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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[291.] PROBLEMA 24. PROPOSITIO 24.
Page: 368 (352)
[292.] DE HOROLOGIIS ad Horizontem inclinatis.
Page: 369 (353)
[293.] PROBLEMA 25. PROPOSITIO 25.
Page: 369 (353)
[294.] PRÆCEPTVM I.
Page: 369 (353)
[295.] PRAECEPTVM II.
Page: 369 (353)
[296.] PRAECEPTVM III.
Page: 370 (354)
[297.] PRAECEPTVM IIII.
Page: 370 (354)
[298.] PRAECEPTVM V.
Page: 370 (354)
[299.] PRAECEPTVM VI.
Page: 370 (354)
[300.] SCHOLIVM.
Page: 372 (356)
[301.] PROBLEMA 26. PROPOSITIO 26.
Page: 374 (358)
[302.] PROBLEMA 27. PROPOSITIO 27.
Page: 376 (360)
[303.] PROBLEMA 28. PROPOSITIO 28.
Page: 376 (360)
[304.] PROBLEMA 29. PROPOSITIO 29.
Page: 377 (361)
[305.] PROBLEMA 30. PROPOSITIO 30.
Page: 378 (362)
[306.] SEQVITVR FIGVRA.
Page: 378 (362)
[307.] PROBLEMA 31. PROPOSITIO 31.
Page: 379 (363)
[308.] PROBLEMA 32. PROPOSITIO 32.
Page: 379 (363)
[309.] PROBLEMA 33. PROPOSITIO 33.
Page: 381 (365)
[310.] SCHOLIVM.
Page: 382 (366)
[311.] PROBLEMA 34. PROPOSITIO 34.
Page: 383 (367)
[312.] PROBLEMA 35. PROPOSITIO 35.
Page: 385 (369)
[313.] SCHOLIVM.
Page: 385 (369)
[314.] PROBLEMA 36. PROPOSITIO 36.
Page: 385 (369)
[315.] DE HOROLOGIIS ET A VERTICALI declinantibus, & ad Horizontem inclinatis.
Page: 386 (370)
[316.] PROBLEMA 37. PROPOSITIO 37.
Page: 386 (370)
[317.] SCHOLIVM.
Page: 403 (387)
[318.] PROBLEMA 38. PROPOSITIO 38.
Page: 411 (395)
[319.] SCHOLIVM.
Page: 415 (399)
[320.] PROBLEMA 39. PROPOSITIQ 39.
Page: 415 (399)
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            <s xml:id="echoid-s16929" xml:space="preserve">
              <pb o="252" file="0268" n="268" rhead="GNOMONICES"/>
            ipſi B D, parallela agatur; </s>
            <s xml:id="echoid-s16930" xml:space="preserve">adeo vt cẽtro E, poſito in cẽtro E, in horologio, et pũcto a, in pũcto A, parallela
              <lb/>
            per a, ducta congruat lineæ æquinoctiali. </s>
            <s xml:id="echoid-s16931" xml:space="preserve">Secabit autem parallela per a, ducta rectas ſignorum ex E, pro
              <lb/>
            deuntes in punctis, quorum diſtantiæ circino acceptæ ex a, transferantur in lineã æquinoctialem horologii
              <lb/>
            f acto initio ab A, tam ſupra lineam horizontalẽ, quàm infra, & </s>
            <s xml:id="echoid-s16932" xml:space="preserve">per puncta notata in linea æquinoctiali
              <lb/>
            ducantur rectę occultę ipſi horizontali lineæ parallelæ ſecantes vtrumque tropicum, etiam ſupra lineam
              <lb/>
            horizontalem deſcriptum, in punctis, per quæ ſigna aſcendentia ſunt educenda: </s>
            <s xml:id="echoid-s16933" xml:space="preserve">hoc tamen ordine ſerua-
              <lb/>
            to. </s>
            <s xml:id="echoid-s16934" xml:space="preserve">In horologio orientali punctum tropici ♋, vbi ſecat lineam horizontalem, pertinet ad ♋; </s>
            <s xml:id="echoid-s16935" xml:space="preserve">proximũ
              <lb/>
              <note position="left" xlink:label="note-0268-01" xlink:href="note-0268-01a" xml:space="preserve">Ordo ſignorũ
                <lb/>
              a ſcendentium,
                <lb/>
              in tropicis.</note>
            infra, ad ♌; </s>
            <s xml:id="echoid-s16936" xml:space="preserve">ſequens ad ♍: </s>
            <s xml:id="echoid-s16937" xml:space="preserve">proximum verò punctum ſupra horizontalẽlineam ſpectat ad ♊; </s>
