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 contents

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[331.] PROBLEMA 46. PROPOSITIO 46.
Page: 427 (411)
[332.] PROBLEMA 47. PROPOSITIO 47.
Page: 429 (413)
[333.] PROBLEMA 48. PROPOSITIO 48.
Page: 429 (413)
[334.] FINIS TERTII LIBRI.
Page: 429 (413)
[335.] GNOMONICES LIBER QVARTVS.
Page: 430 (414)
[336.] AVCTORE
Page: 430 (414)
[337.] CHRISTOPHORO CLAVIO BAMBER GENSI SOCIETATIS IESV.
Page: 430 (414)
[338.] PROBLEMA 1. PROPOSITIO 1.
Page: 430 (414)
[339.] I. SOLE EXISTENTE IN PRINCIPIO ♈.
Page: 432 (416)
[340.] II. SOLE EXISTENTE IN PRINCIPIO ♎.
Page: 432 (416)
[341.] III. SOLE EXISTENTE IN PRINCIPIO ♋.
Page: 432 (416)
[342.] IIII. SOLE EXISTENTE IN PRINCIPIO ♑.
Page: 432 (416)
[343.] PROBLEMA 2. PROPOSITIO 2.
Page: 432 (416)
[344.] PROBLEMA 3. PROPOSITIO 3.
Page: 433 (417)
[345.] PROBLEMA 4. PROPOSITIO 4.
Page: 434 (418)
[346.] PROBLEMA 5. PROPOSITIO 5.
Page: 434 (418)
[347.] PROBLEMA 6. PROPOSITIO 6.
Page: 434 (418)
[348.] PROBLEMA 7. PROPOSITIO 7.
Page: 437 (421)
[349.] PROBLEMA 8. PROPOSITIO 8.
Page: 439 (423)
[350.] PROBLEMA 9. PROPOSITIO 9.
Page: 440 (424)
[351.] PROBLEMA 10. PROPOSITIO 10.
Page: 442 (426)
[352.] PROBLEMA 11. PROPOSITIO 11.
Page: 443 (427)
[353.] SCHOLIVM.
Page: 445 (429)
[354.] PROBLEMA 12. PROPOSITIO 12.
Page: 447 (431)
[355.] SCHOLIVM.
Page: 448 (432)
[356.] PROBLEMA 13. PROPOSITIO 13.
Page: 449 (433)
[357.] PROBLEMA 14. PROPOSITIO 14.
Page: 458 (442)
[358.] SCHOLIVM.
Page: 461 (445)
[359.] FINIS QV ARTI LIBRI.
Page: 462 (446)
[360.] GNOMONICES LIBER QVINTVS.
Page: 463 (447)
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        <div xml:id="echoid-div999" type="section" level="1" n="246">
          <p>
            <s xml:id="echoid-s19355" xml:space="preserve">
              <pb o="287" file="0303" n="303" rhead="LIBER SECVNDVS."/>
            æquinoctiali in partes æquales, vt ex iis, quæ propoſ. </s>
            <s xml:id="echoid-s19356" xml:space="preserve">49. </s>
            <s xml:id="echoid-s19357" xml:space="preserve">& </s>
            <s xml:id="echoid-s19358" xml:space="preserve">in ſcholio propoſ. </s>
            <s xml:id="echoid-s19359" xml:space="preserve">50. </s>
            <s xml:id="echoid-s19360" xml:space="preserve">huius libri ſcri-
              <lb/>
            pſimus, conſtat. </s>
            <s xml:id="echoid-s19361" xml:space="preserve">Quare cum circulus maximus per polos, & </s>
            <s xml:id="echoid-s19362" xml:space="preserve">per horam 24. </s>
            <s xml:id="echoid-s19363" xml:space="preserve">ductus ſecet paralle-
              <lb/>
            lum ♋, horologii in eo puncto, vbi eundem Horizon ſecat, quòd in illud punctum vmbra gno-
              <lb/>
            monis cadat, Sole exiſtente in communi ſectione Horizontis, ſeu paralleli ♋, & </s>
            <s xml:id="echoid-s19364" xml:space="preserve">dicti circuli, vt
              <lb/>
            ex demonſtratis in ſuperiori lib perſpicuum eſt; </s>
            <s xml:id="echoid-s19365" xml:space="preserve">incedent alij circuli maximi per alia puncta pa-
              <lb/>
            ralleli ♋, in horologio, quæ ipſum in partes æquales partiuntur, cum in ea cadat quoque vmbra
