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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        <div xml:id="echoid-div1073" type="section" level="1" n="256">
          <p>
            <s xml:id="echoid-s21148" xml:space="preserve">
              <pb o="315" file="0331" n="331" rhead="LIBER TERTIVS."/>
            rologio horizontali factum eſt, atque in Verticali propoſ. </s>
            <s xml:id="echoid-s21149" xml:space="preserve">2. </s>
            <s xml:id="echoid-s21150" xml:space="preserve">& </s>
            <s xml:id="echoid-s21151" xml:space="preserve">14. </s>
            <s xml:id="echoid-s21152" xml:space="preserve">antecedentis lib. </s>
            <s xml:id="echoid-s21153" xml:space="preserve">Nam & </s>
            <s xml:id="echoid-s21154" xml:space="preserve">ibi li-
              <lb/>
            neæ vltram rectam H V, in figura radiorum translatæ referunt eaſdem horas numero, æquinoctia
              <lb/>
            lem tamen lineam non ſecantes, quibus reſpondent aliæ lineæ citra rectam H V; </s>
            <s xml:id="echoid-s21155" xml:space="preserve">quia nimirum
              <lb/>
            quæuis linea horaria in horologio horizontali & </s>
            <s xml:id="echoid-s21156" xml:space="preserve">Verticali cum linea horæ 6. </s>
            <s xml:id="echoid-s21157" xml:space="preserve">quę lineæ æquino-
              <lb/>
            ctiali æquidiſtat, ad verticem, ſeu centrum H, æquales angulos conſtituit; </s>
            <s xml:id="echoid-s21158" xml:space="preserve">quemadmodum & </s>
            <s xml:id="echoid-s21159" xml:space="preserve">hic
              <lb/>
            cum linea C d, ipſi æquinoctiali lineæ parallela, cui reſpondet recta C A, radio Aequatoris paralle
              <lb/>
            la in figura radiorum, inſtar rectæ H V, radio Aequatoris ibi in figura radiorum æquidiſtantis, & </s>
            <s xml:id="echoid-s21160" xml:space="preserve">
              <lb/>
            horæ 6. </s>
            <s xml:id="echoid-s21161" xml:space="preserve">reſpondentis, quæ lineæ æquinoctiali parallela eſt. </s>
            <s xml:id="echoid-s21162" xml:space="preserve">Ita vides hic tran slatam eſſe vltra rectã
              <lb/>
            C A, lineam horæ 3. </s>
            <s xml:id="echoid-s21163" xml:space="preserve">à media nocte, quia hora 3. </s>
            <s xml:id="echoid-s21164" xml:space="preserve">à meridie æquinoctialem lineam ſecat, nec non
              <lb/>
            lineam horæ 4. </s>
            <s xml:id="echoid-s21165" xml:space="preserve">à meridie, quia hora 4. </s>
            <s xml:id="echoid-s21166" xml:space="preserve">à media nocte ſecat æquinoctialem, vt in horologio appa-
              <lb/>
              <note position="left" xlink:label="note-0331-01" xlink:href="note-0331-01a" xml:space="preserve">10</note>
            ret. </s>
            <s xml:id="echoid-s21167" xml:space="preserve">Eademq́ue ratio habenda eſt de alijs.</s>
            <s xml:id="echoid-s21168" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s21169" xml:space="preserve">QVOD ſi quando linea ſtyli vna ſit ex lineis horarijs, vel æqualiter à duabus horarijs lineis
              <lb/>
              <note position="right" xlink:label="note-0331-02" xlink:href="note-0331-02a" xml:space="preserve">Quando linea
                <lb/>
              ſiyli una eſt ex
                <lb/>
              li
                <unsure/>
              neis horariis.
