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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[241.] PROBLEMA 55. PROPOSITIO 55.
[242.] PROBLEMA 56. PROPOSITIO 56.
[243.] SCHOLIVM.
[244.] PROBLEMA 57. PROPOSITIO 57.
[245.] SCHOLIVM.
[246.] PROBLEMA 58. PROPOSITIO 58. HOROLOGIVM Italicum æquinoctiale conſtruere.
[247.] PROBLEMA 59. PROPOSITIO 59. HOROLOGIVM Babylonicum ęquinoctiale componere.
[248.] SCHOLIVM.
[249.] PROBLEMA 60. PROPOSITIO 60. HOROLOGIVM Antiquum æquinoctiale conſtituere.
[250.] SCHOLIVM.
[251.] FINIS SECVNDI LIBRI.
[252.] GNOMONICES LIBER TERTIVS.
[253.] AVCTORE CHRISTOPHORO CLAVIO BAMBER GENSI SOCIETATIS IESV.
[254.] DE HOROLOGIIS, QVAE A VER-ticali circulo declinant. PROBLEMA 1. PROPOSITIO 1.
[255.] SCHOLIVM.
[256.] PROBLEMA 2. PROPOSITIO 2.
[257.] SCHOLIVM.
[258.] PROBLEMA 3. PROPOSITIO 3.
[259.] SCHOLIVM.
[260.] PROBLEMA 4. PROPOSITIO 4.
[261.] SCHOLIVM.
[262.] PROBLEMA 5. PROPOSITIO 5.
[263.] PROBLEMA 6. PROPOSITIO 6.
[264.] PROBLEMA 7. PROPOSITIO 7.
[265.] PROBLEMA 8. PROPOSITIO 8.
[266.] PROBLEMA 9. PROPOSITIO 9.
[267.] SCHOLIVM.
[268.] PROBLEMA 10. PROPOSITIO 10.
[269.] PROBLEMA 11. PROPOSITIO 11.
[270.] SCHOLIVM.
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          <p>
            <s xml:id="echoid-s22021" xml:space="preserve">
              <pb o="331" file="0347" n="347" rhead="LIBER TERTIVS."/>
            ctiones mutuas horarum à meridie, vel media nocte, & </s>
            <s xml:id="echoid-s22022" xml:space="preserve">ab ortu, vel occaſu in linea horizontali,
              <lb/>
            vel linea horæ 12. </s>
            <s xml:id="echoid-s22023" xml:space="preserve">ab ortu, vel occaſu, & </s>
            <s xml:id="echoid-s22024" xml:space="preserve">c. </s>
            <s xml:id="echoid-s22025" xml:space="preserve">abſoluuntur, nulla difficultas prorſus eſt, ſi attentè conſi
              <lb/>
            derentur tabulæ propoſ. </s>
            <s xml:id="echoid-s22026" xml:space="preserve">19. </s>
            <s xml:id="echoid-s22027" xml:space="preserve">20. </s>
            <s xml:id="echoid-s22028" xml:space="preserve">& </s>
            <s xml:id="echoid-s22029" xml:space="preserve">23. </s>
            <s xml:id="echoid-s22030" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s22031" xml:space="preserve">1. </s>
            <s xml:id="echoid-s22032" xml:space="preserve">ſæpius iam adductæ. </s>
            <s xml:id="echoid-s22033" xml:space="preserve">Nam (vt aliquod exemplum
              <lb/>
            habeas) hora 11. </s>
            <s xml:id="echoid-s22034" xml:space="preserve">ab occaſu ducitur per horam 6. </s>
            <s xml:id="echoid-s22035" xml:space="preserve">à media nocte in arcu, diurno horarum 14. </s>
            <s xml:id="echoid-s22036" xml:space="preserve">& </s>
            <s xml:id="echoid-s22037" xml:space="preserve">
              <lb/>
            per 5. </s>
            <s xml:id="echoid-s22038" xml:space="preserve">à media nocte in arcu nocturno horarum 12. </s>
            <s xml:id="echoid-s22039" xml:space="preserve">nec non per horam 4. </s>
