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-div1010" type="section" level="1" n="248">
          <p style="it">
            <s xml:id="echoid-s19693" xml:space="preserve">
              <pb o="291" file="0307" n="307" rhead="LIBER SECVNDVS."/>
            quoque recta ducta per ſecunda puncta diuiſionum, quorum vnum ſit primæ diuiſionis, & </s>
            <s xml:id="echoid-s19694" xml:space="preserve">infra rectam
              <lb/>
            C D, & </s>
            <s xml:id="echoid-s19695" xml:space="preserve">alterum ſecundæ diuiſionis, & </s>
            <s xml:id="echoid-s19696" xml:space="preserve">ſupra rectam C D, perpendicularis erit ad lineam ipſi B A, proxi-
              <lb/>
            mam, tanget{q́ue} circulum B G F, in puncto proximo ipſi B. </s>
            <s xml:id="echoid-s19697" xml:space="preserve">Ita quoque cum tertijs punctis diuiſionum,
              <lb/>
            quartis, & </s>
            <s xml:id="echoid-s19698" xml:space="preserve">cæteris agatur. </s>
            <s xml:id="echoid-s19699" xml:space="preserve">Ratio huius rei hæc eſt: </s>
            <s xml:id="echoid-s19700" xml:space="preserve">quia dictæ lineæ horarum ab or. </s>
            <s xml:id="echoid-s19701" xml:space="preserve">& </s>
            <s xml:id="echoid-s19702" xml:space="preserve">occ. </s>
            <s xml:id="echoid-s19703" xml:space="preserve">diuidunt ſin-
              <lb/>
            gulos circulos ex A, deſcriptos in 24. </s>
            <s xml:id="echoid-s19704" xml:space="preserve">partes æquales, vt ex demonstratis in propoſ. </s>
            <s xml:id="echoid-s19705" xml:space="preserve">præcedenti liquet,
              <lb/>
            initio facto tam à puncto C, quàm à puncto D; </s>
            <s xml:id="echoid-s19706" xml:space="preserve">ita vt ſi proximum punctum infra C, fuerit hora 23. </s>
            <s xml:id="echoid-s19707" xml:space="preserve">ab
              <lb/>
            occ. </s>
            <s xml:id="echoid-s19708" xml:space="preserve">proximum punctum ſupra punctum D, ſit hora 23. </s>
            <s xml:id="echoid-s19709" xml:space="preserve">ab or. </s>
            <s xml:id="echoid-s19710" xml:space="preserve">& </s>
            <s xml:id="echoid-s19711" xml:space="preserve">c.</s>
            <s xml:id="echoid-s19712" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s19713" xml:space="preserve">LONGITVDINEM ſtyli, qui in centro collocatus horas indicet in horologio hac arte deli-
              <lb/>
              <note position="right" xlink:label="note-0307-01" xlink:href="note-0307-01a" xml:space="preserve">Longitudo ſty-
                <lb/>
              li quomodo in
                <lb/>
              ueſtigetur in po
                <lb/>
              ſteriori hac d
                <unsure/>
              e-
                <lb/>
              ſcriptione horo
                <lb/>
              logii Italici &
                <lb/>
              Babylonici.</note>
            neato, ita inueniemus. </s>
            <s xml:id="echoid-s19714" xml:space="preserve">Fiat angulus A B E, complemento altitudinis poli æqualis, quod quidem facile
              <lb/>
            efficietur, ſi ex B, arcus circuli deſcribatur, in eo{q́ue} complementum altitudinis poli à recta B A, verſus
              <lb/>
              <note position="left" xlink:label="note-0307-02" xlink:href="note-0307-02a" xml:space="preserve">10</note>
            C, ſupputetur. </s>
            <s xml:id="echoid-s19715" xml:space="preserve">Nam recta B E, ducta ex B, per finem ſupputationis conſtituet angulum A B F, com-
              <lb/>
            plemento altitudinis poli æqualem, abſcindet{q́ue} ex recta A E, longitudinem ſtyli A E, in centro A, affi-
              <lb/>
            gendi ad angulos rectos. </s>
            <s xml:id="echoid-s19716" xml:space="preserve">Si enim horologio in propria poſitione conſtituto, ita vt æquinoctiali circulo
              <lb/>
            æquidiſtet, & </s>
            <s xml:id="echoid-s19717" xml:space="preserve">recta C D, Horizonti ſit parallela, triangulum A B E, circa rectam A E, quæ commu-
              <lb/>
            nis ſectio eſt plani horologii, & </s>
            <s xml:id="echoid-s19718" xml:space="preserve">Meridiani circuli, moueri intelligatur, donec in plano Meridiani ſtatua-