              <lb/>
            ſtyli, Sole exiſtente in communi ſectione paralleli ♋, & </s>
            <s xml:id="echoid-s19366" xml:space="preserve">illorum circulorum; </s>
            <s xml:id="echoid-s19367" xml:space="preserve">atque adeo per ea-
              <lb/>
            dem puncta circuli horarum ab occaſu tranſibunt, eadem de cauſa; </s>
            <s xml:id="echoid-s19368" xml:space="preserve">quia nimirum vmbra ſtyli in
              <lb/>
            ea puncta cadit, cum Sol in communibus ſectionibus paralleli ♋, & </s>
            <s xml:id="echoid-s19369" xml:space="preserve">circulorum horarum ab oc-
              <lb/>
            caſu, nec non circulorum maximorum per polos mundi, & </s>
            <s xml:id="echoid-s19370" xml:space="preserve">per horas ab occaſu in parallelo ♋,
              <lb/>
              <note position="left" xlink:label="note-0303-01" xlink:href="note-0303-01a" xml:space="preserve">10</note>
            tranſeuntium exiſtit. </s>
            <s xml:id="echoid-s19371" xml:space="preserve">Radius enim Solis à communibus ſectionibus illorum circulorum maxi-
              <lb/>
            morum tunc non differet, cum hæ ſectiones per centrum mundi, hoc eſt, per verticem ſtyli, ſicut
              <lb/>
            & </s>
            <s xml:id="echoid-s19372" xml:space="preserve">radius Solis, ducantur. </s>
            <s xml:id="echoid-s19373" xml:space="preserve">Cum ergo tunc radius Solis cadat in prædicta puncta paralleli ♋, in
              <lb/>
            horologio, cadent quoque in eadem communes illę ſectiones; </s>
            <s xml:id="echoid-s19374" xml:space="preserve">ac proinde in illis punctis plana
              <lb/>
            circulorum horarum ab occaſu plano horologii occurrent. </s>
            <s xml:id="echoid-s19375" xml:space="preserve">Eodem modo oſtendemus, circulos
              <lb/>
            horarum ab occaſu trãſire per puncta aliorum parallelorum in horologio, quæ ipſos in partes di-
              <lb/>
            ſtribuunt æquales, ſi videlicet concipiantur duci alii circuli maximi per polos mundi, & </s>
            <s xml:id="echoid-s19376" xml:space="preserve">per ho-
              <lb/>
            ras ab occaí
              <unsure/>
            u in ipſis parallellis. </s>
            <s xml:id="echoid-s19377" xml:space="preserve">Quare rectæ lineæ puncta dicta arcuum ſignorum connectentes,
              <lb/>
            ſunt communes ſectiones plani horologii, & </s>
            <s xml:id="echoid-s19378" xml:space="preserve">circulorum horas ab occaſu Solis monſtrantium.</s>
            <s xml:id="echoid-s19379" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s19380" xml:space="preserve">EADEM ratione inferius horologium Italicum conſtruemus, ſi diuiſionem parallelorum
              <lb/>
              <note position="left" xlink:label="note-0303-02" xlink:href="note-0303-02a" xml:space="preserve">20</note>
            in inferiori horologio, quod nobis repreſentat portio abſciſſa à linea horizontali, inchoemus ex
              <lb/>
            ea parte, in quam vmbra ſtyli proiicitur ſub ſolis occaſum, qualis eſt pars dextra ad ortum vergẽs.
