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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          <p>
            <s xml:id="echoid-s19228" xml:space="preserve">
              <pb o="285" file="0301" n="301" rhead="LIBER SECVNDVS."/>
            circulum A C B D, qui tropicum refert, contingunt) deſcripta erunt ſigna aſcendentia, hoc or-
              <lb/>
            dine. </s>
            <s xml:id="echoid-s19229" xml:space="preserve">In vtroque horologio ſignum ♈, tranſit per A; </s>
            <s xml:id="echoid-s19230" xml:space="preserve">ſignum ♉, per punctum ſequens verſus D;
              <lb/>
            </s>
            <s xml:id="echoid-s19231" xml:space="preserve">
              <note position="right" xlink:label="note-0301-01" xlink:href="note-0301-01a" xml:space="preserve">Ordo ſignorú
                <lb/>
              aſcendentium
                <lb/>
              in æquinoctia-
                <lb/>
              li horologio.</note>
            ſignum ♊, per ſequens, & </s>
            <s xml:id="echoid-s19232" xml:space="preserve">ſic deinceps, accipiendo tantum illas portiones linearum in ſuperiori
              <lb/>
            horologio, quæ infra lineam horizontalem in horologium ſuperius cadunt; </s>
            <s xml:id="echoid-s19233" xml:space="preserve">in inferiori autem
              <lb/>
            illas duntaxat earundem linearum portiones, quæ infra horizontalem lineam in horologium
              <lb/>
            inferius cadunt. </s>
            <s xml:id="echoid-s19234" xml:space="preserve">Atque hic ordo facile ex dictis tabellis, tertia & </s>
            <s xml:id="echoid-s19235" xml:space="preserve">quarta, colligitur, ſi diligenter in
              <lb/>
            vtroq; </s>
            <s xml:id="echoid-s19236" xml:space="preserve">horologio conſideretur pars antemeridiana, pomeridianaque. </s>
            <s xml:id="echoid-s19237" xml:space="preserve">Sumimus hic, vt in præce-
              <lb/>
            dentibus, pro inferiori horologio portionem illam, quam horizontalis linea abſcindit, inuerſis ta-
              <lb/>
            men omnibus partibus, vt ſæpe diximus. </s>
            <s xml:id="echoid-s19238" xml:space="preserve">Vnde in inferiori horologio horæ ante meridiem nu-
              <lb/>
            merandæ erunt à puncto A, verſus C, poſt meridiem verò verſus D. </s>
            <s xml:id="echoid-s19239" xml:space="preserve">Tranſibunt autem ſigna a-
              <lb/>
              <note position="left" xlink:label="note-0301-02" xlink:href="note-0301-02a" xml:space="preserve">10</note>
            ſcendentia, ſi in deſcriptione error non fuerit commiſſus, per ea puncta lineæ horizontalis, in
              <lb/>
            quibus paralleli per initia ſignorum ducti eam interſecant, cuiuſmodi ſunt puncta F, G, H, I, K, L,
              <lb/>
            vt perſpicuum eſt ex ijs, quæ in verticali horologio tradidimus propoſ. </s>
            <s xml:id="echoid-s19240" xml:space="preserve">21. </s>
            <s xml:id="echoid-s19241" xml:space="preserve">huius libri. </s>
            <s xml:id="echoid-s19242" xml:space="preserve">Quæ qui-
              <lb/>
            dem puncta inuenientur quoqne hac ratione, etiam ſi paralleli ſignorum non deſcribantur. </s>
            <s xml:id="echoid-s19243" xml:space="preserve">Ex
              <lb/>
              <note position="right" xlink:label="note-0301-03" xlink:href="note-0301-03a" xml:space="preserve">Inuentio pun-
                <lb/>
              ctorum in li-
                <lb/>
              nea horizonta-
                <lb/>
              li, per quę ſigna
                <lb/>
              aſcendentia du
                <lb/>
              cenda ſunt.</note>
            centro E, ducantur lineæ occultæ terminantes in vtroque tropico arcus ſemidiurnos, ſignorum
              <lb/>
            quidem borealium in ſuperiori horologio, auſtralium verò in inferiori, prout in tabella 5. </s>
            <s xml:id="echoid-s19244" xml:space="preserve">propoſ.
