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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[311.] PROBLEMA 34. PROPOSITIO 34.
[312.] PROBLEMA 35. PROPOSITIO 35.
[313.] SCHOLIVM.
[314.] PROBLEMA 36. PROPOSITIO 36.
[315.] DE HOROLOGIIS ET A VERTICALI declinantibus, & ad Horizontem inclinatis.
[316.] PROBLEMA 37. PROPOSITIO 37.
[317.] SCHOLIVM.
[318.] PROBLEMA 38. PROPOSITIO 38.
[319.] SCHOLIVM.
[320.] PROBLEMA 39. PROPOSITIQ 39.
[321.] SCHOLIVM.
[322.] PROBLEMA 40. PROPOSITIO 40.
[323.] SCHOLIVM.
[324.] PROBLEMA 41. PROPOSITIO 41.
[325.] PROBLEMA 42. PROPOSITIO 42.
[326.] PROBLEMA 43. PROPOSITIO 43.
[327.] PROBLEMA 44. PROPOSITIO 44.
[328.] SCHOLIVM.
[329.] PROBLEMA 45. PROPOSITIO 45.
[330.] SCHOLIVM.
[331.] PROBLEMA 46. PROPOSITIO 46.
[332.] PROBLEMA 47. PROPOSITIO 47.
[333.] PROBLEMA 48. PROPOSITIO 48.
[334.] FINIS TERTII LIBRI.
[335.] GNOMONICES LIBER QVARTVS.
[336.] AVCTORE
[337.] CHRISTOPHORO CLAVIO BAMBER GENSI SOCIETATIS IESV.
[338.] PROBLEMA 1. PROPOSITIO 1.
[339.] I. SOLE EXISTENTE IN PRINCIPIO ♈.
[340.] II. SOLE EXISTENTE IN PRINCIPIO ♎.
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            <s xml:id="echoid-s33586" xml:space="preserve">
              <pb o="522" file="0538" n="538" rhead="GNOMONICES"/>
            ximi, cui horologiũ parallelum eſt, inter circulũ maximum, qui inclinationem metitur, & </s>
            <s xml:id="echoid-s33587" xml:space="preserve">Meridia
              <lb/>
            num horologii propriũ intercepto, quem in dato plano inuenimus eſſe gr. </s>
            <s xml:id="echoid-s33588" xml:space="preserve">43. </s>
            <s xml:id="echoid-s33589" xml:space="preserve">M. </s>
            <s xml:id="echoid-s33590" xml:space="preserve">20. </s>
            <s xml:id="echoid-s33591" xml:space="preserve">ſupputabi-
              <lb/>
            mus eum à D, verſus A, ſeu partes orientales horologii, vſq; </s>
            <s xml:id="echoid-s33592" xml:space="preserve">ad F; </s>
            <s xml:id="echoid-s33593" xml:space="preserve">propterea quòd horologiũ datũ
              <lb/>
            à ſeptentr. </s>
            <s xml:id="echoid-s33594" xml:space="preserve">in occ. </s>
            <s xml:id="echoid-s33595" xml:space="preserve">deflectit, caditq́ eius centrũ ſupra lineã æquinoctialem: </s>
            <s xml:id="echoid-s33596" xml:space="preserve">(Vtrum autem centrũ
              <lb/>
            ſupra, vel infra lineã æquinoctialem cadat, cognoſcetur exiis, quæ propoſ. </s>
            <s xml:id="echoid-s33597" xml:space="preserve">37. </s>
            <s xml:id="echoid-s33598" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s33599" xml:space="preserve">3. </s>
            <s xml:id="echoid-s33600" xml:space="preserve">tradidimus.
