoid-s14157" xml:space="preserve">Q R, ſectio communis Aequa-
              <lb/>
            toris, et circuli horæ ſecundæ à meridie, vel media nocte, etc. </s>
            <s xml:id="echoid-s14158" xml:space="preserve">Quare vt ibidem demonſtrauimus,
              <lb/>
            crunt rectæ ex H, per puncta rectæ F K, ductæ, lineæ horarum à meridie, vel media nocte. </s>
            <s xml:id="echoid-s14159" xml:space="preserve">Eadem
              <lb/>
            enim demonſtratio huc afferri poteſt. </s>
            <s xml:id="echoid-s14160" xml:space="preserve">Sola linea horæ ſextæ ducenda eſt per H, perpendicularis,
              <lb/>
            ad H I, vel æquidiſtans ipſi F K, qualis eſt C L. </s>
            <s xml:id="echoid-s14161" xml:space="preserve">Cum enim ex ſcholio propoſ. </s>
            <s xml:id="echoid-s14162" xml:space="preserve">22. </s>
            <s xml:id="echoid-s14163" xml:space="preserve">ſuperioris lib. </s>
            <s xml:id="echoid-s14164" xml:space="preserve">in
              <lb/>
            horologio Verticali parallelæ ſint linea æquinoctialis, & </s>
            <s xml:id="echoid-s14165" xml:space="preserve">linea horæ ſextæ à meridie, vel media no-
              <lb/>
            cte, perſpicuum eſt, rectam C L, eſſe lineam horæ ſextæ, quandoquidem parallela eſt æquinoctiali
              <lb/>
            lineæ F K, tranſitq́ue per punctum H, vbi omnes horariæ lineæ à meridie, vel media nocte ſe
              <lb/>
              <note position="left" xlink:label="note-0227-01" xlink:href="note-0227-01a" xml:space="preserve">10</note>
            interſecant.</s>
            <s xml:id="echoid-s14166" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14167" xml:space="preserve">IN auſtrali porrò horologio meridiana linea H I, à centro verſus lineam æquinoctialem indi-
              <lb/>
              <note position="right" xlink:label="note-0227-02" xlink:href="note-0227-02a" xml:space="preserve">Ordo horarum
                <lb/>
              in vtroque ho-
                <lb/>
              rologio Verti-
                <lb/>
              cali.</note>
            cat horam 12. </s>
            <s xml:id="echoid-s14168" xml:space="preserve">meridiei, & </s>
            <s xml:id="echoid-s14169" xml:space="preserve">reliqua portio ſurſum verſus horam 12. </s>
            <s xml:id="echoid-s14170" xml:space="preserve">mediæ noctis: </s>
            <s xml:id="echoid-s14171" xml:space="preserve">Lineæ verò ad ſi-
              <lb/>
            niſtram meridianæ lineæ oſtendunt horas à media nocte, & </s>
            <s xml:id="echoid-s14172" xml:space="preserve">earum portiones ad dexteram eiuſdẽ
              <lb/>
            lineæ meridianæ horas à meridie monſtrant. </s>
            <s xml:id="echoid-s14173" xml:space="preserve">Contrariũ intelligatur in horologio boreali. </s>
            <s xml:id="echoid-s14174" xml:space="preserve">Quæ
              <lb/>
            omnia perſpicua ſunt, ſi circulorum horariorum poſitio rectè intelligatur, & </s>
            <s xml:id="echoid-s14175" xml:space="preserve">ea atttente conſideren
              <lb/>
            tur, quæ in ſcholio propoſ. </s>
            <s xml:id="echoid-s14176" xml:space="preserve">1. </s>
            <s xml:id="echoid-s14177" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s14178" xml:space="preserve">ſcripſimus obſeruanda eſſe in lineis, quæ in horologio de-
              <lb/>
            ſcribuntur: </s>
            <s xml:id="echoid-s14179" xml:space="preserve">nempe quem ſemicirculum cœleſtem ſingulæ referant, & </s>
            <s xml:id="echoid-s14180" xml:space="preserve">qua ratione quælibet hora
              <lb/>
            à mer. </s>
            <s xml:id="echoid-s14181" xml:space="preserve">producta vltra centrum horologii monſtret eandem horam numero à med. </s>
            <s xml:id="echoid-s14182" xml:space="preserve">noc. </s>
            <s xml:id="echoid-s14183" xml:space="preserve">& </s>
            <s xml:id="echoid-s14184" xml:space="preserve">contra.