            <s xml:id="echoid-s22040" xml:space="preserve">à media nocte in arcu
              <lb/>
            nocturno herarum 14. </s>
            <s xml:id="echoid-s22041" xml:space="preserve">Ita quoque hora 20. </s>
            <s xml:id="echoid-s22042" xml:space="preserve">ab occaſu tranſit per horam 1. </s>
            <s xml:id="echoid-s22043" xml:space="preserve">à meridie in arcu diur-
              <lb/>
            no horarum 10. </s>
            <s xml:id="echoid-s22044" xml:space="preserve">& </s>
            <s xml:id="echoid-s22045" xml:space="preserve">per horam 2. </s>
            <s xml:id="echoid-s22046" xml:space="preserve">à meridie in arcu diurno horarum 12. </s>
            <s xml:id="echoid-s22047" xml:space="preserve">Hora verò 21. </s>
            <s xml:id="echoid-s22048" xml:space="preserve">ab occaſu,
              <lb/>
            quæ vnum ſolum in noſtro exemplo punctum habet, qnod eſt in hora 2. </s>
            <s xml:id="echoid-s22049" xml:space="preserve">à meridie arcus diurni
              <lb/>
            horarum 10. </s>
            <s xml:id="echoid-s22050" xml:space="preserve">per quod tranſit, habebitur, ſi hora 21. </s>
            <s xml:id="echoid-s22051" xml:space="preserve">ab ortu ducatur per horam 4. </s>
            <s xml:id="echoid-s22052" xml:space="preserve">à media nocte
              <lb/>
            in arcu nocturno horarum 14. </s>
            <s xml:id="echoid-s22053" xml:space="preserve">& </s>
            <s xml:id="echoid-s22054" xml:space="preserve">per horam 2. </s>
            <s xml:id="echoid-s22055" xml:space="preserve">à meridie in arcu diurno horarum 10. </s>
            <s xml:id="echoid-s22056" xml:space="preserve">extenda-
              <lb/>
              <note position="left" xlink:label="note-0347-01" xlink:href="note-0347-01a" xml:space="preserve">10</note>
            tur. </s>
            <s xml:id="echoid-s22057" xml:space="preserve">Sic etiam pro hora 22. </s>
            <s xml:id="echoid-s22058" xml:space="preserve">ab occaſu ducenda erit hora 22. </s>
            <s xml:id="echoid-s22059" xml:space="preserve">ab ortu per horam 5. </s>
            <s xml:id="echoid-s22060" xml:space="preserve">à media nocte
              <lb/>
            in arcu nocturno horarum 14. </s>
            <s xml:id="echoid-s22061" xml:space="preserve">& </s>
            <s xml:id="echoid-s22062" xml:space="preserve">per horam 4. </s>
            <s xml:id="echoid-s22063" xml:space="preserve">à media nocte in arcu nocturno horarum 12. </s>
            <s xml:id="echoid-s22064" xml:space="preserve">Hæc
              <lb/>
            enim producta vltra parallelum omnium ſemper latentium maximum, qui per punctum K, du-
              <lb/>
            citur, dabit 22. </s>
            <s xml:id="echoid-s22065" xml:space="preserve">ab occaſu. </s>
            <s xml:id="echoid-s22066" xml:space="preserve">Eadem denique ratione pro hora 23. </s>
            <s xml:id="echoid-s22067" xml:space="preserve">ab occaſu ducenda erit hora 23.
