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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[121.] COROLLARIVM.
Page: 112 (92)
[122.] PROBLEMA 6. PROPOSITIO 27.
Page: 113 (93)
[123.] PROBLEMA. 7. PROPOSITIO 28.
Page: 113 (93)
[124.] SCHOLIVM I.
Page: 115 (95)
[125.] COROLLARIVM.
Page: 115 (95)
[126.] SCHOLIVM II.
Page: 116 (96)
[127.] PROBLEMA 8. PROPOSITIO 29.
Page: 119 (99)
[128.] PROBLEMA. 9. PROPOSITIO 30.
Page: 121 (101)
[129.] PROBLEMA 10. PROPOSITIO 31.
Page: 123 (103)
[130.] PROBLEMA 11. PROPOSITIO 32.
Page: 125 (105)
[131.] SCHOLIVM.
Page: 125 (105)
[132.] PROBLEMA 12. PROPOSITIO 33.
Page: 126 (106)
[133.] SCHOLIVM.
Page: 129 (109)
[134.] PROBLEMA 13. PROPOSITIO 34.
Page: 134 (114)
[135.] SCHOLIVM.
Page: 137 (117)
[136.] PROBLEMA 14. PROPOSITIO 35.
Page: 138 (118)
[137.] SCHOLIVM.
Page: 140 (120)
[138.] PROBLEMA 15. PROPOSITIO 36.
Page: 144 (124)
[139.] SCHOLIVM.
Page: 158 (138)
[140.] FINIS PRIMI LIBRI.
Page: 160 (140)
[141.] GNOMONICES LIBER SECVNDVS.
Page: 161 (141)
[142.] AVCTORE CHRISTOPHORO CLAVIO BAMBER GENSI SOCIETATIS IESV.
Page: 161 (141)
[143.] DE HOROLOGIIS HORIZONTALIBVS. PROBLEMA 1. PROPOSITIO 1.
Page: 162 (142)
[144.] SCHOLIVM.
Page: 165 (145)
[145.] PROBLEMA 2. PROPOSITIO 2.
Page: 177 (157)
[146.] SCHOLIVM.
Page: 186 (166)
[147.] PROBLEMA 3. PROPOSITIO 3.
Page: 189 (169)
[148.] SCHOLIVM.
Page: 190 (170)
[149.] PROBLEMA. 4. PROPOSITIO 4.
Page: 190 (170)
[150.] SCHOLIVM.
Page: 191 (171)
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          <p>
            <s xml:id="echoid-s9313" xml:space="preserve">
              <pb o="145" file="0165" n="165" rhead="LIBER SECVNDVS."/>
            cumferentiam Aequatoris, initio facto à Meridiano, in totidem partes æquales: </s>
            <s xml:id="echoid-s9314" xml:space="preserve">Ac propterea, cũ
              <lb/>
            circuli horarum à meridie, vel media nocte eundem Aequatorem diuidant in partes 24. </s>
            <s xml:id="echoid-s9315" xml:space="preserve">æquales,
              <lb/>
            initio quoque facto à Meridiano, vt patet ex propoſ. </s>
            <s xml:id="echoid-s9316" xml:space="preserve">9. </s>
            <s xml:id="echoid-s9317" xml:space="preserve">ſuperioris lib. </s>
            <s xml:id="echoid-s9318" xml:space="preserve">efficitur, vt eędem rectę oc-
              <lb/>
            cultę è centro E, egredientes ſint communes ſectiones Aequatoris, & </s>
            <s xml:id="echoid-s9319" xml:space="preserve">circulorum horariorũ, qui
              <lb/>
            horas à mer. </s>
            <s xml:id="echoid-s9320" xml:space="preserve">vel med. </s>
            <s xml:id="echoid-s9321" xml:space="preserve">noc. </s>
            <s xml:id="echoid-s9322" xml:space="preserve">indicant; </s>
            <s xml:id="echoid-s9323" xml:space="preserve">nempe N M, communis ſectio Aequatoris, & </s>
            <s xml:id="echoid-s9324" xml:space="preserve">circuli horę 12.
