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

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          <p>
            <s xml:id="echoid-s25074" xml:space="preserve">
              <pb o="382" file="0398" n="398" rhead="GNOMONICES"/>
            dam meridianæ, in qua ſtylus collocandus eſt, & </s>
            <s xml:id="echoid-s25075" xml:space="preserve">G H, lineam æquinoctialem, quemadmodũ
              <lb/>
            in horizontali horologio recta H E, meridiana linea eſt, hoc eſt, communis ſectio plani horolo-
              <lb/>
            gii, & </s>
            <s xml:id="echoid-s25076" xml:space="preserve">Meridiani
              <unsure/>
            , in qua ſtylus collocatur, recta autem F K, munere lineæ æquinoctialis fungitur.
              <lb/>
            </s>
            <s xml:id="echoid-s25077" xml:space="preserve">In rectam autem G N, quæ inſtar eſt lineæ meridianæ, ſi planum inclinatum pro Horizonte
              <lb/>
            quopiam accipiatur, transferenda eſt recta H I, quæ in portione Analemmatis inter axem, & </s>
            <s xml:id="echoid-s25078" xml:space="preserve">dia-
              <lb/>
            metrum Æquatoris interponitur, initio facto à linea æquinoctiali in puncto G, uſque ad pun-
              <lb/>
            ctum ρ, ut centrum horologii habeatur; </s>
            <s xml:id="echoid-s25079" xml:space="preserve">ſicut etiam in horologio horizontali in recta H E, linea
              <lb/>
            I H, inter lineam æquinoctialem, & </s>
            <s xml:id="echoid-s25080" xml:space="preserve">centrum horologii æqualis eſt rectæ H I, in portione Analem
              <lb/>
            matis. </s>
            <s xml:id="echoid-s25081" xml:space="preserve">Sed quoniam in hiſce horologiis declinantibus ſimul & </s>
            <s xml:id="echoid-s25082" xml:space="preserve">inclinatis centrum ρ, exiſtit ali-
              <lb/>
            quando infra lineam æquinoctialem, & </s>
            <s xml:id="echoid-s25083" xml:space="preserve">aliquando ſupra eandem, ut ſciamus, quando infra ip-
              <lb/>
              <note position="left" xlink:label="note-0398-01" xlink:href="note-0398-01a" xml:space="preserve">10</note>
            ſam cẽtrum exiſtat, ac proinde infra eandem recta H I, transferenda ſit, ut centrum ρ, habeamus,
              <lb/>
            & </s>
            <s xml:id="echoid-s25084" xml:space="preserve">quando ſupra, & </s>
            <s xml:id="echoid-s25085" xml:space="preserve">c. </s>
            <s xml:id="echoid-s25086" xml:space="preserve">inueſtigandus erit, per propoſ. </s>
            <s xml:id="echoid-s25087" xml:space="preserve">28. </s>
            <s xml:id="echoid-s25088" xml:space="preserve">primi libri arcus Meridiani interiectus
              <lb/>
            inter planum inclinatum, & </s>
            <s xml:id="echoid-s25089" xml:space="preserve">Horizontem. </s>
            <s xml:id="echoid-s25090" xml:space="preserve">Ex hoc enim cognito ſine ullo negotio id, quod quę-
              <lb/>
            ritur, aſſequemur. </s>
            <s xml:id="echoid-s25091" xml:space="preserve">In prima figura deprehendimus hunc arcum ex parte boreali ſupra Horizontẽ
              <lb/>
              <note position="left" xlink:label="note-0398-02" xlink:href="note-0398-02a" xml:space="preserve">Quanti ſint ar
                <lb/>
              @us Meridiani
                <lb/>
              inter Horizon-
                <lb/>
              tẽ & plana ſex
                <lb/>
              figurarum hu-
                <lb/>
              ius propoſ. in-
                <lb/>
              terpoſiti.</note>
            gr. </s>
            <s xml:id="echoid-s25092" xml:space="preserve">15. </s>
            <s xml:id="echoid-s25093" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s25094" xml:space="preserve">35. </s>
            <s xml:id="echoid-s25095" xml:space="preserve">In ſecunda autẽ grad. </s>
            <s xml:id="echoid-s25096" xml:space="preserve">68. </s>
            <s xml:id="echoid-s25097" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s25098" xml:space="preserve">50. </s>
            <s xml:id="echoid-s25099" xml:space="preserve">In tertia denique gr. </s>
            <s xml:id="echoid-s25100" xml:space="preserve">42. </s>
            <s xml:id="echoid-s25101" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s25102" xml:space="preserve">o adeò ut planum
              <lb/>
            huius figuræ per polum tranſeat. </s>
            <s xml:id="echoid-s25103" xml:space="preserve">Rurſus in quarta figura inuenimus eundem arcum ex parte au-
              <lb/>
            ſtrali ſupra Horizontẽ grad. </s>
            <s xml:id="echoid-s25104" xml:space="preserve">28. </s>
            <s xml:id="echoid-s25105" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s25106" xml:space="preserve">29. </s>
            <s xml:id="echoid-s25107" xml:space="preserve">In quinta autem, grad. </s>
            <s xml:id="echoid-s25108" xml:space="preserve">72. </s>
            <s xml:id="echoid-s25109" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s25110" xml:space="preserve">57. </s>
            <s xml:id="echoid-s25111" xml:space="preserve">In 6. </s>
            <s xml:id="echoid-s25112" xml:space="preserve">denique gra.