              <lb/>
            </s>
            <s xml:id="echoid-s19245" xml:space="preserve">9. </s>
            <s xml:id="echoid-s19246" xml:space="preserve">huius libri continentur; </s>
            <s xml:id="echoid-s19247" xml:space="preserve">ita tamen, vt arcus ſemidiurni ſignorum borealium ſupputentur à B,
              <lb/>
            vtrinque in tropico ♋, auſtralium verò ab A, vtrinque in tropico ♑. </s>
            <s xml:id="echoid-s19248" xml:space="preserve">Hæ etenim lineæ ſecabunt
              <lb/>
            lineam horizontalem in dictis punctis.</s>
            <s xml:id="echoid-s19249" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s19250" xml:space="preserve">EADEM puncta reperiemus ex vltima figura propoſ. </s>
            <s xml:id="echoid-s19251" xml:space="preserve">21. </s>
            <s xml:id="echoid-s19252" xml:space="preserve">huius libri. </s>
            <s xml:id="echoid-s19253" xml:space="preserve">Si enim in recta E B,
              <lb/>
              <note position="left" xlink:label="note-0301-04" xlink:href="note-0301-04a" xml:space="preserve">20</note>
              <note position="right" xlink:label="note-0301-05" xlink:href="note-0301-05a" xml:space="preserve">Alia inuentio
                <lb/>
              corundem pun
                <unsure/>
                <lb/>
              ctorum.</note>
            vel E D, illius figuræ accipiatur recta E h, æqualis rectæ l m, in horologio propoſ. </s>
            <s xml:id="echoid-s19254" xml:space="preserve">50. </s>
            <s xml:id="echoid-s19255" xml:space="preserve">huius lib.
              <lb/>
            </s>
            <s xml:id="echoid-s19256" xml:space="preserve">per quam in horologio lineam horizontalem deſcripſimus; </s>
            <s xml:id="echoid-s19257" xml:space="preserve">& </s>
            <s xml:id="echoid-s19258" xml:space="preserve">per h, ad B D, perpendicularis ex-
              <lb/>
            citetur, erit hæc linea horizontalis in horologio, vt perſpicuum eſt, ſi Horizon A B C D, in horo-
              <lb/>
            logio concipiatur in proprio ſitu, vt nimirum punctum h, ſit in m, & </s>
            <s xml:id="echoid-s19259" xml:space="preserve">perpendicularis per h, du-
              <lb/>
            cta fiat eadem quæ horizontalis per m, ducta; </s>
            <s xml:id="echoid-s19260" xml:space="preserve">ac proinde centrum E, figuræ propoſ. </s>
            <s xml:id="echoid-s19261" xml:space="preserve">21. </s>
            <s xml:id="echoid-s19262" xml:space="preserve">huius li-
              <lb/>
            bri cum centro mundi, & </s>
            <s xml:id="echoid-s19263" xml:space="preserve">vertice ſtyli coniungatur, propter æqualitatẽ rectarum E h, l m. </s>
            <s xml:id="echoid-s19264" xml:space="preserve">Itaque ſi
              <lb/>
            interualla perpendicularis lineæ per h, ductæ, inter h, & </s>
            <s xml:id="echoid-s19265" xml:space="preserve">puncta, in quibus à radiis ex E, proceden
              <lb/>
            tibus ſecatur, in horizontalem lineam ex m, transferantur, habebuntur eadem puncta, vt prius.</s>
            <s xml:id="echoid-s19266" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s19267" xml:space="preserve">RVRSVM, ſi ex tabella 6. </s>
            <s xml:id="echoid-s19268" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s19269" xml:space="preserve">9. </s>
            <s xml:id="echoid-s19270" xml:space="preserve">huius libri ſumantur declinationes mediationum cæ-
              <lb/>
              <note position="right" xlink:label="note-0301-06" xlink:href="note-0301-06a" xml:space="preserve">Alia deſcriptio
                <lb/>
              ſignorum aſcẽ-
                <lb/>
              dentium in eo
                <lb/>
              dem horologio
                <lb/>
              æquinoctiali P
                <unsure/>
                <lb/>
              mediationes cę
                <lb/>
              li, & angulos
                <lb/>
              tetræ.</note>
            li, & </s>
            <s xml:id="echoid-s19271" xml:space="preserve">angulorum terræ, earumq́; </s>