              <lb/>
            </s>
            <s xml:id="echoid-s22068" xml:space="preserve">ab ortu per horam 6. </s>
            <s xml:id="echoid-s22069" xml:space="preserve">à media nocte in arcu nocturno horarum 14. </s>
            <s xml:id="echoid-s22070" xml:space="preserve">& </s>
            <s xml:id="echoid-s22071" xml:space="preserve">per horam 5. </s>
            <s xml:id="echoid-s22072" xml:space="preserve">à media no-
              <lb/>
            cte in arcu nocturno horarum 12. </s>
            <s xml:id="echoid-s22073" xml:space="preserve">& </s>
            <s xml:id="echoid-s22074" xml:space="preserve">c. </s>
            <s xml:id="echoid-s22075" xml:space="preserve">Linea autem horæ 12. </s>
            <s xml:id="echoid-s22076" xml:space="preserve">ab ortu, vel occaſu (ſi ſorte in de-
              <lb/>
            ſcriptione horologii Italici vti voles tabula ſecunda propoſ. </s>
            <s xml:id="echoid-s22077" xml:space="preserve">20. </s>
            <s xml:id="echoid-s22078" xml:space="preserve">primi libri, quæ ad horam 12. </s>
            <s xml:id="echoid-s22079" xml:space="preserve">@ab
              <lb/>
            ortu vel occaſu pertinet) ducenda eſt per punctum, vbi linea æquinoctialis, horizontalis, & </s>
            <s xml:id="echoid-s22080" xml:space="preserve">horæ
              <lb/>
            6 à meridie, vel média nocte ſe mutuo interſecant, & </s>
            <s xml:id="echoid-s22081" xml:space="preserve">per punctum lineæ horæ 12. </s>
            <s xml:id="echoid-s22082" xml:space="preserve">à meridie, per
              <lb/>
              <note position="left" xlink:label="note-0347-02" xlink:href="note-0347-02a" xml:space="preserve">20</note>
            quod arcus diurnus horarum o, hoc eſt, parallelus omnium ſemper latentium maximus tranſit,
              <lb/>
            vt patet ex tabulis 5. </s>
            <s xml:id="echoid-s22083" xml:space="preserve">6. </s>
            <s xml:id="echoid-s22084" xml:space="preserve">& </s>
            <s xml:id="echoid-s22085" xml:space="preserve">8. </s>
            <s xml:id="echoid-s22086" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s22087" xml:space="preserve">33. </s>
            <s xml:id="echoid-s22088" xml:space="preserve">primi libri. </s>
            <s xml:id="echoid-s22089" xml:space="preserve">Hoc porro punctum inueniemus, ſi ex figura
              <lb/>
            radiorum propoſ. </s>
            <s xml:id="echoid-s22090" xml:space="preserve">2. </s>
            <s xml:id="echoid-s22091" xml:space="preserve">huius libri lineam horæ 12. </s>
            <s xml:id="echoid-s22092" xml:space="preserve">mediæ noctis, vel poſt meridiem, quæ ex C, duci
              <lb/>
            tur ad dextram rectæ C A, interceptam inter C, & </s>
            <s xml:id="echoid-s22093" xml:space="preserve">radium horarum o, transferamus ex C, centro
              <lb/>
            horologii in lineam meridianam ſupra centrum C. </s>
            <s xml:id="echoid-s22094" xml:space="preserve">Portio enim lineæ meridianæ ſupra centrum
              <lb/>
            C, ad mediam noctem pertinet, ita vt indicet horam 12. </s>
            <s xml:id="echoid-s22095" xml:space="preserve">à meridie. </s>
            <s xml:id="echoid-s22096" xml:space="preserve">In noſtro exemplo ægrè
              <lb/>
            admodum huiuſinodi punctum reperiri poteſt, vt patet. </s>
            <s xml:id="echoid-s22097" xml:space="preserve">Horologium igitur Italicum à Vertica-
              <lb/>
            li circulo declinans deſcripſimus. </s>
            <s xml:id="echoid-s22098" xml:space="preserve">Quod faciendum erat.</s>
            <s xml:id="echoid-s22099" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1126" type="section" level="1" n="269">