              <lb/>
            tur rectum ad horologij planum, erit A E, axis mundi, & </s>
            <s xml:id="echoid-s19719" xml:space="preserve">B E, communis@ ſectio Horizontis per C D,
              <lb/>
            ducti, & </s>
            <s xml:id="echoid-s19720" xml:space="preserve">Meridiani, cum eſficiat cum meridiana linea A B, angulum complemento altitudinis poli æqua-
              <lb/>
            lem, vt res poſtulat, vt ex demonſtratis in propoſ. </s>
            <s xml:id="echoid-s19721" xml:space="preserve">50. </s>
            <s xml:id="echoid-s19722" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s19723" xml:space="preserve">colligitur. </s>
            <s xml:id="echoid-s19724" xml:space="preserve">Quare A E, longitudo ſtyli
              <lb/>
            erit, cum Sole in Horizonte, qui per C D, & </s>
            <s xml:id="echoid-s19725" xml:space="preserve">E B, ducitur, exiſtente extremitas vmbræ ipſius in lineam
              <lb/>
            horizontalem C D, proijciatur, vt conſtat. </s>
            <s xml:id="echoid-s19726" xml:space="preserve">Quòd ſi non placeat deſcribere arcum circuli ex B, ad conſti-
              <lb/>
              <note position="left" xlink:label="note-0307-03" xlink:href="note-0307-03a" xml:space="preserve">20</note>
            tuendum angulum complemento altitudinis poli æqualem, ſupputetur in circulo B G F, duplum comple-
              <lb/>
            menti altitudinis poli ab F, vſque ad G. </s>
            <s xml:id="echoid-s19727" xml:space="preserve">Recta enim ducta B G, conſtituet angulum A B G, comple-
              <lb/>
            mento altitudinis poli æqualem. </s>
            <s xml:id="echoid-s19728" xml:space="preserve">Cum enim (ſi ducta eſſet recta G A) angulus G A F, in centro duplus
              <lb/>
              <note position="right" xlink:label="note-0307-04" xlink:href="note-0307-04a" xml:space="preserve">33. ſext@.</note>
            ſit anguli complementi altitudinis poli in eodem centro conſtituti, quòd & </s>
            <s xml:id="echoid-s19729" xml:space="preserve">arcus F G, eiuſdem comple-
              <lb/>
            menti ſii duplus: </s>
            <s xml:id="echoid-s19730" xml:space="preserve">Duplus autem ſit angulus G A F, in centro anguli G B F, in circumferentia; </s>
            <s xml:id="echoid-s19731" xml:space="preserve">erit an-
              <lb/>
              <note position="right" xlink:label="note-0307-05" xlink:href="note-0307-05a" xml:space="preserve">20. tertij</note>
            gulus G B F, complemento altitudinis poli æqualis.</s>
            <s xml:id="echoid-s19732" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s19733" xml:space="preserve">INVENTO autem ſtylo A E, poterunt pro eius magnitudine deſcribi arcus, ſeu paralleli ſigno-
              <lb/>
              <note position="right" xlink:label="note-0307-06" xlink:href="note-0307-06a" xml:space="preserve">Quomodo in
                <lb/>
              poſteriori hoc
                <lb/>
              horologio arcus
                <lb/>
              ſignornm de-
                <lb/>
              ſeribantur.</note>
            rum, veluti propoſ. </s>
            <s xml:id="echoid-s19734" xml:space="preserve">50. </s>
            <s xml:id="echoid-s19735" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s19736" xml:space="preserve">docuimus; </s>
            <s xml:id="echoid-s19737" xml:space="preserve">vt videlicet in remotiſſimo eorum, & </s>
            <s xml:id="echoid-s19738" xml:space="preserve">in arcu ♋, vel ♑, ho-
              <lb/>
            rariæ lineæ terminentur, vt in præcedentis propoſ. </s>
            <s xml:id="echoid-s19739" xml:space="preserve">horologio factum eſt.</s>
            <s xml:id="echoid-s19740" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">30</note>
        </div>
        <div xml:id="echoid-div1015" type="section" level="1" n="249">
          <head xml:id="echoid-head257" xml:space="preserve">PROBLEMA 60. PROPOSITIO 60.</head>
          <head xml:id="echoid-head258" xml:space="preserve">HOROLOGIVM Antiquum æquinoctiale conſtituere.</head>
          <p>
            <s xml:id="echoid-s19741" xml:space="preserve">DIVIDANTVR ſingulæ portiones arcuum ſignorum, quas horizontalis linea amputat, in