            <s xml:id="echoid-s19272" xml:space="preserve">puncta inueniantur in linea meridiana, per quæ ſcilicet paralleli
              <lb/>
              <note position="left" xlink:label="note-0301-07" xlink:href="note-0301-07a" xml:space="preserve">30</note>
            illarum declinationum tranſeunt, ſecundum doctrinam propoſ. </s>
            <s xml:id="echoid-s19273" xml:space="preserve">50. </s>
            <s xml:id="echoid-s19274" xml:space="preserve">huius libri, tranſibunt quoque
              <lb/>
            ſigna aſcendentia per ea puncta, ſi erratum non fuerit in eorum deſcriptione. </s>
            <s xml:id="echoid-s19275" xml:space="preserve">In ſuperiori quidem
              <lb/>
            horologio mediationes cæli ſignorum borealiũ continentur in portione lineæ meridianæ ex pun
              <lb/>
            cto E, per B, extenſa, cum hæc horam 12. </s>
            <s xml:id="echoid-s19276" xml:space="preserve">meridiei indicet; </s>
            <s xml:id="echoid-s19277" xml:space="preserve">angulorũ vero terræ in portione reli-
              <lb/>
            qua lineæ meridianæ ex eodem puncto E, per A, educta, quæ nimirum horam 12. </s>
            <s xml:id="echoid-s19278" xml:space="preserve">mediæ noctis
              <lb/>
            monſtrat; </s>
            <s xml:id="echoid-s19279" xml:space="preserve">adeo vt hæc ſigna ♌, ♐; </s>
            <s xml:id="echoid-s19280" xml:space="preserve">♍, ♏, & </s>
            <s xml:id="echoid-s19281" xml:space="preserve">♎, tranſeant per puncta inuenta in linea E B, protracta;
              <lb/>
            </s>
            <s xml:id="echoid-s19282" xml:space="preserve">quia his ſignis aſcendentibus, mediant cælum puncta Eclipticæ borealia: </s>
            <s xml:id="echoid-s19283" xml:space="preserve">hæc vero ſigna ♋, ♑, ♊,
              <lb/>
            ♒, ♉, ♓, & </s>
            <s xml:id="echoid-s19284" xml:space="preserve">♈, ducantur per puncta inuenta in recta E A, producta, quòd, his ſignis orientibus,
              <lb/>
            cõſtituantur in angulo terræ puncta eclipticæ borealia, vt ex dicta tabella 6. </s>
            <s xml:id="echoid-s19285" xml:space="preserve">apparet. </s>
            <s xml:id="echoid-s19286" xml:space="preserve">In horologio
              <lb/>
            vero inferiori mediationes cæli ſignorum auſtralium continentur in linea meridiana E A, produ-
              <lb/>
              <note position="left" xlink:label="note-0301-08" xlink:href="note-0301-08a" xml:space="preserve">40</note>
            cta, angulorum autem terræ in linea mediæ noctis E B, protracta; </s>
            <s xml:id="echoid-s19287" xml:space="preserve">ita vt hæc ſigna ♋, ♑, ♊, ♒,
              <lb/>
            ♉, ♓, & </s>
            <s xml:id="echoid-s19288" xml:space="preserve">♈, incedant per puncta reperta incta E A, proptetea quòd, hiſce ſignis aſcendentibus,
              <lb/>
            in medio cæli reperiantur puncta eclipticæ auſtralia; </s>
            <s xml:id="echoid-s19289" xml:space="preserve">hæc autem ſigna ♌, ♐, ♍, ♏, & </s>
            <s xml:id="echoid-s19290" xml:space="preserve">♎, tranſeant
              <lb/>
            per puncta inuenta in recta E B, protracta; </s>
            <s xml:id="echoid-s19291" xml:space="preserve">Nam illis orientibus, puncta Eclipticæ auſtralia in an-
              <lb/>
            gulo terræ exiſtunt. </s>
            <s xml:id="echoid-s19292" xml:space="preserve">Perſpicuum autem eſt, in ſuperiori horologio deſcribi tantum poſſe declina-
              <lb/>
            tiones boreales, & </s>
            <s xml:id="echoid-s19293" xml:space="preserve">auſtrales in inferiori.</s>
            <s xml:id="echoid-s19294" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">Alia defcriptio
            <lb/>
          ſignorũ aſcen-
            <lb/>
          dentium in ho
            <lb/>
          rologio æquino
            <lb/>
          ctiali, per pun-
            <lb/>
          cta Eclipticæ in
            <lb/>
          linea horæ 6. à
            <lb/>
          mer. uel med.