          <head xml:id="echoid-head278" xml:space="preserve">PROBLEMA 11. PROPOSITIO 11.</head>
          <note position="left" xml:space="preserve">30</note>
          <p>
            <s xml:id="echoid-s22100" xml:space="preserve">HOROLOGIVM Babylonicum à Verticali circulo declinans
              <lb/>
            delineare.</s>
            <s xml:id="echoid-s22101" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s22102" xml:space="preserve">VT Italicum horologium, ita & </s>
            <s xml:id="echoid-s22103" xml:space="preserve">Babylonicum deſcribitur, hoc excepto, quòd in priori modo
              <lb/>
              <note position="right" xlink:label="note-0347-04" xlink:href="note-0347-04a" xml:space="preserve">Deſcriptio ho-
                <lb/>
              rologii Babylo
                <lb/>
              nici à Vertica-
                <lb/>
              li deelinantie.</note>
            diuiſio circuli in partes 24. </s>
            <s xml:id="echoid-s22104" xml:space="preserve">æquales principiũ habere debet à punctis b, e, quæ orientalia ſunt, vt
              <lb/>
            patet, ſi horologiom, & </s>
            <s xml:id="echoid-s22105" xml:space="preserve">circulus in propria poſitione concipiantur eſſe collocata; </s>
            <s xml:id="echoid-s22106" xml:space="preserve">ita vt puncta b, e,
              <lb/>
            ſignificent horam 24. </s>
            <s xml:id="echoid-s22107" xml:space="preserve">& </s>
            <s xml:id="echoid-s22108" xml:space="preserve">proxima puncta verſus N, horam 1. </s>
            <s xml:id="echoid-s22109" xml:space="preserve">ab ortu, & </s>
            <s xml:id="echoid-s22110" xml:space="preserve">c.</s>
            <s xml:id="echoid-s22111" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s22112" xml:space="preserve">IN alijs modis res omnino facilis eſt, ex tabulis propoſ. </s>
            <s xml:id="echoid-s22113" xml:space="preserve">19. </s>
            <s xml:id="echoid-s22114" xml:space="preserve">20. </s>
            <s xml:id="echoid-s22115" xml:space="preserve">& </s>
            <s xml:id="echoid-s22116" xml:space="preserve">33. </s>
            <s xml:id="echoid-s22117" xml:space="preserve">primi libri, quarum fre-
              <lb/>
            quens mentio facta eſt hactenus. </s>
            <s xml:id="echoid-s22118" xml:space="preserve">Id quod figuta præcedentis propoſ. </s>
            <s xml:id="echoid-s22119" xml:space="preserve">apertè declarat, in qua horæ
              <lb/>
              <note position="left" xlink:label="note-0347-05" xlink:href="note-0347-05a" xml:space="preserve">40</note>
            punctis ſolum diſtinctæ numerantur à meridie, vel media nocte, quæ verò characteres numero-
              <lb/>
            rum habent communes, ab occaſu; </s>
            <s xml:id="echoid-s22120" xml:space="preserve">quæ denique characteribus numerorum antiquis inſignitæ
              <lb/>
            ſunt, ab ortu Solis. </s>
            <s xml:id="echoid-s22121" xml:space="preserve">Igitur horologium Babylonicum à Verticali circulo declinans delineaui-
              <lb/>
            mus. </s>
            <s xml:id="echoid-s22122" xml:space="preserve">Quod faciendum erat.</s>
            <s xml:id="echoid-s22123" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1129" type="section" level="1" n="270">
          <head xml:id="echoid-head279" style="it" xml:space="preserve">SCHOLIVM.</head>
          <p style="it">
            <s xml:id="echoid-s22124" xml:space="preserve">SI horæ ab ortu, & </s>
            <s xml:id="echoid-s22125" xml:space="preserve">occaſu vltra lineam horizontalem producantur in horologio, quod à meridic de-
              <lb/>
            clinat, habebimus eaſdem horas in facie plani oppoſita, quæ à borea declinat, ſi partium cõmutatio fiat,