                <lb/>
              vel æqualiter à
                <lb/>
              duabus hinc in
                <lb/>
              de diſtat, perti-
                <lb/>
              nebit quælibet
                <lb/>
              linea horaria
                <lb/>
              in figuta ra dio
                <lb/>
              rũ ad duas ho-
                <lb/>
              ras, vt in hori-
                <lb/>
              zontali horolo
                <lb/>
              gio.</note>
            in medio earum poſita diſtet, (quod aliquando contingere poteſt) inſeruiet quælibet horaria li
              <lb/>
            nea in proximè conſtructa figura radiorum ex C, ducta duabus horis æqualiter à linea ſtyli hinc
              <lb/>
            inde remotis: </s>
            <s xml:id="echoid-s21170" xml:space="preserve">quia tunc interualla illarum horarum inter centrum L, & </s>
            <s xml:id="echoid-s21171" xml:space="preserve">æquinoctialem lineam
              <lb/>
            æqualia ſunt, vt propoſ. </s>
            <s xml:id="echoid-s21172" xml:space="preserve">2. </s>
            <s xml:id="echoid-s21173" xml:space="preserve">ſuperioris lib. </s>
            <s xml:id="echoid-s21174" xml:space="preserve">de horizontali horologio oſtendimus, atque adeò trans-
              <lb/>
            lata in radium Æ quatoris ex puncto I, vnum & </s>
            <s xml:id="echoid-s21175" xml:space="preserve">idem punctum offerunt, &</s>
            <s xml:id="echoid-s21176" xml:space="preserve">c. </s>
            <s xml:id="echoid-s21177" xml:space="preserve">Vnde tunc ſingulis
              <lb/>
            lineis bini numeri aſcribendi erunt, reſpondentes binis illis horis hinc inde à linea ſtyli æquali
              <lb/>
            ſpatio remotis, quemadmodum & </s>
            <s xml:id="echoid-s21178" xml:space="preserve">in horizontali horologio, ac in Verticali factum eſt. </s>
            <s xml:id="echoid-s21179" xml:space="preserve">Sed quan-
              <lb/>
            do linea ſtyli inæqualiter à lineis horarijs circumſtantibus remouetur, (quod frequentius ſolet ac-
              <lb/>
              <note position="left" xlink:label="note-0331-03" xlink:href="note-0331-03a" xml:space="preserve">20</note>
            cidere) vt in dato exemplo euenit, reſpondebunt ſingulæ lineæ ſingulis tantum horis; </s>
            <s xml:id="echoid-s21180" xml:space="preserve">propterea
              <lb/>
            quòd tunc interualla horarũ inter centrũ L, & </s>
            <s xml:id="echoid-s21181" xml:space="preserve">æquinoctialem lineã hinc inde à linea ſtyli diſtan-
              <lb/>
            tium inæqualia ſunt, atque adeò in radium Aequatoris ex I, translata diuerſa puncta offerunt, &</s>
            <s xml:id="echoid-s21182" xml:space="preserve">c.</s>
            <s xml:id="echoid-s21183" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s21184" xml:space="preserve">NON eſſet autem præter rem, quando linea ſtyli inæqualiter à proximis duabus horis diſtat,
              <lb/>
              <note position="right" xlink:label="note-0331-04" xlink:href="note-0331-04a" xml:space="preserve">Quando linea
                <lb/>
              ſtyli inæquali-
                <lb/>
              ter diſtat à dua
                <lb/>
              bus proximis
                <lb/>
              horis, conſtruẽ-
                <lb/>
              dæ eſſent duæ
                <lb/>
              figuræ radiorũ,
                <lb/>
              vt omnis confu
                <lb/>
              ſio linearũ tol-
                <lb/>
              leretur.</note>
            immo verò expediret, ſi conſtruerentur duæ figuræ radiorum Zodiaci, in quarum vna duceren-
              <lb/>
            tur horariæ lineæ ex C, reſpondentes illis lineis horariis in horologio, quæ ex vna parte, nempe ſi-
              <lb/>
            niſtra lineæ ſtyli continentur; </s>
            <s xml:id="echoid-s21185" xml:space="preserve">in alia verò horariæ lineæ reſpondentes lineis horarijs horologii ex
              <lb/>
            altera parte lineæ ſtyli. </s>
            <s xml:id="echoid-s21186" xml:space="preserve">Ita enim omnis linearum confuſio tolleretur, quæ, neceſſario ſequitur,
              <lb/>
            quando linea ſtyli ferè æqualiter à lineis hinc inde poſitis diſtat, quia tunc puncta in radio Aequa
              <lb/>