              <lb/>
            </s>
            <s xml:id="echoid-s9325" xml:space="preserve">hoc eſt, Meridiani; </s>
            <s xml:id="echoid-s9326" xml:space="preserve">O P, Aequatoris, & </s>
            <s xml:id="echoid-s9327" xml:space="preserve">circuli horę primę à meridie, vel media nocte; </s>
            <s xml:id="echoid-s9328" xml:space="preserve">Q R, Aequa
              <lb/>
            toris, & </s>
            <s xml:id="echoid-s9329" xml:space="preserve">circuli horę 2. </s>
            <s xml:id="echoid-s9330" xml:space="preserve">à meridie vel media nocte; </s>
            <s xml:id="echoid-s9331" xml:space="preserve">S T, Aequatoris, & </s>
            <s xml:id="echoid-s9332" xml:space="preserve">circuli horę 3. </s>
            <s xml:id="echoid-s9333" xml:space="preserve">à meridie,
              <lb/>
            vel media nocte, &</s>
            <s xml:id="echoid-s9334" xml:space="preserve">c. </s>
            <s xml:id="echoid-s9335" xml:space="preserve">vt patet, ſi circulus ex E, deſcriptus in propria poſitione intelligatur. </s>
            <s xml:id="echoid-s9336" xml:space="preserve">Vergent
              <lb/>
            enim puncta O, Q, S, in hemiſphærio ſupero ad partes occidentales, ſeu pomeridianas, &</s>
            <s xml:id="echoid-s9337" xml:space="preserve">c.</s>
            <s xml:id="echoid-s9338" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9339" xml:space="preserve">QVARE circuli horarij à meridie, vel media nocte ſecant in plano horologii rectam F K,
              <lb/>
              <note position="left" xlink:label="note-0165-01" xlink:href="note-0165-01a" xml:space="preserve">10</note>
            in punctis I, A, B, &</s>
            <s xml:id="echoid-s9340" xml:space="preserve">c. </s>
            <s xml:id="echoid-s9341" xml:space="preserve">(quæ quidem puncta non variantur, etiamſi planum circuli circa E, deſcri
              <lb/>
            pti aliam poſitionem habeat, nempe in plano horologii, in quo ipſum deſcripſimus, exiſtat. </s>
            <s xml:id="echoid-s9342" xml:space="preserve">Nam
              <lb/>
            ſi planum huius circuli circumuertatur circa rectam F K, tanguam cardinem immobilem, ita vt
              <lb/>
            recta I E, ſemper perpendicularis ſit ad F K, occurrent recte N E, O E, Q E, & </s>
            <s xml:id="echoid-s9343" xml:space="preserve">c. </s>
            <s xml:id="echoid-s9344" xml:space="preserve">in eiſdem ſemper
              <lb/>
            punctis ęquinoctiali lineę F K, vt perſpicuum eſt) ac idcirco per hęc puncta incedent communes
              <lb/>
            ſectiones illorum circulorum horariorum, & </s>
            <s xml:id="echoid-s9345" xml:space="preserve">plani horologij, quæ quidem ſunt lineę horarię à
              <lb/>
            meridie, vel media nocte; </s>
            <s xml:id="echoid-s9346" xml:space="preserve">Atqui per corollar. </s>
            <s xml:id="echoid-s9347" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s9348" xml:space="preserve">21. </s>
            <s xml:id="echoid-s9349" xml:space="preserve">præcedentis lib. </s>
            <s xml:id="echoid-s9350" xml:space="preserve">eędem communes ſe-
              <lb/>
            ctiones, ſeu lineæ horarię, ſecant ſe mutuo in horologij centro H, in quo axis D H, plano horolo-
              <lb/>
            gij occurrit. </s>
            <s xml:id="echoid-s9351" xml:space="preserve">Igitur rectę per puncta I, A, B, &</s>
            <s xml:id="echoid-s9352" xml:space="preserve">c. </s>
            <s xml:id="echoid-s9353" xml:space="preserve">æquinoctialis lineę F k, & </s>