              <lb/>
            </s>
            <s xml:id="echoid-s19381" xml:space="preserve">Voco partem dextram, quę nobis ad horologium inferius, hoc eſt, ad portionem à linea horizon-
              <lb/>
            tali abciſſam conuerſis, & </s>
            <s xml:id="echoid-s19382" xml:space="preserve">horizontali linea ſuperiorem occupante locum, ad dexteram poſita eſt: </s>
            <s xml:id="echoid-s19383" xml:space="preserve">
              <lb/>
            non enim ad hanc rem vtimur illa inuerſione partium, de qua in ſuperioribus locuti ſumus. </s>
            <s xml:id="echoid-s19384" xml:space="preserve">Nam
              <lb/>
            proxima linea ſupra lineam horizontalem dabit horam 1. </s>
            <s xml:id="echoid-s19385" xml:space="preserve">ab occaſu, quæ nimirum in ſ@periori
              <lb/>
            horologio indicabat horam 23. </s>
            <s xml:id="echoid-s19386" xml:space="preserve">& </s>
            <s xml:id="echoid-s19387" xml:space="preserve">ſequens, quæ erat linea horæ 22. </s>
            <s xml:id="echoid-s19388" xml:space="preserve">dabit 2. </s>
            <s xml:id="echoid-s19389" xml:space="preserve">& </s>
            <s xml:id="echoid-s19390" xml:space="preserve">ſic deinceps, aſſumẽ
              <lb/>
            do ſemper complementa horarum ſuperioris horologij vſque ad 24. </s>
            <s xml:id="echoid-s19391" xml:space="preserve">ita vt linea horæ 1. </s>
            <s xml:id="echoid-s19392" xml:space="preserve">ab occa-
              <lb/>
            ſu in horologio ſuperiori; </s>
            <s xml:id="echoid-s19393" xml:space="preserve">quæ nimirum eſt prima ſub linea horizontali in inferiori horologio, in
              <lb/>
            dicet horam 23. </s>
            <s xml:id="echoid-s19394" xml:space="preserve">ab occaſu, &</s>
            <s xml:id="echoid-s19395" xml:space="preserve">c. </s>
            <s xml:id="echoid-s19396" xml:space="preserve">Hæc autem complementa horarum non ſcripſimus in figura, ſed
              <lb/>
              <note position="left" xlink:label="note-0303-03" xlink:href="note-0303-03a" xml:space="preserve">30</note>
            cogitatione tantum intelligenda ſunt.</s>
            <s xml:id="echoid-s19397" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s19398" xml:space="preserve">ALITER. </s>
            <s xml:id="echoid-s19399" xml:space="preserve">Per doctrinam propoſ. </s>
            <s xml:id="echoid-s19400" xml:space="preserve">51. </s>
            <s xml:id="echoid-s19401" xml:space="preserve">huius libri deſcribatur arcus diurnus horarum 14. </s>
            <s xml:id="echoid-s19402" xml:space="preserve">cu
              <lb/>
              <note position="right" xlink:label="note-0303-04" xlink:href="note-0303-04a" xml:space="preserve">Alia deſcriptio
                <lb/>
              horologii Itali-
                <lb/>
              ci ęquinoctialis
                <lb/>
              per arcus diur-
                <lb/>
              nos nocturnos-
                <lb/>
              que horarum
                <lb/>
              14. & 10.</note>
            ius portio à linea horizontali abſciſſa erit arcus diurnus horarum 10. </s>
            <s xml:id="echoid-s19403" xml:space="preserve">in inferiori horologio, vel
              <lb/>
            arcus nocturnus horarum 10. </s>
            <s xml:id="echoid-s19404" xml:space="preserve">in horologio nocturno, quod idem eſt, quod horologium Inſerius,
              <lb/>
            cum portio illa horologij, quam horizontalis linea abſcindit, vtrumque horologiũ exhibeat & </s>
            <s xml:id="echoid-s19405" xml:space="preserve">
              <lb/>
            inferius, & </s>
            <s xml:id="echoid-s19406" xml:space="preserve">nocturnum, vt ex ſuperioribus perſpicuum eſt. </s>
            <s xml:id="echoid-s19407" xml:space="preserve">Si enim per horas à meridie, vel media
              <lb/>