              <lb/>
              <note position="right" xlink:label="note-0307-08" xlink:href="note-0307-08a" xml:space="preserve">Conſtructio ho
                <lb/>
              rologii Antiqui
                <lb/>
              æquinoctialis.</note>
            vtroque horologio tam ſuperiori, quàm inferiori, in 12. </s>
            <s xml:id="echoid-s19742" xml:space="preserve">partes æquales. </s>
            <s xml:id="echoid-s19743" xml:space="preserve">Deinde per proxima pun
              <lb/>
            cta infra, & </s>
            <s xml:id="echoid-s19744" xml:space="preserve">ſupra lineam horizontalem ad vtraſque partes quatuor lineæ rectæ ducantur, idemq́;
              <lb/>
            </s>
            <s xml:id="echoid-s19745" xml:space="preserve">fiat in ſequentibus punctis ſibi reſpondentibus, deſcriptumq́ue erit horologium Antiquum. </s>
            <s xml:id="echoid-s19746" xml:space="preserve">Nã
              <lb/>
            proxima linea infra lineam horizontalem ad dextram dabit in ſuperiori horologio horam 1. </s>
            <s xml:id="echoid-s19747" xml:space="preserve">in-
              <lb/>
              <note position="left" xlink:label="note-0307-09" xlink:href="note-0307-09a" xml:space="preserve">40</note>
            æqualem, ſubſequens ſecundam, & </s>
            <s xml:id="echoid-s19748" xml:space="preserve">c. </s>
            <s xml:id="echoid-s19749" xml:space="preserve">In inferiori idem cernitur ad ſiniſtrã horizontalis lineæ, hoc
              <lb/>
            eſt, in portione abſciſſa à linea horizontali, ſi tamen omnes eius partes inuertantur. </s>
            <s xml:id="echoid-s19750" xml:space="preserve">Demonſtrabi-
              <lb/>
            mus autem, rectè hac ratione deſcriptas eſſe horas inæquales, non aliter, ac oſtendimus propoſ.
              <lb/>
            </s>
            <s xml:id="echoid-s19751" xml:space="preserve">58. </s>
            <s xml:id="echoid-s19752" xml:space="preserve">huius libri, rectè ductas eſſe lineas horarum ab occaſu ſecundum primum modum; </s>
            <s xml:id="echoid-s19753" xml:space="preserve">ſi intelli-
              <lb/>
            gantur circuli maximi per polos mundi, & </s>
            <s xml:id="echoid-s19754" xml:space="preserve">per horas inæquales parallelorum Solis tranſire. </s>
            <s xml:id="echoid-s19755" xml:space="preserve">Hi
              <lb/>
            enim ſecabunt quoque arcus ſignorum in horologio æquinoctiali in partes æquales, per ea, quæ
              <lb/>
            propoſ. </s>
            <s xml:id="echoid-s19756" xml:space="preserve">49. </s>
            <s xml:id="echoid-s19757" xml:space="preserve">huius libri demonſtrauimus: </s>
            <s xml:id="echoid-s19758" xml:space="preserve">ac proinde per puncta diuiſionum arcuum ſignorum
              <lb/>
            circuli horarum inæqualium ducentur, vt de circulis horarum ab occaſu dictum eſt propoſ. </s>
            <s xml:id="echoid-s19759" xml:space="preserve">58. </s>
            <s xml:id="echoid-s19760" xml:space="preserve">
              <lb/>
            huius libri.</s>
            <s xml:id="echoid-s19761" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s19762" xml:space="preserve">IDEM horologium Antiquum, horarumve inæqualium delineabimus beneficio arcus diur
              <lb/>
              <note position="left" xlink:label="note-0307-10" xlink:href="note-0307-10a" xml:space="preserve">50</note>
              <note position="right" xlink:label="note-0307-11" xlink:href="note-0307-11a" xml:space="preserve">Eiuſdẽ
                <unsure/>
              horolo-
                <lb/>
              gii Antiqui æ-
                <lb/>
              quinoctialis de
                <lb/>
              ſcriptio per ar-
                <lb/>
              cum diurnum
                <lb/>
              horarum 18. &
                <lb/>
              nocturnum ho
                <lb/>
              rarum 6.</note>
            ni horarum 18. </s>
            <s xml:id="echoid-s19763" xml:space="preserve">& </s>
            <s xml:id="echoid-s19764" xml:space="preserve">nocturni horarum 6. </s>
            <s xml:id="echoid-s19765" xml:space="preserve">Nam hora 1. </s>
            <s xml:id="echoid-s19766" xml:space="preserve">inæqualis ducenda eſt in arcu diurno hora-