            <s xml:id="echoid-s9354" xml:space="preserve">per punctum H, ſeu cen
              <lb/>
            trum horologij, emiſſę ſunt lineę horarũ à meridie, vel media nocte, ita vt meridiana linea H I E,
              <lb/>
              <note position="left" xlink:label="note-0165-02" xlink:href="note-0165-02a" xml:space="preserve">20</note>
            indicet horam 12. </s>
            <s xml:id="echoid-s9355" xml:space="preserve">meridiei, & </s>
            <s xml:id="echoid-s9356" xml:space="preserve">lineę ad ſiniſtram illius monſtrent horas à meridie; </s>
            <s xml:id="echoid-s9357" xml:space="preserve">lineę verò ad
              <lb/>
            dexteram horas à media nocte, vt in ſigura apparet, & </s>
            <s xml:id="echoid-s9358" xml:space="preserve">in ſcholio ſequenti declarabimus.</s>
            <s xml:id="echoid-s9359" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9360" xml:space="preserve">SOLA linea horę 6. </s>
            <s xml:id="echoid-s9361" xml:space="preserve">ducenda eſt per H, perpendicularis ad H I, vel ęquidiſtans ipſi F k, qua-
              <lb/>
            lis eſt C L. </s>
            <s xml:id="echoid-s9362" xml:space="preserve">Cum enim, vt in ſcholio propoſ. </s>
            <s xml:id="echoid-s9363" xml:space="preserve">22. </s>
            <s xml:id="echoid-s9364" xml:space="preserve">ſuperioris lib. </s>
            <s xml:id="echoid-s9365" xml:space="preserve">docuimus, in horologio horizon-
              <lb/>
            tali parallelæ ſint linea ęquinoctialis, & </s>
            <s xml:id="echoid-s9366" xml:space="preserve">linea horę ſextę à meridie, vel media nocte, perſpicuum
              <lb/>
            eſt, rectam C L, lineam eſſe horę ſextę à meridie, vel media nocte, quandoquidem parallela eſt
              <lb/>
            ęquinoctiali lineę F K, tranſitq́; </s>
            <s xml:id="echoid-s9367" xml:space="preserve">per punctum H, vbi omnes horarię lineę à meridie, vel media
              <lb/>
            nocte ſe interſecant. </s>
            <s xml:id="echoid-s9368" xml:space="preserve">Horologium igitur Aſtronomicum horizontale conſtituimus, &</s>
            <s xml:id="echoid-s9369" xml:space="preserve">c. </s>
            <s xml:id="echoid-s9370" xml:space="preserve">Quod
              <lb/>
            faciendum erat.</s>
            <s xml:id="echoid-s9371" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div524" type="section" level="1" n="144">
          <head xml:id="echoid-head147" style="it" xml:space="preserve">SCHOLIVM.</head>
          <note position="left" xml:space="preserve">30</note>
          <note position="right" xml:space="preserve">Alia deſcriptio
            <lb/>
          horologii Aſtro
            <lb/>
          nomici horizõ-
            <lb/>
          talis, commodiſ
            <lb/>
          ſima pro horis
            <lb/>
          deli@eãdis, quæ
            <lb/>
          propinquæ ſunt
            <lb/>
          hotæ 6. à mer.
            <lb/>
          vel med. noc.</note>
          <p style="it">
            <s xml:id="echoid-s9372" xml:space="preserve">ANDREAS Schonerus proponit aliam rationem horarum à meridie, vel media nocte deſcriben-
              <lb/>
            darum, quæ per commoda eſt pro illis horis delineandis, quæ æquinoctialem lineam in punctis valde remo
              <lb/>
            tis ſecant, quales ſunt horæ, quæ propinquæ ſunt horæ ſextæ à mer. </s>
            <s xml:id="echoid-s9373" xml:space="preserve">vel med. </s>
            <s xml:id="echoid-s9374" xml:space="preserve">noc. </s>
            <s xml:id="echoid-s9375" xml:space="preserve">Ea autem est huiuſmodi.