            <lb/>
          noc. exiſtentia,
            <lb/>
          cũ ſignorũ prin
            <lb/>
          cipia oriuntur.</note>
          <p>
            <s xml:id="echoid-s19295" xml:space="preserve">POSTREMO, ſi ex tabella 7. </s>
            <s xml:id="echoid-s19296" xml:space="preserve">ciuſdem propoſ. </s>
            <s xml:id="echoid-s19297" xml:space="preserve">9. </s>
            <s xml:id="echoid-s19298" xml:space="preserve">huius lib accipiantur declinationes pun-
              <lb/>
            ctorum Eclipticæ borealium in linea horæ 6. </s>
            <s xml:id="echoid-s19299" xml:space="preserve">ante meridiem, & </s>
            <s xml:id="echoid-s19300" xml:space="preserve">poſt exiſtentium, cum principia
              <lb/>
            ſignorum oriuntut
              <unsure/>
            , eorumq́; </s>
            <s xml:id="echoid-s19301" xml:space="preserve">puncta in linea horę 6. </s>
            <s xml:id="echoid-s19302" xml:space="preserve">ante, vel poſt meridiem inueniantur in horo
              <lb/>
            logio ſuperiori; </s>
            <s xml:id="echoid-s19303" xml:space="preserve">Itemq́; </s>
            <s xml:id="echoid-s19304" xml:space="preserve">fiat de declinationibus punctorum Eclipticæ auſtralium in eadem linea
              <lb/>
              <note position="left" xlink:label="note-0301-10" xlink:href="note-0301-10a" xml:space="preserve">50</note>
            exiſtentium in inferiori horologio; </s>
            <s xml:id="echoid-s19305" xml:space="preserve">tranſibunt eadem ſigna aſcedentia per hæc puncta inuenta in
              <lb/>
            linea horæ 6. </s>
            <s xml:id="echoid-s19306" xml:space="preserve">Quocirca ſigna zodiaci aſcendentia in eodem æquinoctiali horologio figurauimus.
              <lb/>
            </s>
            <s xml:id="echoid-s19307" xml:space="preserve">Quod faciendum erat.</s>
            <s xml:id="echoid-s19308" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div996" type="section" level="1" n="245">
          <head xml:id="echoid-head252" style="it" xml:space="preserve">SCHOLIVM.</head>
          <p style="it">
            <s xml:id="echoid-s19309" xml:space="preserve">SIGNA Zodiaci aſcendentia cum Andrea Schonero ita depingemus. </s>
            <s xml:id="echoid-s19310" xml:space="preserve">In prima figura ſcholij
              <lb/>
              <note position="right" xlink:label="note-0301-11" xlink:href="note-0301-11a" xml:space="preserve">Qua ratione ſe
                <lb/>
              c
                <unsure/>
              ũdum praxim
                <unsure/>
                <lb/>
              Andreæ Scho-
                <lb/>
              neri eadem ſi-
                <lb/>
              gna aſcenden-
                <lb/>
              tia in horolo-
                <lb/>
              gio æquinoctia
                <lb/>
              li delincentu@.</note>
            propoſ. </s>
            <s xml:id="echoid-s19311" xml:space="preserve">9. </s>
            <s xml:id="echoid-s19312" xml:space="preserve">huius libri in recta E B, accipiatur recta E β, æqualis portioni meridianæ lineæ E M, inter
              <lb/>
            centrum horologij, & </s>
            <s xml:id="echoid-s19313" xml:space="preserve">lineam horizontalem interiectæ in ſigura propoſ. </s>
            <s xml:id="echoid-s19314" xml:space="preserve">50. </s>
            <s xml:id="echoid-s19315" xml:space="preserve">huius libri, & </s>
            <s xml:id="echoid-s19316" xml:space="preserve">per β, ipſi
              <lb/>
            A C, parallela agatur, ita vt centro E, illius figuræ in puncto m, collocato in horologio, & </s>
            <s xml:id="echoid-s19317" xml:space="preserve">puncto β, in
              <lb/>
            centro E, parallela per β, ducta congruat lineæ horæ 6. </s>
            <s xml:id="echoid-s19318" xml:space="preserve">ſecabit hæc par allela per β, ducta rectas </s>
          </p>
        </div>
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