            nocte in arcu diurno horarum 14. </s>
            <s xml:id="echoid-s19408" xml:space="preserve">& </s>
            <s xml:id="echoid-s19409" xml:space="preserve">nocturno horarum 10. </s>
            <s xml:id="echoid-s19410" xml:space="preserve">reſpondentes horis ab occaſu, vt in ta
              <lb/>
            bula 3. </s>
            <s xml:id="echoid-s19411" xml:space="preserve">& </s>
            <s xml:id="echoid-s19412" xml:space="preserve">4. </s>
            <s xml:id="echoid-s19413" xml:space="preserve">ſcholii propoſ. </s>
            <s xml:id="echoid-s19414" xml:space="preserve">33 ſuperioris lib. </s>
            <s xml:id="echoid-s19415" xml:space="preserve">videre licet, lineas rectas duxerimus, deſcriptũ erit ho-
              <lb/>
            rologium Italicum ſuperius, vt prius. </s>
            <s xml:id="echoid-s19416" xml:space="preserve">Aduertendum tamen eſt, horas ſingulas ab occaſu, ſingulas
              <lb/>
            tantum horas à meridie, vel media nocte reſpondentes habere in dictis tabulis. </s>
            <s xml:id="echoid-s19417" xml:space="preserve">Vnde vt recte duci
              <lb/>
              <note position="left" xlink:label="note-0303-05" xlink:href="note-0303-05a" xml:space="preserve">40</note>
            poſſint, ſumendæ erunt quoque horæ à meridie, vel media nocte reſpondentes eiſdem numero
              <lb/>
            horis ab ortu ex eiſdem tabulis. </s>
            <s xml:id="echoid-s19418" xml:space="preserve">Exempli gratia Hora 23. </s>
            <s xml:id="echoid-s19419" xml:space="preserve">ab occaſu ducitur per horam 6. </s>
            <s xml:id="echoid-s19420" xml:space="preserve">à meridie
              <lb/>
            in arcu diurno horarum 14. </s>
            <s xml:id="echoid-s19421" xml:space="preserve">& </s>
            <s xml:id="echoid-s19422" xml:space="preserve">quia eadem vltra. </s>
            <s xml:id="echoid-s19423" xml:space="preserve">arcum diurnum horarum 24. </s>
            <s xml:id="echoid-s19424" xml:space="preserve">qui horizontalem
              <lb/>
            lineam in puncto m, tangit, producta indicat horam 23. </s>
            <s xml:id="echoid-s19425" xml:space="preserve">ab ortu, vt in ſcholio propoſ. </s>
            <s xml:id="echoid-s19426" xml:space="preserve">10. </s>
            <s xml:id="echoid-s19427" xml:space="preserve">huius
              <lb/>
            libri docuimus; </s>
            <s xml:id="echoid-s19428" xml:space="preserve">tranſit autem hora 23. </s>
            <s xml:id="echoid-s19429" xml:space="preserve">ab ortu per horam 4. </s>
            <s xml:id="echoid-s19430" xml:space="preserve">à media nocte in arcu nocturno ho-
              <lb/>
            rarum 10. </s>
            <s xml:id="echoid-s19431" xml:space="preserve">idcirco, vt recte hora 23. </s>
            <s xml:id="echoid-s19432" xml:space="preserve">ab occaſu ducatur per horam 6. </s>
            <s xml:id="echoid-s19433" xml:space="preserve">à meridie in arcu diurno ho-
              <lb/>
            rarum 14. </s>
            <s xml:id="echoid-s19434" xml:space="preserve">accipienda etiam erit hora 4. </s>
            <s xml:id="echoid-s19435" xml:space="preserve">à media nocte reſpondens horæ 23. </s>
            <s xml:id="echoid-s19436" xml:space="preserve">ab ortu in arcu noctur
              <lb/>
            no horarum 10. </s>
            <s xml:id="echoid-s19437" xml:space="preserve">Eodem pacto hora 22. </s>
            <s xml:id="echoid-s19438" xml:space="preserve">ab occaſu ducitur per horam 5. </s>
            <s xml:id="echoid-s19439" xml:space="preserve">à meridie in arcu diurno
              <lb/>
            horarum 14. </s>
            <s xml:id="echoid-s19440" xml:space="preserve">& </s>
            <s xml:id="echoid-s19441" xml:space="preserve">per horam 3. </s>
            <s xml:id="echoid-s19442" xml:space="preserve">à media nocte in arcu nocturno horarum 10. </s>