              <lb/>
            </s>
            <s xml:id="echoid-s14185" xml:space="preserve">Horologium igitur Aſtronomicum Verticale conſtituimus, & </s>
            <s xml:id="echoid-s14186" xml:space="preserve">c. </s>
            <s xml:id="echoid-s14187" xml:space="preserve">Quod erat faciendum.</s>
            <s xml:id="echoid-s14188" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">20</note>
        </div>
        <div xml:id="echoid-div717" type="section" level="1" n="178">
          <head xml:id="echoid-head181" style="it" xml:space="preserve">SCHOLIVM.</head>
          <note position="right" xml:space="preserve">Alia deſcriptio
            <lb/>
          horologii Ver-
            <lb/>
          ticalis Aſtrono
            <lb/>
          mici cõmodiſ-
            <lb/>
          ſima pro illis
            <lb/>
          horis delinean-
            <lb/>
          dis, quæ propin
            <lb/>
          quæ ſunt lineæ
            <lb/>
          horæ 6. à mer.
            <lb/>
          vel med. noc.</note>
          <p style="it">
            <s xml:id="echoid-s14189" xml:space="preserve">TRADIT Andreas Schonerus aliam viam, qua horariæ lineæ deſcribi poſſint, ſimilem illi, quam
              <lb/>
            ex eodem in ſcholio propoſ. </s>
            <s xml:id="echoid-s14190" xml:space="preserve">1. </s>
            <s xml:id="echoid-s14191" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s14192" xml:space="preserve">explicauimus pro horologio horizontali deſcribendo. </s>
            <s xml:id="echoid-s14193" xml:space="preserve">Eſt autem
              <lb/>
            ferèhæc. </s>
            <s xml:id="echoid-s14194" xml:space="preserve">In æquinoctiali linea F K, accipiatur recta I a, æqualis rectæ I E, vel I D, & </s>
            <s xml:id="echoid-s14195" xml:space="preserve">per a, ducatur re-
              <lb/>
            cta a b, ad lineam æquinoctialem perpendicularis, vel meridianæ lineæ parallela, ſecans lineam horæ ſex-
              <lb/>
            tæ, quæ videlicet ex H, ducitur perpendicularis ad H I, in b, puncto. </s>
            <s xml:id="echoid-s14196" xml:space="preserve">Sumpta autem recta b d, æquali ipſi
              <lb/>
            a b, ducatur per d, ad b d, perpendicularis e f, vel parallela meridianæ lineæ. </s>
            <s xml:id="echoid-s14197" xml:space="preserve">Ex centro denique d, circu-
              <lb/>
            lo deſcripto, eo diuiſo in partes 24. </s>
            <s xml:id="echoid-s14198" xml:space="preserve">æquales, initio facto à recta b d, ducantur ex centro d, per puncta di-
              <lb/>
              <note position="left" xlink:label="note-0227-05" xlink:href="note-0227-05a" xml:space="preserve">30</note>
            uiſionum rectæ lineæ occultæ. </s>
            <s xml:id="echoid-s14199" xml:space="preserve">Hę namque rectam a b, ſecabunt in punctis, per quæ ex centro horologij H,
              <lb/>
              <note position="right" xlink:label="note-0227-06" xlink:href="note-0227-06a" xml:space="preserve">Segmẽta lineæ
                <lb/>
              ęquinoctialis in
                <lb/>
              horologio Ver-
                <lb/>
              ticali inter li-
                <lb/>
              neam meridia-
                <lb/>
              nam, & binas
                <lb/>
              horas vtrinque
                <lb/>
              à meridiana li-
                <lb/>
              nea æquali tem
                <lb/>
              poris ſpatio re-
                <lb/>
              motas, ſunt æ-
                <lb/>
              qualia.</note>
            lineæ horariæ ſunt educendæ. </s>
            <s xml:id="echoid-s14200" xml:space="preserve">Exemplum huius deſcriptionis poſuimus in horologio Auſtrali.</s>
            <s xml:id="echoid-s14201" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s14202" xml:space="preserve">IN horologio autem quolibet Verticali lineæ binæ quæcunque horariæ hinc inde à meridiana linea
              <lb/>