              <lb/>
            </s>
            <s xml:id="echoid-s9376" xml:space="preserve">In æquinoctiali linea F k, ſumatur recta I a, æqualis rectæ I E, vel I D, & </s>
            <s xml:id="echoid-s9377" xml:space="preserve">per a, ducatur ad ęquinoctia-
              <lb/>
            lem lineam perpendicularis a b, vel ipſi H I, parallela ſecans lineam horæ ſextæ C L, (quæ ſemper ex
              <lb/>
            H, centro horologij ducitur perpendicularis ad H I, vel parallela lineæ ęquinoctiali, vt oſtenſum eſt) in b. </s>
            <s xml:id="echoid-s9378" xml:space="preserve">
              <lb/>
            Sumpta deinde b d, æquali ipſi a b, ducatur per d, ad b d, perpendicularis e f, vel parallela ipſi H I. </s>
            <s xml:id="echoid-s9379" xml:space="preserve">
              <lb/>
            Poſtremo ex d, centro deſcripto circulo, eo{q́ue} in partes 24. </s>
            <s xml:id="echoid-s9380" xml:space="preserve">diuiſo, initio facto à recta b d, ducantur ex d,
              <lb/>
              <note position="right" xlink:label="note-0165-05" xlink:href="note-0165-05a" xml:space="preserve">Segmenta æqui
                <lb/>
              noctialis lineæ
                <lb/>
              in horologio ho
                <lb/>
              rizontali inter
                <lb/>
              lineam meridia
                <lb/>
              nam, & binas
                <lb/>
              horas vtrinque
                <lb/>
              à meridie æqua
                <lb/>
              li temporis ſpa-
                <lb/>
              lio diſtãtes, ſunt
                <lb/>
              æqualia.</note>
            centro per diuiſionum puncta lineæ occultæ. </s>
            <s xml:id="echoid-s9381" xml:space="preserve">Hæ enim rectam a b, ſecabunt in punctis, per quæ ſi ex H,
              <lb/>
              <note position="left" xlink:label="note-0165-06" xlink:href="note-0165-06a" xml:space="preserve">40</note>
            centro horologij rectæ emittantur, dabunt hæ, vt prius, horas à meridie, vel media nocte.</s>
            <s xml:id="echoid-s9382" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s9383" xml:space="preserve">IN horologio porrò quouis horizontali binæ lineæ quęcunque horariæ hinc inde à meridiana linea
              <lb/>
            æquali temporis ſpatio remotæ auferunt ex linea ęquinoctiali F K, lineas æquales, illas nimirum, quæ in-
              <lb/>
            ter lineas borarias, & </s>
            <s xml:id="echoid-s9384" xml:space="preserve">meridianam lineam interijciuntur. </s>
            <s xml:id="echoid-s9385" xml:space="preserve">Vt lineæ H F, H K, quarum vtraque quin-
              <lb/>
            que horis à meridiana linea diſtat, auferunt lineas I F, I K, æquales. </s>
            <s xml:id="echoid-s9386" xml:space="preserve">Cum enim anguli I E F, I E k, qui
              <lb/>
            continentur ſub linea meridiana, & </s>
            <s xml:id="echoid-s9387" xml:space="preserve">rectis occultis ex E, ad F, K, ductis, (licet enim E F, ducta non
              <lb/>
            ſit, eam tamen ductam eſſe concipiendum eſt) æquales ſint, quòd in centro E, ab æqualibus arcubus circuli
              <lb/>
              <note position="right" xlink:label="note-0165-07" xlink:href="note-0165-07a" xml:space="preserve">27. tertij.</note>
            ex E, deſcripti ſubtendantur, & </s>
            <s xml:id="echoid-s9388" xml:space="preserve">anguli ad I, recti, erunt duo anguli I E F, E I F, trianguli E I F, æqua-
              <lb/>
            les duobus angulis I E K, E I K, trianguli E I K; </s>
            <s xml:id="echoid-s9389" xml:space="preserve">ac propterea cum habeant latus I E, commune, erunt
              <lb/>
              <note position="right" xlink:label="note-0165-08" xlink:href="note-0165-08a" xml:space="preserve">26. primi.</note>