            <s xml:id="echoid-s16938" xml:space="preserve">ſequens ad
              <lb/>
            ♉. </s>
            <s xml:id="echoid-s16939" xml:space="preserve">Item punctum tropici ♑, vbi lineam horizontalem ſecat, ſpectat ad ♑; </s>
            <s xml:id="echoid-s16940" xml:space="preserve">proximum infra, ad ♒; </s>
            <s xml:id="echoid-s16941" xml:space="preserve">ſe-
              <lb/>
            quens ad ♓; </s>
            <s xml:id="echoid-s16942" xml:space="preserve">proximum autem punctum ſupra lineam horizontalem pertinet ad ♐; </s>
            <s xml:id="echoid-s16943" xml:space="preserve">ſequens ad ♏. </s>
            <s xml:id="echoid-s16944" xml:space="preserve">At
              <lb/>
              <note position="left" xlink:label="note-0268-02" xlink:href="note-0268-02a" xml:space="preserve">10</note>
            in horologio occidentali punctum tropici ♋, vbi interſecat lineam horizontalem, pertinet ad ♑, proxi-
              <lb/>
            mum infra, ad ♐; </s>
            <s xml:id="echoid-s16945" xml:space="preserve">ſequens ad ♏: </s>
            <s xml:id="echoid-s16946" xml:space="preserve">proximum verò punctum ſupra lineam horizontalem ſpectat ad ♒; </s>
            <s xml:id="echoid-s16947" xml:space="preserve">ſe-
              <lb/>
            quens ad ♓. </s>
            <s xml:id="echoid-s16948" xml:space="preserve">Item punctum tropici ♑, ubi lineam horizontalem interſecat, ſpectat ad ♋; </s>
            <s xml:id="echoid-s16949" xml:space="preserve">proximum ve-
              <lb/>
            rò infra, ad ♊; </s>
            <s xml:id="echoid-s16950" xml:space="preserve">ſequens ad ♉: </s>
            <s xml:id="echoid-s16951" xml:space="preserve">proximum autem ſupra horizontalem lineam pertinet ad ♌; </s>
            <s xml:id="echoid-s16952" xml:space="preserve">ſe-
              <lb/>
            quens ad ♍.</s>
            <s xml:id="echoid-s16953" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s16954" xml:space="preserve">RVRSVS in ſecunda figura ſcholij propoſ. </s>
            <s xml:id="echoid-s16955" xml:space="preserve">9. </s>
            <s xml:id="echoid-s16956" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s16957" xml:space="preserve">ex recta E C, aufer atur E a, æqualis gnomo
              <lb/>
            ni, & </s>
            <s xml:id="echoid-s16958" xml:space="preserve">per a, ipſi B D, parallela agatur; </s>
            <s xml:id="echoid-s16959" xml:space="preserve">ita vt rurſus centro E, poſito in E, centro horologii, & </s>
            <s xml:id="echoid-s16960" xml:space="preserve">puncto a,
              <lb/>
            in puncto A, parallela per a, ducta lineæ æquinoctiali congruat. </s>
            <s xml:id="echoid-s16961" xml:space="preserve">Secabit autem hęc parallela per a, ducta
              <lb/>
            rectas ſignorum ex E, prodeuntes, etiam illorum ſignorum, quæ ſunt ſupra rectam B D, ſi tamen eorum li
              <lb/>
            neæ infra centrum E, producantur, in punctis, quorum distantiæ circino acceptæ ex a, ſi trans fer antur in
              <lb/>
              <note position="left" xlink:label="note-0268-03" xlink:href="note-0268-03a" xml:space="preserve">20</note>
            lineam æquinoctialem horologij, initio facto ab A, tam ſupra lineam horizontalem, quàm infra, habebun-
              <lb/>
            tur
              <unsure/>