            <s xml:id="echoid-s19443" xml:space="preserve">quæ horæ 22. </s>
            <s xml:id="echoid-s19444" xml:space="preserve">ab ortu
              <lb/>
            correſpondet. </s>
            <s xml:id="echoid-s19445" xml:space="preserve">Sic quoque (vt rem totam paucis complectar) hora 11. </s>
            <s xml:id="echoid-s19446" xml:space="preserve">ab occaſu incedit per horam
              <lb/>
              <note position="left" xlink:label="note-0303-06" xlink:href="note-0303-06a" xml:space="preserve">50</note>
            6. </s>
            <s xml:id="echoid-s19447" xml:space="preserve">à media nocte in arcu diurno horarum 14. </s>
            <s xml:id="echoid-s19448" xml:space="preserve">& </s>
            <s xml:id="echoid-s19449" xml:space="preserve">per horam 4. </s>
            <s xml:id="echoid-s19450" xml:space="preserve">à meridie in eodem arcu, quæ horæ
              <lb/>
            11. </s>
            <s xml:id="echoid-s19451" xml:space="preserve">ab ortu reſpondet. </s>
            <s xml:id="echoid-s19452" xml:space="preserve">Item hora 1. </s>
            <s xml:id="echoid-s19453" xml:space="preserve">ab occaſu ducta eſt per horam 8. </s>
            <s xml:id="echoid-s19454" xml:space="preserve">à meridie in arcu nocturno
              <lb/>
            horarum 10. </s>
            <s xml:id="echoid-s19455" xml:space="preserve">& </s>
            <s xml:id="echoid-s19456" xml:space="preserve">per horam 6. </s>
            <s xml:id="echoid-s19457" xml:space="preserve">à media nocte in arcu diurno horarum 14. </s>
            <s xml:id="echoid-s19458" xml:space="preserve">horæ 1. </s>
            <s xml:id="echoid-s19459" xml:space="preserve">ab ortu re-
              <lb/>
            ſpondentem, &</s>
            <s xml:id="echoid-s19460" xml:space="preserve">c.</s>
            <s xml:id="echoid-s19461" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">Quomodo In-
            <lb/>
          ferius horolo-
            <lb/>
          gium Italicum
            <lb/>
          ex ſuperiori col
            <lb/>
          ligatur.</note>
          <p>
            <s xml:id="echoid-s19462" xml:space="preserve">NON aliter horologium Italicum inferius conficiemus. </s>
            <s xml:id="echoid-s19463" xml:space="preserve">Sed ſatius erit illud ex ſuperiori col-
              <lb/>
            ligere. </s>
            <s xml:id="echoid-s19464" xml:space="preserve">Nam horæ ab occaſu ſuperioris horologij productæ vltra lineam horizõtalem dabunt eaſ-
              <lb/>
            dem numero horas ab occaſu in inferiori horologio, ſi tamen omnes eius partes inuertantur, vt
              <lb/>
            in ſuperioribus dictum eſt, & </s>
            <s xml:id="echoid-s19465" xml:space="preserve">demonſtratum in ſcholio propoſ. </s>
            <s xml:id="echoid-s19466" xml:space="preserve">14. </s>
            <s xml:id="echoid-s19467" xml:space="preserve">huius libri.</s>
            <s xml:id="echoid-s19468" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">Eiuſdem horo-
            <lb/>
          logii@ Italici æ-
            <lb/>
          quinoctialis de
            <lb/>
          ſcriptio, per ar-
            <lb/>
          cum diurnum
            <lb/>
          horarum 24.</note>
          <p>
            <s xml:id="echoid-s19469" xml:space="preserve">FACILI quoque negotio idem Italicum horologium abſoluemus per arcum diurnum ho-
              <lb/>
            rarum 24. </s>
            <s xml:id="echoid-s19470" xml:space="preserve">ſeu parallelum omnium ſemper apparentium maximum, qui horizontalem lineam
              <lb/>
            tangit in m, eſtq; </s>
            <s xml:id="echoid-s19471" xml:space="preserve">in inferiori horologio arcus nocturnus horarum 24. </s>
            <s xml:id="echoid-s19472" xml:space="preserve">ſiue parallelus ſemper </s>
          </p>
        </div>
      </text>
    </echo>
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