            reliqua later a vnius æqualia reliquis lateribus alterius, nempe I F, ipſi I K, quod eſt propoſitũ. </s>
            <s xml:id="echoid-s9390" xml:space="preserve">Eadem
              <lb/>
              <note position="left" xlink:label="note-0165-09" xlink:href="note-0165-09a" xml:space="preserve">50</note>
              <note position="right" xlink:label="note-0165-10" xlink:href="note-0165-10a" xml:space="preserve">Arcus circuli ex
                <lb/>
              H, centro horo
                <lb/>
              logij horizon@a
                <lb/>
              lis deſcripti, in-
                <lb/>
              ter metidianã
                <lb/>
              lineam & binas
                <lb/>
              horas vtrinque
                <lb/>
              à metidie æqua
                <lb/>
              liter diſtantes
                <lb/>
              interiecti ſunt
                <lb/>
              æquales.</note>
            eſt ratio de cęteris. </s>
            <s xml:id="echoid-s9391" xml:space="preserve">Itaque ſpatia horaria ante meridiem æqualia ſunt ſpatijs horarijs poſt meridiem, ſin-
              <lb/>
            gula ſingulis, in linea æquinoctiali horologij horizontalis.</s>
            <s xml:id="echoid-s9392" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s9393" xml:space="preserve">EX hoc ſequitur, arcus circuli cuiuſuis ex H, deſcripti in horologio horizontali inter ceptos inter li-
              <lb/>
            neam meridianam, & </s>
            <s xml:id="echoid-s9394" xml:space="preserve">binas quaſcunque lineas horarias æquali ſpatio temporis à meridie diſtantes, qua-
              <lb/>
            les ſunt v. </s>
            <s xml:id="echoid-s9395" xml:space="preserve">g. </s>
            <s xml:id="echoid-s9396" xml:space="preserve">arcus circuli ex H, deſcripti inter meridianam lineam H I, & </s>
            <s xml:id="echoid-s9397" xml:space="preserve">lineas H F, H K, interiecti,
              <lb/>
            æquales eſſe. </s>
            <s xml:id="echoid-s9398" xml:space="preserve">Nam cum latera I H, I F, trianguli I H F, lateribus I H, I K, trianguli I H K, ęqualia
              <lb/>
            ſint, angulos{q́ue} comprehendant æquales, nempe rectos, erunt & </s>
            <s xml:id="echoid-s9399" xml:space="preserve">anguli I H F, I H K, æquales, ac propte-
              <lb/>
              <note position="right" xlink:label="note-0165-11" xlink:href="note-0165-11a" xml:space="preserve">4. primi.</note>
            rea in circulo ex H, deſcripto ab arcubus ęqualibus ſubtendentur, & </s>
            <s xml:id="echoid-s9400" xml:space="preserve">ſic de cęteris.
              <lb/>
            </s>
            <s xml:id="echoid-s9401" xml:space="preserve">
              <note position="right" xlink:label="note-0165-12" xlink:href="note-0165-12a" xml:space="preserve">26. tertij.</note>
            </s>
          </p>
          <p style="it">
            <s xml:id="echoid-s9402" xml:space="preserve">SEQVITVR rurſus, interualla inter centrum E, Aequatoris, & </s>
            <s xml:id="echoid-s9403" xml:space="preserve">binas horas quaſcunque in ęqui
              <lb/>
              <note position="right" xlink:label="note-0165-13" xlink:href="note-0165-13a" xml:space="preserve">Interualla in-
                <lb/>
              ter E, centrum
                <lb/>
              Aequatoris &
                <lb/>
              binas horas v
                <unsure/>
              -</note>
            noctiali linea F K, ęquali temporis interuallo à linea meridiana diſtantes, qualia ſunt interualla E F,
              <lb/>
            E K, eſſe ę
              <unsure/>
            qualia. </s>
            <s xml:id="echoid-s9404" xml:space="preserve">Cum enim ęqualia ſint latera I E, I F, trianguli I E F, lateribus I E, I K, </s>
          </p>
        </div>
      </text>
    </echo>
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