            puncta in æquinoctiali linea, per quæ tranſibunt lineæ aſcendentium ſignorum, hoc ordine. </s>
            <s xml:id="echoid-s16962" xml:space="preserve">In horologio
              <lb/>
              <note position="left" xlink:label="note-0268-04" xlink:href="note-0268-04a" xml:space="preserve">Ordo ſignorũ
                <lb/>
              aſcendentium
                <lb/>
              in linea æqui-
                <lb/>
              noctiali.</note>
            orientali puncta lineæ æquinoctialis ſignata infra horizontalem lineam debentur ſignis, quæ ſunt ad ſini-
              <lb/>
            ſtram rectæ E C, computando etiam ſigna ſupra rectam BD, quæ infra centrum E, ſunt, & </s>
            <s xml:id="echoid-s16963" xml:space="preserve">vltra centrũ
              <lb/>
            E, producta, qualia ſunt ♉, ♊, ♋, ♐, ♏: </s>
            <s xml:id="echoid-s16964" xml:space="preserve">puncta verò lineæ æquinoctialis ſupra horizontalẽ lineã illis
              <lb/>
            ſignis tribuenda ſunt, quæ ad dexteram rectæ E C, reperiuntur, cuiuſmodi ſunt ♓, ♒, ♑, ♌, ♍. </s>
            <s xml:id="echoid-s16965" xml:space="preserve">At in
              <lb/>
            horologio occidentali contrarium omnino intelligatur. </s>
            <s xml:id="echoid-s16966" xml:space="preserve">Nam ſignis, quæ ſunt ad ſiniſtram rectæ E C, re-
              <lb/>
            ſpondent puncta æquinoctialis lineæ ſupra horizontalem lineã; </s>
            <s xml:id="echoid-s16967" xml:space="preserve">ſignis verò, quæ ſunt ad dexteram eiuſdem
              <lb/>
            rectæ E C, conueniunt puncta æquinoctialis lineæ infra horizontalem lineam. </s>
            <s xml:id="echoid-s16968" xml:space="preserve">His ritè peractis, ſi puncta
              <lb/>
            reſpondentium ſignorum in linea æquinoctiali, & </s>
            <s xml:id="echoid-s16969" xml:space="preserve">tropicis inuenta rectis lineis iungantur, deſcripta erunt
              <lb/>
              <note position="left" xlink:label="note-0268-05" xlink:href="note-0268-05a" xml:space="preserve">30</note>
            ſigna aſcendentia. </s>
            <s xml:id="echoid-s16970" xml:space="preserve">Lineas tamen ♈, & </s>
            <s xml:id="echoid-s16971" xml:space="preserve">♎, deſcribemus, vt prius.</s>
            <s xml:id="echoid-s16972" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s16973" xml:space="preserve">IAM verò lineæ aſcendentium ſignorum vtriuslibet horologij vltra horizõtalem lineam productæ,
              <lb/>
            exhibent eorundem ſignorum lineas in oppoſita facie plani horologij, dummodo pars illa ſuperior ablata
              <lb/>
            à linea horizontali inuertatur, vt in ſcholio propoſ. </s>
            <s xml:id="echoid-s16974" xml:space="preserve">14. </s>
            <s xml:id="echoid-s16975" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s16976" xml:space="preserve">demonſtrauimus. </s>
            <s xml:id="echoid-s16977" xml:space="preserve">Itaque ſatis erit, ſi ſi-
              <lb/>
            gna aſcendentia deſcribantur in orientali horologio, vel occidentali. </s>
            <s xml:id="echoid-s16978" xml:space="preserve">Nam omnia eius lineamenta vltra
              <lb/>
            horizontalem lineã producta dabunt eadẽ ſigna aſcendentia in oppoſito horologio, ſi illa inuerſio fiat, & </s>
            <s xml:id="echoid-s16979" xml:space="preserve">c.