            toris inuenta vix inter ſe diſcernuntur, vt manifeſtum eſt. </s>
            <s xml:id="echoid-s21187" xml:space="preserve">Hac ratione in noſtro exemplo in vna
              <lb/>
              <note position="left" xlink:label="note-0331-05" xlink:href="note-0331-05a" xml:space="preserve">30</note>
            figurarum ducerentur lineæ ex C, reſpondentes hiſce horis 1. </s>
            <s xml:id="echoid-s21188" xml:space="preserve">2. </s>
            <s xml:id="echoid-s21189" xml:space="preserve">3. </s>
            <s xml:id="echoid-s21190" xml:space="preserve">4. </s>
            <s xml:id="echoid-s21191" xml:space="preserve">5. </s>
            <s xml:id="echoid-s21192" xml:space="preserve">6. </s>
            <s xml:id="echoid-s21193" xml:space="preserve">7. </s>
            <s xml:id="echoid-s21194" xml:space="preserve">8. </s>
            <s xml:id="echoid-s21195" xml:space="preserve">9. </s>
            <s xml:id="echoid-s21196" xml:space="preserve">à media no-
              <lb/>
            cte, quæ ſunt ad ſiniſtram lineæ ſtyli. </s>
            <s xml:id="echoid-s21197" xml:space="preserve">In altera verò continerentur lineæ reſpondentes horis ad
              <lb/>
            dexteram eiuſdem lineæ ſtyli, quales ſunt 10. </s>
            <s xml:id="echoid-s21198" xml:space="preserve">11. </s>
            <s xml:id="echoid-s21199" xml:space="preserve">12. </s>
            <s xml:id="echoid-s21200" xml:space="preserve">à media nocte, & </s>
            <s xml:id="echoid-s21201" xml:space="preserve">1. </s>
            <s xml:id="echoid-s21202" xml:space="preserve">2. </s>
            <s xml:id="echoid-s21203" xml:space="preserve">3. </s>
            <s xml:id="echoid-s21204" xml:space="preserve">4. </s>
            <s xml:id="echoid-s21205" xml:space="preserve">5. </s>
            <s xml:id="echoid-s21206" xml:space="preserve">6. </s>
            <s xml:id="echoid-s21207" xml:space="preserve">&</s>
            <s xml:id="echoid-s21208" xml:space="preserve">c. </s>
            <s xml:id="echoid-s21209" xml:space="preserve">à meridie.
              <lb/>
            </s>
            <s xml:id="echoid-s21210" xml:space="preserve">In qualibet tamen figura ducenda eſſet C G, pro linea ſtyli. </s>
            <s xml:id="echoid-s21211" xml:space="preserve">Huius rei exemplum poſitum eſſe vi-
              <lb/>
            debis in propoſ. </s>
            <s xml:id="echoid-s21212" xml:space="preserve">38. </s>
            <s xml:id="echoid-s21213" xml:space="preserve">huius libri.</s>
            <s xml:id="echoid-s21214" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s21215" xml:space="preserve">EX his hoc modo paratis deſcribentur arcus ſignorum, vt in horologio horizontali, & </s>
            <s xml:id="echoid-s21216" xml:space="preserve">Ver-
              <lb/>
            ticali, transferendo nimirum interualla horarum inter C, & </s>
            <s xml:id="echoid-s21217" xml:space="preserve">radios ſignorum intercepta ex cen-
              <lb/>
            tro horologii C, in horas horologii reſpondentes, vel etiam transferendo horaria interualla in-
              <lb/>
            ter radium Aequatoris, & </s>
            <s xml:id="echoid-s21218" xml:space="preserve">ſignorum radios poſita in lineas horarias horologij reſpondentes, ini-
              <lb/>
            tio facto à linea æquinoctiali, &</s>
            <s xml:id="echoid-s21219" xml:space="preserve">c. </s>
            <s xml:id="echoid-s21220" xml:space="preserve">Eadem enim demonſtratio hic erit, quæ in horologio horizon-
              <lb/>
              <note position="left" xlink:label="note-0331-06" xlink:href="note-0331-06a" xml:space="preserve">40</note>
            tali, cum planum horologij declinantis ſit tanquam Horizon quidam, & </s>
            <s xml:id="echoid-s21221" xml:space="preserve">angulus G C I, æqualis
              <lb/>
            altitudini poli ſupra ipſum, vt diximus, atque linea ſtyli inſtar lineæ meridianæ, licet non indicet
              <lb/>
            horam 12. </s>
            <s xml:id="echoid-s21222" xml:space="preserve">quia non computamus horas à Meridiano circulo plani declinantis, ſed à Meridiano
              <lb/>
            Horizontis illius loci, vbi declinans horologium deſcribitur. </s>
            <s xml:id="echoid-s21223" xml:space="preserve">Monſtraret autem proculdubio
              <lb/>
            dicta linea meridiana horam 12. </s>
