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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          <pb o="361" file="0377" n="377" rhead="LIBER TERTIVS."/>
          <p>
            <s xml:id="echoid-s23887" xml:space="preserve">INTELLIGATVR triangulum A B C, ad planum horologij rectum, ita vt in plano Me
              <lb/>
              <note position="right" xlink:label="note-0377-01" xlink:href="note-0377-01a" xml:space="preserve">Demonſtratio
                <lb/>
              de@cripti@is cir
                <lb/>
              culorum Verti
                <lb/>
              calium.</note>
            ridiani iaceat, vertexq́ue ſtyli A, idem ſit, quod centrum mundi. </s>
            <s xml:id="echoid-s23888" xml:space="preserve">Et quia, vt in propoſ. </s>
            <s xml:id="echoid-s23889" xml:space="preserve">26. </s>
            <s xml:id="echoid-s23890" xml:space="preserve">huius li-
              <lb/>
            bri demonſtrauimus, recta A B communis ſectio eſt Horizontis, ac Meridiani; </s>
            <s xml:id="echoid-s23891" xml:space="preserve">eſtq́ue angulus
              <lb/>
            B A C, rectus, quippe qui ex angulo inclinationis G A C, & </s>
            <s xml:id="echoid-s23892" xml:space="preserve">angulo complementi inclinationis
              <lb/>
            G A B, componatur; </s>
            <s xml:id="echoid-s23893" xml:space="preserve">erit recta A C, communis ſectio Verticalis proprie dicti, & </s>
            <s xml:id="echoid-s23894" xml:space="preserve">Meridiani, ita vt
              <lb/>
            C, punctum ſit Verticale, in quod nimirum axis Horizontis cadit. </s>
            <s xml:id="echoid-s23895" xml:space="preserve">Quoniam enim tam Meridia-
              <lb/>
            nus, quàm Verticalis ad Horizontem rectus eſt, erit eorum communis ſectio (nempe axis Hori-
              <lb/>
            zontis) ad eundem Horizontem recta; </s>
            <s xml:id="echoid-s23896" xml:space="preserve">atque adeo per defin. </s>
            <s xml:id="echoid-s23897" xml:space="preserve">3. </s>
            <s xml:id="echoid-s23898" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s23899" xml:space="preserve">11. </s>
            <s xml:id="echoid-s23900" xml:space="preserve">Euclidis, ad rectam A B, in
              <lb/>
              <note position="right" xlink:label="note-0377-02" xlink:href="note-0377-02a" xml:space="preserve">19. vndec.</note>
            Horizonte exiſtentem perpendicularis in centro mundi A. </s>
            <s xml:id="echoid-s23901" xml:space="preserve">Recta igitur A C, in plano Meridiani
              <lb/>
            perpendicularis exiſtens ad A B, communis ſectio eſt Meridiani, & </s>
            <s xml:id="echoid-s23902" xml:space="preserve">Verticalis propriè dicti, ac pro-
              <lb/>
              <note position="left" xlink:label="note-0377-03" xlink:href="note-0377-03a" xml:space="preserve">10</note>
            inde & </s>
            <s xml:id="echoid-s23903" xml:space="preserve">omnium Verticalium. </s>
            <s xml:id="echoid-s23904" xml:space="preserve">Quod etiam inde manifeſtum eſſe poteſt, quòd angulus A C G, cõ-
              <lb/>
            plemento inclinationis æqualis eſt, qualem nimirum facit planum inclinatum cum Verticali. </s>
            <s xml:id="echoid-s23905" xml:space="preserve">Iam
              <lb/>
            verò ſi circulus ex D, deſcriptus intelligatur moueri circa horizontalem lineam, donec centrum
              <lb/>
            eius D, cum centro mundi A, & </s>
            <s xml:id="echoid-s23906" xml:space="preserve">recta B D, cum recta B A, coniungatur, ob æqualitatem rectarum
              <lb/>
            B D, B A, iacebit dictus circulus in plano Horizontis circa eius centrum deſcriptus. </s>
            <s xml:id="echoid-s23907" xml:space="preserve">Quare cum