              <lb/>
            </s>
            <s xml:id="echoid-s33601" xml:space="preserve">
              <figure xlink:label="fig-0538-01" xlink:href="fig-0538-01a" number="328">
                <image file="0538-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0538-01"/>
              </figure>
              <note position="left" xlink:label="note-0538-01" xlink:href="note-0538-01a" xml:space="preserve">10</note>
              <note position="left" xlink:label="note-0538-02" xlink:href="note-0538-02a" xml:space="preserve">20</note>
              <note position="left" xlink:label="note-0538-03" xlink:href="note-0538-03a" xml:space="preserve">30</note>
            Quando enim arcus Meridiani inter Horizontem, & </s>
            <s xml:id="echoid-s33602" xml:space="preserve">planũ ex parte auſtrali inclinatũ minor eſt
              <lb/>
            cõplemento altitudinis poli, vt in noſtro exẽplo cõtingit, cũ dictus arcus, ex propoſ. </s>
            <s xml:id="echoid-s33603" xml:space="preserve">28. </s>
            <s xml:id="echoid-s33604" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s33605" xml:space="preserve">1. </s>
            <s xml:id="echoid-s33606" xml:space="preserve">inue-
              <lb/>
            ſtigatus cõtineat gr. </s>
            <s xml:id="echoid-s33607" xml:space="preserve">28. </s>
            <s xml:id="echoid-s33608" xml:space="preserve">M. </s>
            <s xml:id="echoid-s33609" xml:space="preserve">29. </s>
            <s xml:id="echoid-s33610" xml:space="preserve">cadet centrũ horologii ſupra lineã æquinoctialem; </s>
            <s xml:id="echoid-s33611" xml:space="preserve">quãdo vero idẽ
              <lb/>
            arcus æqualis eſt, vel maior cõplemento altitudinis poli, infra, vt in dicta propoſ. </s>
            <s xml:id="echoid-s33612" xml:space="preserve">diximus in ſe-
              <lb/>
            cunda cõſtructione horologij declinantis ſimul & </s>
            <s xml:id="echoid-s33613" xml:space="preserve">inclinati.) </s>
            <s xml:id="echoid-s33614" xml:space="preserve">Recta enim F C, erit linea ſtyli, id
              <lb/>
              <note position="left" xlink:label="note-0538-04" xlink:href="note-0538-04a" xml:space="preserve">Linea ſtyli.</note>
            eſt, cõmunis ſectio plani horologij, & </s>
            <s xml:id="echoid-s33615" xml:space="preserve">Meridiani ipſius proprii. </s>
            <s xml:id="echoid-s33616" xml:space="preserve">Nã ſi horologium in proprio ſitu
              <lb/>
            collocetur, ſi quidé à ſeptentr. </s>
            <s xml:id="echoid-s33617" xml:space="preserve">declinet in occ. </s>
            <s xml:id="echoid-s33618" xml:space="preserve">cadet punctũ E, in quadrantem hemiſphærij ſuperi
              <lb/>
            auſtralẽ, orientalemq́;</s>
            <s xml:id="echoid-s33619" xml:space="preserve">, & </s>
            <s xml:id="echoid-s33620" xml:space="preserve">punctũ D, in quadrantem in ſeri hemiſphærij borealem, & </s>
            <s xml:id="echoid-s33621" xml:space="preserve">occidentalẽ,
              <lb/>
            ita vt, nobis ad horologiũ conuerſis, polus arcticus ſit ad ſiniſtrã puncti D. </s>
            <s xml:id="echoid-s33622" xml:space="preserve">Quare ſi circulus maxi-
              <lb/>
              <note position="left" xlink:label="note-0538-05" xlink:href="note-0538-05a" xml:space="preserve">40</note>
            mus inclinationẽ metiens per rectam D E, & </s>
            <s xml:id="echoid-s33623" xml:space="preserve">ſtylũ ductus intelligatur moueri circa ſtylum in C,
              <lb/>
            collocatũ donec per polum arcticũ tranſeat, hoc eſt, donec cum Meridiano proprio horologij cõ-
              <lb/>
            iungatur, faciet omnino cũ horologio ſectionem, quę infra ſtylum inter puncta A, D, cadet, qua-
              <lb/>
            lis eſt D C E, &</s>
            <s xml:id="echoid-s33624" xml:space="preserve">c. </s>
            <s xml:id="echoid-s33625" xml:space="preserve">Contrariũ accidet, ſi planum à ſeptentr. </s>
            <s xml:id="echoid-s33626" xml:space="preserve">in ortũ deflectat, & </s>
            <s xml:id="echoid-s33627" xml:space="preserve">centrũ horologij ſit
              <lb/>
            ſupra ſtylum. </s>
            <s xml:id="echoid-s33628" xml:space="preserve">A recta igitur G H, rectã F C, in C, ad angulos rectos ſecante cõputandæ erunt lati-
              <lb/>
            tudines vmbrarum, tanquam à cõmuni ſectione plani horologii, & </s>
            <s xml:id="echoid-s33629" xml:space="preserve">proprii Verticalis ipſius. </s>
            <s xml:id="echoid-s33630" xml:space="preserve">Parata
              <lb/>
            autem linea H I, in partes gnomoni æquales diuiſa, vtſupra, inuentaq́; </s>
            <s xml:id="echoid-s33631" xml:space="preserve">per propoſ. </s>