            <s xml:id="echoid-s21224" xml:space="preserve">ſi horas computaremus à Meridiano plani declinantis; </s>
            <s xml:id="echoid-s21225" xml:space="preserve">quia tunc
              <lb/>
            circulus proprius Meridianus plani declinantis efficiens lineam ſtyli in horologio æqualiter diſta-
              <lb/>
            ret ab ortu, & </s>
            <s xml:id="echoid-s21226" xml:space="preserve">occaſu Solis, atque adeo Sol in eo exiſtens meridiem efficeret, vel mediam noctem,
              <lb/>
            quemadmodum in Horizonte contingit.</s>
            <s xml:id="echoid-s21227" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s21228" xml:space="preserve">PERSPICVVM autẽ eſt ex demonſtratis in propoſ. </s>
            <s xml:id="echoid-s21229" xml:space="preserve">2. </s>
            <s xml:id="echoid-s21230" xml:space="preserve">ſuperioris libri, quando recta C G,
              <lb/>
              <note position="right" xlink:label="note-0331-07" xlink:href="note-0331-07a" xml:space="preserve">Qui arens fi-
                <lb/>
              gnorũ ſint hy-
                <lb/>
              perbolæ, qui pa
                <lb/>
              rabolæ, & qui
                <lb/>
              ellipſes in horo
                <lb/>
              logio declinan
                <lb/>
              te à Verticali.</note>
            in figura radiorum oppoſitos radios ſecat, arcus illorum ſignorum eſſe hyperbolas oppoſitas, & </s>
            <s xml:id="echoid-s21231" xml:space="preserve">
              <lb/>
              <note position="left" xlink:label="note-0331-08" xlink:href="note-0331-08a" xml:space="preserve">50</note>
            æquales: </s>
            <s xml:id="echoid-s21232" xml:space="preserve">quando verò æquidiſtat alteri radiorum oppoſitorum, & </s>
            <s xml:id="echoid-s21233" xml:space="preserve">alterum ſecat, arcum ſigni il-
              <lb/>
            lius, cuius radius ſecatur, eſſe Parabolam, & </s>
            <s xml:id="echoid-s21234" xml:space="preserve">alterius arcum deſcribi non poſſe: </s>
            <s xml:id="echoid-s21235" xml:space="preserve">quando denique
              <lb/>
            alterum oppoſitorum radiorum ſecat, alterum autem non, neque ei æquidiſtat, arcum illius ſigni,
              <lb/>
            cuius radius ſecatur, eſſe Ellipſim, & </s>
            <s xml:id="echoid-s21236" xml:space="preserve">alterius arcum nullo modo poſſe deſcribi. </s>
            <s xml:id="echoid-s21237" xml:space="preserve">Eadem enim de-
              <lb/>
            monſtratio hic erit, quæ ibi: </s>
            <s xml:id="echoid-s21238" xml:space="preserve">quoniam ita hic ſe habet recta C G, in figura radiorum reſpondens
              <lb/>
            lineæ ſtyli in horologio, & </s>
            <s xml:id="echoid-s21239" xml:space="preserve">diameter omnium ſectionum conicarum exiſtens, vt ibi recta H B, in
              <lb/>
              <note position="right" xlink:label="note-0331-09" xlink:href="note-0331-09a" xml:space="preserve">Arcus paralle-
                <lb/>
              lorum ſemper
                <lb/>
              apparentium,
                <lb/>
              ſemperq; laten
                <lb/>
              titum maximo-
                <lb/>
              rum ſunt hy-
                <lb/>
              perbolæ in ſu-
                <lb/>
              periori horolo-
                <lb/>
              gio.</note>
            figura radiorum referẽs lineam meridianam horologij, & </s>
            <s xml:id="echoid-s21240" xml:space="preserve">diameter exiſtens omnium conicarum
              <lb/>
            ſectionum: </s>
            <s xml:id="echoid-s21241" xml:space="preserve">propterea quòd angulus C G I, æqualis eſt hic altitudini poli ſupra planum declinãs,
              <lb/>
            vt ibi angulus D H B, æqualis eſt poli altitudini ſupra Horizontem. </s>
            <s xml:id="echoid-s21242" xml:space="preserve">Ex his ſequitur, arcus paralle-
              <lb/>
            lorum, qui omnium ſemper apparentium, & </s>
            <s xml:id="echoid-s21243" xml:space="preserve">ſemper latentium maximi ſunt, eſſe in noſtro exem-
              <lb/>
            plo hyperbolas oppoſitas. </s>
            <s xml:id="echoid-s21244" xml:space="preserve">Quoniã enim angulus, quem radius arcus horarum 24. </s>
            <s xml:id="echoid-s21245" xml:space="preserve">cũ radio Æ </s>
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