              <lb/>
            Verticales circuli ſecent Horizontem, atque adeò & </s>
            <s xml:id="echoid-s23908" xml:space="preserve">circulum ex D, deſcriptũ illi concentricum,
              <lb/>
            in partes æquales, initio facto à Verticali, vel Meridiano, qui vnus etiam eſt ex Verticalibus circu-
              <lb/>
            lis, erunt rectæ per D, & </s>
            <s xml:id="echoid-s23909" xml:space="preserve">per puncta diuiſionum ductæ, communes ſectiones Verticalium circu-
              <lb/>
            lorum, & </s>
            <s xml:id="echoid-s23910" xml:space="preserve">Horizontis. </s>
            <s xml:id="echoid-s23911" xml:space="preserve">Igitur Verticales circuli plano horologij occurrent in punctis lineæ hori-
              <lb/>
            zontalis, in quæ dictæ rectæ cadunt, ac proinde per illa puncta ducendæ erunt communes ſectio-
              <lb/>
              <note position="left" xlink:label="note-0377-04" xlink:href="note-0377-04a" xml:space="preserve">20</note>
            nes Verticalium circulorum, & </s>
            <s xml:id="echoid-s23912" xml:space="preserve">plani horologij. </s>
            <s xml:id="echoid-s23913" xml:space="preserve">Cum ergo eædem ſectiones coeant omnes quo-
              <lb/>
            que in C, puncto, per propoſ. </s>
            <s xml:id="echoid-s23914" xml:space="preserve">18. </s>
            <s xml:id="echoid-s23915" xml:space="preserve">primi libri, in quod cadit axis Horizontis, ſeu eorum ſectio cõ-
              <lb/>
            munis, erunt rectæ per C, & </s>
            <s xml:id="echoid-s23916" xml:space="preserve">per puncta inuenta in linea horizontali ductæ communes ſectiones
              <lb/>
            Verticalium circulorum, & </s>
            <s xml:id="echoid-s23917" xml:space="preserve">plani horologij. </s>
            <s xml:id="echoid-s23918" xml:space="preserve">Communis porrò ſectio Verticalis proprie dicti, & </s>
            <s xml:id="echoid-s23919" xml:space="preserve">
              <lb/>
            plani horologii per C, ducta, parallela eſt, ex eadem propoſ. </s>
            <s xml:id="echoid-s23920" xml:space="preserve">18. </s>
            <s xml:id="echoid-s23921" xml:space="preserve">primi libri, lineæ ęquinoctiali,
              <lb/>
            vel etiam horizontali; </s>
            <s xml:id="echoid-s23922" xml:space="preserve">propterea quòd Aequator, Horizon, Verticalis proprie dictus, & </s>
            <s xml:id="echoid-s23923" xml:space="preserve">circulus
              <lb/>
            maximus, cui horologium æquidiſtat, vnam eandemq́ue communem ſectionem habeant. </s>
            <s xml:id="echoid-s23924" xml:space="preserve">Quo-
              <lb/>
            circa circulos Verticales in eodem horologio inclinato ad Horizontem delineauimus. </s>
            <s xml:id="echoid-s23925" xml:space="preserve">Quod
              <lb/>
            erat faciendum.</s>
            <s xml:id="echoid-s23926" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">30</note>
        </div>
        <div xml:id="echoid-div1233" type="section" level="1" n="304">
          <head xml:id="echoid-head314" xml:space="preserve">PROBLEMA 29. PROPOSITIO 29.</head>
          <p>
            <s xml:id="echoid-s23927" xml:space="preserve">PARALLELOS Horizontis in eodem horologio ad Horizon-
              <lb/>
            tem inclinato depingere.</s>
            <s xml:id="echoid-s23928" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s23929" xml:space="preserve">IN hoc horologio parallelos Horizontis ita deſcribemus, vt in polari horologio propoſ. </s>
            <s xml:id="echoid-s23930" xml:space="preserve">41. </s>
            <s xml:id="echoid-s23931" xml:space="preserve">ſu-
              <lb/>