            æquali temporis interuallo remotæ, auferũt ex linea æquinoctiali F K, lineas ęquales, illas videlicet, quę
              <lb/>
            inter ipſas, & </s>
            <s xml:id="echoid-s14203" xml:space="preserve">lineam meridianã interijciuntur, ita vt in linea æquinoctiali ſpatia hor aria ante meridiem
              <lb/>
            æqualia ſint horarijs ſpatijs post meridiem, ſingula ſingulis. </s>
            <s xml:id="echoid-s14204" xml:space="preserve">Ex quo ſequitur, arcus circuli cuiuſuis ex
              <lb/>
            H, deſcripti in horologio Verticali interceptos inter lineam meridianam, & </s>
            <s xml:id="echoid-s14205" xml:space="preserve">binas quaſcunque lineas
              <lb/>
            horarias æquali temporis ſpatio hinc inde à meridiana linea diſtantes, æquales eſſe. </s>
            <s xml:id="echoid-s14206" xml:space="preserve">Item interualla inter
              <lb/>
            E, centrũ Aequatoris, & </s>
            <s xml:id="echoid-s14207" xml:space="preserve">binas horas quaſcunque in æquinoctiali linea ęquali temporis interuallo hinc
              <lb/>
              <note position="right" xlink:label="note-0227-07" xlink:href="note-0227-07a" xml:space="preserve">Satis eſt ad de-
                <lb/>
              ſcriptionẽ Ver-
                <lb/>
              ticalis horolo-
                <lb/>
              gii A ſtronomi-
                <lb/>
              ci, ſi vnus tan
                <lb/>
              tum quadrans
                <lb/>
              circuli ex E, de-
                <lb/>
              ſcripti in 6. par-
                <lb/>
              tes æqu ales di-
                <lb/>
              ſtribuatur.</note>
            inde à meridiana linea remotas, eſſe æqualia. </s>
            <s xml:id="echoid-s14208" xml:space="preserve">Quæ omnia demonſtrabũtur eo modo, quo in ſcholio propoſ.
              <lb/>
            </s>
            <s xml:id="echoid-s14209" xml:space="preserve">
              <note position="left" xlink:label="note-0227-08" xlink:href="note-0227-08a" xml:space="preserve">40</note>
            1. </s>
            <s xml:id="echoid-s14210" xml:space="preserve">huius libri vſi ſumus ad eadem hæc demonstranda in horologio horizontali.</s>
            <s xml:id="echoid-s14211" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s14212" xml:space="preserve">EX quo fit, vt ſatis ſit ad deſcriptionẽ horologij Verticalis, ſi vnus tantum quadrans circuli ex E, de-
              <lb/>
            ſcripti diuidatur in ſex partes ęquales, cuiuſmodi eſt v.</s>
            <s xml:id="echoid-s14213" xml:space="preserve">g. </s>
            <s xml:id="echoid-s14214" xml:space="preserve">quadrans Mg. </s>
            <s xml:id="echoid-s14215" xml:space="preserve">Qua de re vide ea, quæ in hunc fi-
              <lb/>
            nem de horologio horizontali ſcripſimus in ſcholio propopoſ. </s>
            <s xml:id="echoid-s14216" xml:space="preserve">1. </s>
            <s xml:id="echoid-s14217" xml:space="preserve">huius lib.</s>
            <s xml:id="echoid-s14218" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s14219" xml:space="preserve">HIC etiam ſi in triangulo D H I, ad planum horologij recto intelligatur axis H D, filum exten-
              <lb/>
              <note position="right" xlink:label="note-0227-09" xlink:href="note-0227-09a" xml:space="preserve">Quomodo vtrũ
                <unsure/>
                <lb/>
              que horologiũ
                <lb/>
              Verticale vnà
                <lb/>
              cum axe mũdi
                <lb/>
              collocandũ ſit,
                <lb/>
              vt monſtret ho
                <lb/>
              ras à mer. vel
                <lb/>
              med. noc.</note>
            tum, vel etiam ferrum aliquod tenue faciens in H, cum linea meridiana angulum æqualem angulo
              <lb/>
            D H I, & </s>
            <s xml:id="echoid-s14220" xml:space="preserve">cum recta C L, angulos rectos; </s>
            <s xml:id="echoid-s14221" xml:space="preserve">vel certè ipſum triangulum D H I, in ſuperiori horologio