              <lb/>
            rum 18. </s>
            <s xml:id="echoid-s19767" xml:space="preserve">per horam 4 {1/2}. </s>
            <s xml:id="echoid-s19768" xml:space="preserve">à media nocte, & </s>
            <s xml:id="echoid-s19769" xml:space="preserve">in nocturno horarum 6. </s>
            <s xml:id="echoid-s19770" xml:space="preserve">per hor. </s>
            <s xml:id="echoid-s19771" xml:space="preserve">9 {1/2}. </s>
            <s xml:id="echoid-s19772" xml:space="preserve">à meridie. </s>
            <s xml:id="echoid-s19773" xml:space="preserve">Ho-
              <lb/>
            ra autem ſecunda per hor. </s>
            <s xml:id="echoid-s19774" xml:space="preserve">6. </s>
            <s xml:id="echoid-s19775" xml:space="preserve">à media nocte in priori arcu, & </s>
            <s xml:id="echoid-s19776" xml:space="preserve">per horam 10. </s>
            <s xml:id="echoid-s19777" xml:space="preserve">à meridie in poſte-
              <lb/>
            riori. </s>
            <s xml:id="echoid-s19778" xml:space="preserve">Hora deinde tertia inæqualis ducenda eſt in arcu diurno horarum 18. </s>
            <s xml:id="echoid-s19779" xml:space="preserve">per hor. </s>
            <s xml:id="echoid-s19780" xml:space="preserve">7 {1/2}. </s>
            <s xml:id="echoid-s19781" xml:space="preserve">à media
              <lb/>
            nocte, & </s>
            <s xml:id="echoid-s19782" xml:space="preserve">in arcu nocturno horarum 6. </s>
            <s xml:id="echoid-s19783" xml:space="preserve">per hor. </s>
            <s xml:id="echoid-s19784" xml:space="preserve">10 {1/2} à meridie. </s>
            <s xml:id="echoid-s19785" xml:space="preserve">Hora vero quarta inæqualis tranſi-
              <lb/>
            re debet in priori arcu per hor. </s>
            <s xml:id="echoid-s19786" xml:space="preserve">9. </s>
            <s xml:id="echoid-s19787" xml:space="preserve">à media nocte, & </s>
            <s xml:id="echoid-s19788" xml:space="preserve">in arcu poſteriori per hor. </s>
            <s xml:id="echoid-s19789" xml:space="preserve">11. </s>
            <s xml:id="echoid-s19790" xml:space="preserve">à meridie. </s>
            <s xml:id="echoid-s19791" xml:space="preserve">Quin
              <lb/>
            ta autem hora inæqualis ducenda eſt per hor. </s>
            <s xml:id="echoid-s19792" xml:space="preserve">10 {1/2}. </s>
            <s xml:id="echoid-s19793" xml:space="preserve">à media nocte in arcu diurno horarum 18. </s>
            <s xml:id="echoid-s19794" xml:space="preserve">& </s>
            <s xml:id="echoid-s19795" xml:space="preserve">
              <lb/>
            in arcu nocturno horarum 6.</s>
            <s xml:id="echoid-s19796" xml:space="preserve">
              <unsure/>
            per hor. </s>
            <s xml:id="echoid-s19797" xml:space="preserve">11 {1/2}. </s>
            <s xml:id="echoid-s19798" xml:space="preserve">à meridie. </s>
            <s xml:id="echoid-s19799" xml:space="preserve">Hora vero ſexta inæqualis à linea meridia-
              <lb/>
            na, ſine horæ 12. </s>
            <s xml:id="echoid-s19800" xml:space="preserve">aſtronomicæ non differt. </s>
            <s xml:id="echoid-s19801" xml:space="preserve">Poſt hæc hora ſeptima inæqualis ducenda eſt in arcu
              <lb/>
            diurno horarum 18. </s>
            <s xml:id="echoid-s19802" xml:space="preserve">per hor 1 {1/2}. </s>
            <s xml:id="echoid-s19803" xml:space="preserve">à meridie, & </s>
            <s xml:id="echoid-s19804" xml:space="preserve">in arcu nocturno horarum 6. </s>
            <s xml:id="echoid-s19805" xml:space="preserve">per hor. </s>
            <s xml:id="echoid-s19806" xml:space="preserve">{1/2}. </s>
            <s xml:id="echoid-s19807" xml:space="preserve">à media
              <lb/>
            nocte. </s>
            <s xml:id="echoid-s19808" xml:space="preserve">Octaua autem hora inæqualis ducenda eſt in priori arcu per hor. </s>
            <s xml:id="echoid-s19809" xml:space="preserve">3. </s>
            <s xml:id="echoid-s19810" xml:space="preserve">à meridie, & </s>
            <s xml:id="echoid-s19811" xml:space="preserve">in </s>
          </p>
        </div>
      </text>
    </echo>
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