              <note position="right" xlink:label="note-0377-06" xlink:href="note-0377-06a" xml:space="preserve">Deſcriptio pa-
                <lb/>
              rallelorum Ho
                <lb/>
              rizontis in eo-
                <lb/>
              dem horologio
                <lb/>
              ad Horizontẽ
                <lb/>
              inclinato.</note>
              <figure xlink:label="fig-0377-01" xlink:href="fig-0377-01a" number="252">
                <image file="0377-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0377-01"/>
              </figure>
            perioris libri, paucis mutatis. </s>
            <s xml:id="echoid-s23932" xml:space="preserve">Nam loco axis
              <lb/>
            E F, (quod ad priorem rationem attinet) du-
              <lb/>
            cenda erit E F, communis ſectio Meridiani, & </s>
            <s xml:id="echoid-s23933" xml:space="preserve">
              <lb/>
              <note position="left" xlink:label="note-0377-07" xlink:href="note-0377-07a" xml:space="preserve">40</note>
            plani inclinati, ita vt arcus C E, inclinatio-
              <lb/>
            nem plani ſupra Horizontem metiatur; </s>
            <s xml:id="echoid-s23934" xml:space="preserve">& </s>
            <s xml:id="echoid-s23935" xml:space="preserve">
              <lb/>
            huic communi ſectioni E F, ducenda paralle-
              <lb/>
            la Q R, vt ibi, pro data ſtyli magnitudine.
              <lb/>
            </s>
            <s xml:id="echoid-s23936" xml:space="preserve">Deinde puncta K, L, M, N, O, ex puncto T,
              <lb/>
            accepta, vbi Horizon B C, rectam Q R, ſe-
              <lb/>
            cat, transferenda erunt in lineam meridia-
              <lb/>
            nam horologii ex B, puncto Horizontis, ver-
              <lb/>
            ſus punctum Verticale C, in horologio ſupe-
              <lb/>
            riori: </s>
            <s xml:id="echoid-s23937" xml:space="preserve">in inferiori vero interualla T S, & </s>
            <s xml:id="echoid-s23938" xml:space="preserve">alia,
              <lb/>
              <note position="left" xlink:label="note-0377-08" xlink:href="note-0377-08a" xml:space="preserve">50</note>
            ſi qua fuerint, ex B, transferenda erunt in al-
              <lb/>
            teram partem meridiane lineæ, &</s>
            <s xml:id="echoid-s23939" xml:space="preserve">c. </s>
            <s xml:id="echoid-s23940" xml:space="preserve">Demon-
              <lb/>
            ſtratio eadem omnino eſt, quæ in propoſ. </s>
            <s xml:id="echoid-s23941" xml:space="preserve">41.
              <lb/>
            </s>
            <s xml:id="echoid-s23942" xml:space="preserve">ſuperioris libri, ſi Meridianus Analemmatis
              <lb/>
            A B C, in propria poſitione intelligatur eſſe
              <lb/>
            conſtitutus, ita vt punctum C, ad boream, ſi
              <lb/>
            planum ex parte ſeptentrionali eleuetur, ſpe-
              <lb/>
            ctet; </s>
            <s xml:id="echoid-s23943" xml:space="preserve">ad auſtrum verò, ſi ex auſtrali parte at-
              <lb/>
            tollatur, vt in noſtro exemplo, &</s>
            <s xml:id="echoid-s23944" xml:space="preserve">c.</s>
            <s xml:id="echoid-s23945" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s23946" xml:space="preserve">QVOD verò ſpectat ad poſteriorem viam, ſumenda eſt A D, æqualis axi Horizontis A C, in
              <lb/>
            figura præcedentis propoſ. </s>
            <s xml:id="echoid-s23947" xml:space="preserve">hoc eſt, rectæ, quæ ex A, vertice ſtyli in C, Zenith cadit; </s>
            <s xml:id="echoid-s23948" xml:space="preserve">& </s>
            <s xml:id="echoid-s23949" xml:space="preserve">in </s>
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