              <lb/>
            vt in ſuperioribus diximus.</s>
            <s xml:id="echoid-s22126" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">50</note>
          <p style="it">
            <s xml:id="echoid-s22127" xml:space="preserve">QVEMADMODVM autem ad finem ſcholii propoſ. </s>
            <s xml:id="echoid-s22128" xml:space="preserve">1. </s>
            <s xml:id="echoid-s22129" xml:space="preserve">huius libri ſcripſimus, vna opera de-
              <lb/>
            ſcribi poſſe quatuor horologia aſtronomica diuerſa, quæ eandem tamen declinationis quantitatem ſeruẽt;
              <lb/>
            </s>
            <s xml:id="echoid-s22130" xml:space="preserve">Ita etiam de horologio Italico, & </s>
            <s xml:id="echoid-s22131" xml:space="preserve">Babylonico dicendum est. </s>
            <s xml:id="echoid-s22132" xml:space="preserve">Nam ſi v. </s>
            <s xml:id="echoid-s22133" xml:space="preserve">g. </s>
            <s xml:id="echoid-s22134" xml:space="preserve">deſcribamus horologium Ita-
              <lb/>
              <note position="right" xlink:label="note-0347-07" xlink:href="note-0347-07a" xml:space="preserve">Qua ratione ex
                <lb/>
              horologio Itali
                <lb/>
              co vel Babylo-
                <lb/>
              nico declipan-
                <lb/>
              te à merldie in
                <lb/>
              ortũ fiat aliud
                <lb/>
              declinans à bo
                <lb/>
              ica in ortum,
                <lb/>
              & à meridiei in
                <lb/>
              occaſum, & à
                <lb/>
              borea in occa-
                <lb/>
              ſum.</note>
            licum, vel Babylonicum declinans à meridie in ortum grad. </s>
            <s xml:id="echoid-s22135" xml:space="preserve">30. </s>
            <s xml:id="echoid-s22136" xml:space="preserve">quale hactenus à nobis conſtructum eſt,
              <lb/>
            habebimus codem labore Italicum horologium, vel Babylonicum declinans 30. </s>
            <s xml:id="echoid-s22137" xml:space="preserve">grad. </s>
            <s xml:id="echoid-s22138" xml:space="preserve">à borea in ortum,
              <lb/>
            quale eſt nocturnum illud, quod linea horizontalis abſcindit, ſi partem illius ſuperiorem commutemus in
              <lb/>
            inferiorem: </s>
            <s xml:id="echoid-s22139" xml:space="preserve">ſed numeri horarum mutandi ſunt in earum complementa vſque ad 24. </s>
            <s xml:id="echoid-s22140" xml:space="preserve">ita vt ex hora 11.
              <lb/>
            </s>
            <s xml:id="echoid-s22141" xml:space="preserve">ab occaſu in portione nocturna fiat hora 13. </s>
            <s xml:id="echoid-s22142" xml:space="preserve">ab occaſu in horologio declinante à borea in ortum; </s>
            <s xml:id="echoid-s22143" xml:space="preserve">& </s>
            <s xml:id="echoid-s22144" xml:space="preserve">ex
              <lb/>
            23. </s>
            <s xml:id="echoid-s22145" xml:space="preserve">ab ortu ſiat 1. </s>
            <s xml:id="echoid-s22146" xml:space="preserve">ab ortu, & </s>
            <s xml:id="echoid-s22147" xml:space="preserve">c. </s>
            <s xml:id="echoid-s22148" xml:space="preserve">Si verò idem horologium à meridie declinans in ortum quotcunque gra-
              <lb/>
            dibus ita inuertamus, vt pars eius dextra ſiat ſiniſtra, & </s>
            <s xml:id="echoid-s22149" xml:space="preserve">contra, non mutata parte eius ſuperiore in in-
              <lb/>
            feriorem, habebimus horologium declinans totidem gradibus à meridie in occaſum, ſed numeri </s>
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