              <lb/>
            contentum conſtruatur ex materia aliqua ſolida, statuatur{q́ue} ad planum horologij rectum, indicabit vm-
              <lb/>
            hra axis D I, ſingulas horas à meridie, vel media nocte, ſi horologium in plano, quod V erticali circulo
              <lb/>
            propriè dicto æquidiſtet, ita collocetur, vt recta H I, nempe linea meridiana, perpendicularis ſit ad Ho-
              <lb/>
              <note position="left" xlink:label="note-0227-10" xlink:href="note-0227-10a" xml:space="preserve">50</note>
            rizontẽ, rectaque F K, eidem Horizonti æquidiſtet; </s>
            <s xml:id="echoid-s14222" xml:space="preserve">& </s>
            <s xml:id="echoid-s14223" xml:space="preserve">in eo quidem horologio, quod ad auſtrum vergit,
              <lb/>
              <note position="right" xlink:label="note-0227-11" xlink:href="note-0227-11a" xml:space="preserve">Si ſtylus D G,
                <lb/>
              in G, rectus ſit
                <lb/>
              ad horologii
                <lb/>
              planum, mon-
                <lb/>
              ſtrabi
                <unsure/>
              t vmbra
                <lb/>
              ſolius verticis
                <lb/>
              D, horas à mer.
                <lb/>
              vel med. noc.</note>
            linea æquinoctialis F K, ſit infra punctum H, quod centrũ est horologij, in eo vero, quod ad Boreã, ſupra.
              <lb/>
            </s>
            <s xml:id="echoid-s14224" xml:space="preserve">Ex quo fit, vt & </s>
            <s xml:id="echoid-s14225" xml:space="preserve">vmbram verticis D, ſtyli D G, recti ad planum horologij in puncto G, qui quidem ver-
              <lb/>
            tex idem eſt, quod centrum mundi, ex propoſ. </s>
            <s xml:id="echoid-s14226" xml:space="preserve">2. </s>
            <s xml:id="echoid-s14227" xml:space="preserve">ſuperioris lib. </s>
            <s xml:id="echoid-s14228" xml:space="preserve">indicet eaſdem horas, hoc eſt, in lineas ho-
              <lb/>
            rarias proijciatur: </s>
            <s xml:id="echoid-s14229" xml:space="preserve">quemadmodum de horologio horizontali dictum eſt in ſcholio propoſ. </s>
            <s xml:id="echoid-s14230" xml:space="preserve">1. </s>
            <s xml:id="echoid-s14231" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s14232" xml:space="preserve">Ea-
              <lb/>
            dem enim hic est demonstratio.</s>
            <s xml:id="echoid-s14233" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s14234" xml:space="preserve">QVOD ſi & </s>
            <s xml:id="echoid-s14235" xml:space="preserve">dimidiatas horas, & </s>
            <s xml:id="echoid-s14236" xml:space="preserve">earum quartas partes, vel octauas, vel quaſuis alias, in horolo-
              <lb/>
              <note position="right" xlink:label="note-0227-12" xlink:href="note-0227-12a" xml:space="preserve">Qua ratione di
                <lb/>
              midiatæ horæ,
                <lb/>
              & eatũ quartæ
                <lb/>
              partes, vel quę-
                <lb/>
              cunque aliæ, in
                <lb/>
              horologio de-
                <lb/>
              ſcribant
                <unsure/>
              ur.</note>
            gio deſcribere velimus, diuidendi erunt ſinguli arcus circuli ex E, deſcripti in duas partes, quatuor, vel
              <lb/>
            octo vel alias quaſcunque, reliqua autem omnia peragenda, vt prius.</s>
            <s xml:id="echoid-s14237" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s14238" xml:space="preserve">IAM vero, quando altitudo poli ſupra Horizontẽ tanta eſt, vt axis E D, in portione Analemmatis
              <lb/>
            à V erticalis Circuli diametro A D, parum differat, & </s>
            <s xml:id="echoid-s14239" xml:space="preserve">idcirco recta H I, ſi ſtylus D G, non ſit </s>
          </p>
        </div>
      </text>
    </echo>
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