              <lb/>
            </s>
            <s xml:id="echoid-s16980" xml:space="preserve">Nos maxime in figur a deſcripſimus hoc loco ſigna aſcendentia ex tabula 8. </s>
            <s xml:id="echoid-s16981" xml:space="preserve">& </s>
            <s xml:id="echoid-s16982" xml:space="preserve">9. </s>
            <s xml:id="echoid-s16983" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s16984" xml:space="preserve">9. </s>
            <s xml:id="echoid-s16985" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s16986" xml:space="preserve">nimi-
              <lb/>
            rum per puncta in lineis horarum 11. </s>
            <s xml:id="echoid-s16987" xml:space="preserve">à med. </s>
            <s xml:id="echoid-s16988" xml:space="preserve">noc. </s>
            <s xml:id="echoid-s16989" xml:space="preserve">& </s>
            <s xml:id="echoid-s16990" xml:space="preserve">1. </s>
            <s xml:id="echoid-s16991" xml:space="preserve">à med. </s>
            <s xml:id="echoid-s16992" xml:space="preserve">noc. </s>
            <s xml:id="echoid-s16993" xml:space="preserve">Item 1. </s>
            <s xml:id="echoid-s16994" xml:space="preserve">à mer. </s>
            <s xml:id="echoid-s16995" xml:space="preserve">& </s>
            <s xml:id="echoid-s16996" xml:space="preserve">11. </s>
            <s xml:id="echoid-s16997" xml:space="preserve">à mer. </s>
            <s xml:id="echoid-s16998" xml:space="preserve">inuenta.</s>
            <s xml:id="echoid-s16999" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div868" type="section" level="1" n="208">
          <head xml:id="echoid-head211" xml:space="preserve">PROBLEMA 34, PROPOSITIO 34.</head>
          <note position="left" xml:space="preserve">40</note>
        </div>
        <div xml:id="echoid-div869" type="section" level="1" n="209">
          <head xml:id="echoid-head212" xml:space="preserve">HOROLOGIVM Italicum Meridianum conſtituere.</head>
          <p>
            <s xml:id="echoid-s17000" xml:space="preserve">SECETVR circulus F G H I, in arcum diurnum & </s>
            <s xml:id="echoid-s17001" xml:space="preserve">nocturnum tropici ♋, vt in ſcholio pro-
              <lb/>
              <note position="left" xlink:label="note-0268-07" xlink:href="note-0268-07a" xml:space="preserve">Deſcriptio ho-
                <lb/>
              rologii Italici
                <lb/>
              Meridiani.</note>
            poſ. </s>
            <s xml:id="echoid-s17002" xml:space="preserve">1. </s>
            <s xml:id="echoid-s17003" xml:space="preserve">ſuperioris lib. </s>
            <s xml:id="echoid-s17004" xml:space="preserve">docuimus, ſitq́ue arcus diurnus B G C, nocturnus C I B; </s>
            <s xml:id="echoid-s17005" xml:space="preserve">qui arcus inuenien
              <lb/>
            tur etiam, vt propoſ. </s>
            <s xml:id="echoid-s17006" xml:space="preserve">10. </s>
            <s xml:id="echoid-s17007" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s17008" xml:space="preserve">ſcripſimus, ſi à puncto G, meridiei vtrinque ſupputetur arcus
              <lb/>
            ſemidiurnus tropici ♋, vſque ad B, & </s>
            <s xml:id="echoid-s17009" xml:space="preserve">C, nempe horæ 7. </s>
            <s xml:id="echoid-s17010" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s17011" xml:space="preserve">32. </s>