            <s xml:id="echoid-s33632" xml:space="preserve">29. </s>
            <s xml:id="echoid-s33633" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s33634" xml:space="preserve">1. </s>
            <s xml:id="echoid-s33635" xml:space="preserve">altitu
              <lb/>
            dine poli ſupta planũ horologii, quã in noſtro exemplo deprehendimus eſſe gr. </s>
            <s xml:id="echoid-s33636" xml:space="preserve">68. </s>
            <s xml:id="echoid-s33637" xml:space="preserve">M. </s>
            <s xml:id="echoid-s33638" xml:space="preserve">13. </s>
            <s xml:id="echoid-s33639" xml:space="preserve">eiusq́ue
              <lb/>
            cõplementum gr. </s>
            <s xml:id="echoid-s33640" xml:space="preserve">21. </s>
            <s xml:id="echoid-s33641" xml:space="preserve">M. </s>
            <s xml:id="echoid-s33642" xml:space="preserve">47. </s>
            <s xml:id="echoid-s33643" xml:space="preserve">Si ex C, loco ſtyli deorſum verſus in linea ſtyli (quoniã centrũ horo-
              <lb/>
            logii, vt diximus, ſupra ſtylũ cadit, & </s>
            <s xml:id="echoid-s33644" xml:space="preserve">æquinoctialis linea infra) numererur vmbra P. </s>
            <s xml:id="echoid-s33645" xml:space="preserve">30. </s>
            <s xml:id="echoid-s33646" xml:space="preserve">M. </s>
            <s xml:id="echoid-s33647" xml:space="preserve">2. </s>
            <s xml:id="echoid-s33648" xml:space="preserve">quã-
              <lb/>
              <note position="left" xlink:label="note-0538-06" xlink:href="note-0538-06a" xml:space="preserve">50</note>
            tam requirit cõplementum altitudinis poli inuentæ, vſq; </s>
            <s xml:id="echoid-s33649" xml:space="preserve">ad I, erit recta I K, ducta per I, ad F C,
              <lb/>
            perpendicularis, linea æquinoctialis Et ſi ex C,ſurſum verſus vſq; </s>
            <s xml:id="echoid-s33650" xml:space="preserve">ad L, numeretur vmbra P. </s>
            <s xml:id="echoid-s33651" xml:space="preserve">4 M.
              <lb/>
            </s>
            <s xml:id="echoid-s33652" xml:space="preserve">
              <note position="left" xlink:label="note-0538-07" xlink:href="note-0538-07a" xml:space="preserve">Linea æquino-
                <lb/>
              ctialis.</note>
            48. </s>
            <s xml:id="echoid-s33653" xml:space="preserve">reſpondens altitudini poli inuentæ, inuenietur L, centrum horologii, ita vt à recta M L, ad FL,
              <lb/>
              <note position="left" xlink:label="note-0538-08" xlink:href="note-0538-08a" xml:space="preserve">Centrum horo
                <lb/>
              logii.</note>
            perpendiculari in circulo M N, ex L, deſcripto numerandi ſint arcus horarij, ſi pro ſingulis horis
              <lb/>
            ſupputẽtur. </s>
            <s xml:id="echoid-s33654" xml:space="preserve">Duo aũt puncta I, L, inuenientur quoq; </s>
            <s xml:id="echoid-s33655" xml:space="preserve">ex angulo C P I, altitudinis poli inuẽtę, & </s>
            <s xml:id="echoid-s33656" xml:space="preserve">an-
              <lb/>
            gulo C P L, complementi eiuſdem altitudinis, ſi in recta G H, abſcindatur C P, ſtylo æqualis.</s>
            <s xml:id="echoid-s33657" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s33658" xml:space="preserve">IN horarũ deſcriptione nulla difficultas eſt, ſi à punctis G, H, rectè ſupputentur latitudines vm
              <lb/>
            brarũ, &</s>
            <s xml:id="echoid-s33659" xml:space="preserve">c. </s>
            <s xml:id="echoid-s33660" xml:space="preserve">vt in appoſita figura manifeſtũ eſt, in qua, quia circulus A D B, integre nõ potuit deſcri
              <lb/>
            bi, numerauimus latitudines vmbrarũ ſuperiores, & </s>
            <s xml:id="echoid-s33661" xml:space="preserve">orientales à puncto H, occidentali deorſum
              <lb/>
            verſus, occidentales autẽ à G, puncto oriẽtali. </s>
            <s xml:id="echoid-s33662" xml:space="preserve">Vt pro latitudine vmbræ horæ 10. </s>
            <s xml:id="echoid-s33663" xml:space="preserve">á med. </s>
            <s xml:id="echoid-s33664" xml:space="preserve">noc. </s>
            <s xml:id="echoid-s33665" xml:space="preserve">in tro-
              <lb/>
            pico ♋, quæ orientalis eſt, & </s>
            <s xml:id="echoid-s33666" xml:space="preserve">ſuperior, cõtinetq́ gr. </s>
            <s xml:id="echoid-s33667" xml:space="preserve">21. </s>
            <s xml:id="echoid-s33668" xml:space="preserve">M. </s>
            <s xml:id="echoid-s33669" xml:space="preserve">49. </s>
            <s xml:id="echoid-s33670" xml:space="preserve">accepimus occidentalem, & </s>
            <s xml:id="echoid-s33671" xml:space="preserve"/>
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