            <s xml:id="echoid-s17012" xml:space="preserve">vbi polus habet altitudinem
              <lb/>
            grad. </s>
            <s xml:id="echoid-s17013" xml:space="preserve">42. </s>
            <s xml:id="echoid-s17014" xml:space="preserve">vt fit Romæ. </s>
            <s xml:id="echoid-s17015" xml:space="preserve">Deinde circulus F G H I, in horas 24. </s>
            <s xml:id="echoid-s17016" xml:space="preserve">æquales diuidatur, ſumpto @initio
              <lb/>
            à termino arcus diurni occidentali, cuiuſmodi in orientali horologio eſt punctum C, in occiden-
              <lb/>
              <note position="left" xlink:label="note-0268-08" xlink:href="note-0268-08a" xml:space="preserve">50</note>
            tali verò B, vt conſtat, ſi circulus F G H I, ad propriam poſitionem moueri intelligatur circa ęqui-
              <lb/>
            noctialem lineam, donec videlicet ſtatuatur in plano Aequatoris. </s>
            <s xml:id="echoid-s17017" xml:space="preserve">Deinde in orientali horologio
              <lb/>
            ex horis inter puncta B, & </s>
            <s xml:id="echoid-s17018" xml:space="preserve">G, ortus Solis, & </s>
            <s xml:id="echoid-s17019" xml:space="preserve">meridiei, in occidentali autem inter puncta B, & </s>
            <s xml:id="echoid-s17020" xml:space="preserve">G, oc-
              <lb/>
            caſus Solis, & </s>
            <s xml:id="echoid-s17021" xml:space="preserve">meridiei, per centrum circuli F G H I, ducantur rectę lineæ, quæ, vt propoſ. </s>
            <s xml:id="echoid-s17022" xml:space="preserve">10. </s>
            <s xml:id="echoid-s17023" xml:space="preserve">huius
              <lb/>
            lib. </s>
            <s xml:id="echoid-s17024" xml:space="preserve">oſtendimus, communes ſectiones ſunt Aequatoris, & </s>
            <s xml:id="echoid-s17025" xml:space="preserve">circulorum maximorum, qui per polos
              <lb/>
            mundi, & </s>
            <s xml:id="echoid-s17026" xml:space="preserve">horas Italicas paralleli ♋, ducuntur, inſtar circulorum horariorum à meridie, vel me-
              <lb/>
            dianocte. </s>
            <s xml:id="echoid-s17027" xml:space="preserve">Secabunt hæ lineæ æquinoctialem lineam in punctis, per quæ ad lineam æquinoctialõ
              <unsure/>
              <lb/>
            perpendiculares lineæ occultæ eductæ ſecabunt tropicum ♋, in horis Italicis, vel ab occaſu Solis,
              <lb/>
            cum hæ perpendiculares ſint lineæ horariæ ab occaſu Solis, inſtar linearum horariarum à mer. </s>
            <s xml:id="echoid-s17028" xml:space="preserve">vel
              <lb/>
            med. </s>
            <s xml:id="echoid-s17029" xml:space="preserve">noc. </s>
            <s xml:id="echoid-s17030" xml:space="preserve">Sole exiſtente in principio ♋, vt ex iis, quæ propoſ. </s>
            <s xml:id="echoid-s17031" xml:space="preserve">25. </s>
            <s xml:id="echoid-s17032" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s17033" xml:space="preserve">demonſtrauimus, per-
              <lb/>
            ſpicuum eſt. </s>
            <s xml:id="echoid-s17034" xml:space="preserve">Eodem modo, ſi arcubus I B, I C, ſumantur æqualesarcus G D, G E, vt D G E, </s>
          </p>
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