              <lb/>
            </s>
            <s xml:id="echoid-s25113" xml:space="preserve">48. </s>
            <s xml:id="echoid-s25114" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s25115" xml:space="preserve">o. </s>
            <s xml:id="echoid-s25116" xml:space="preserve">adeò ut planum huius figuræ per punctum illud Meridiani tranſeat, ubi ab Æquato-
              <lb/>
            re ſecatur. </s>
            <s xml:id="echoid-s25117" xml:space="preserve">Si igitur planum ex parte boreali ad Horizontem fuerit inclinatum, fueritq́ue arcus
              <lb/>
              <note position="left" xlink:label="note-0398-03" xlink:href="note-0398-03a" xml:space="preserve">Quando cen-
                <lb/>
              trum horologii
                <lb/>
              eſt infra lineã
                <lb/>
              ęquinocti alem,
                <lb/>
              & quando ſu-
                <lb/>
              pra.</note>
            Meridiani inter ipſum, & </s>
            <s xml:id="echoid-s25118" xml:space="preserve">Horizontem poſitus minor altitudine poli ſupra Horizontem, ſumen-
              <lb/>
              <note position="left" xlink:label="note-0398-04" xlink:href="note-0398-04a" xml:space="preserve">20</note>
            da eſt ex portione Analemmatis recta H I, transferendaq́ue in lineam G N, ex G, infra lineam æ-
              <lb/>
            quinoctialem uſq; </s>
            <s xml:id="echoid-s25119" xml:space="preserve">ad punctum ρ, quod centrum erit horologii; </s>
            <s xml:id="echoid-s25120" xml:space="preserve">quia tunc centrum horologii
              <lb/>
            infra lineã ęquinoctialem exiſtit, ut in prima figura contingit: </s>
            <s xml:id="echoid-s25121" xml:space="preserve">quoniam axis mundi tunc occurrit
              <lb/>
            ſuperiori faciei plani horologii ex parte auſtrali non ſecus, ac in horizontali horologio.</s>
            <s xml:id="echoid-s25122" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s25123" xml:space="preserve">SI uerò plano ex eadem parte boreali ſupra Horizontem eleuato arcus Meridiani inter ipſum,
              <lb/>
            & </s>
            <s xml:id="echoid-s25124" xml:space="preserve">Horizontem poſitus fuerit altitudine poli ſupra Horizontem maior, transferenda eſt recta H I,
              <lb/>
            ex portione Analemmatis in rectam G N, ex G, ſupra lineam æquinoctialẽ uſque ad punctum ρ,
              <lb/>
            quod centrum erit horologii ſupra lineam æquinoctialem exiſtens, ut in ſecunda figura conſpici-
              <lb/>
            tur; </s>
            <s xml:id="echoid-s25125" xml:space="preserve">quia tunc axis mundi ſuperiori faciei plani horologit
              <unsure/>
            occurrit ad partes ſuperiores, ſiue borea-
              <lb/>
            les, ita ut cum linea ſtyli ea facie deſcripta faciat angulum acutum uerſus polum oppoſitum, ſeu
              <lb/>
              <note position="left" xlink:label="note-0398-05" xlink:href="note-0398-05a" xml:space="preserve">30</note>
            uerſus partes inferiores, ut in Verticali horologio auſtrali contingit.</s>
            <s xml:id="echoid-s25126" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s25127" xml:space="preserve">SI denique plano ex eadem parte boreali eleuato ſupra Horizontem, arcus Meridiani inter
              <lb/>
            ipſum & </s>
            <s xml:id="echoid-s25128" xml:space="preserve">Horizontem poſitus æqualis altitudini poli fuerit, ita ut planum per polos mundi tran
              <lb/>
            ſeat, carebit horologium centro, ut accidit in tertia figura. </s>
            <s xml:id="echoid-s25129" xml:space="preserve">Vnde nihil tunc transferendum eſt, ſed
              <lb/>
            alio modo horologium conſtruendum, ut paulo infra docebimus.</s>
            <s xml:id="echoid-s25130" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s25131" xml:space="preserve">QVOD ſi planum ex parte auſtrali inclinatum fuerit ad Horizontem, fueritq́ue arcus inter
              <lb/>
            ipſum, & </s>
            <s xml:id="echoid-s25132" xml:space="preserve">Horizontem incluſus minor complemento altitudi@s poli ſupra Horizontem, trans-
              <lb/>
            ferenda erit eadem recta H I, ex portione Analemmatis in rectam G N, ex G, ſupra lineam æ-
              <lb/>
            quinoctialem uſque ad punctum ρ, quod centrum horologii erit ſupra lineam æquinoctialem
              <lb/>
            exiſtens, ut in quarta figura uidere licet; </s>
            <s xml:id="echoid-s25133" xml:space="preserve">quoniam tunc axis mundi faciei ſuperiori plani horolo-
              <lb/>
              <note position="left" xlink:label="note-0398-06" xlink:href="note-0398-06a" xml:space="preserve">40</note>
            gii occurrit ſupra lineã æquinoctialem uerſus partes ſuperiores, hoc eſt, auſtrales, ut in horizon-
              <lb/>
            tali horologio.</s>
            <s xml:id="echoid-s25134" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s25135" xml:space="preserve">POSTREMO ſi planum ex eadem parte auſtrali fuerit inclinatum ad Horizontem, & </s>
            <s xml:id="echoid-s25136" xml:space="preserve">ar-
              <lb/>
            cus Meridiani inter ipſum, & </s>
            <s xml:id="echoid-s25137" xml:space="preserve">Horizontem extiterit uel æqualis, uel maior complemento altitudi-
              <lb/>
            nis poli ſupra Horizontem, transferenda erit recta H I, ex portione Analemmatis in rectã G N, ex
              <lb/>
            G, infra lineam æquinoctialem uſque ad punctum ρ, quod centrum erit horologii infra lineam æ-
              <lb/>
            quinoctialem exiſtens, ut in poſtremis duabus figuris apparet; </s>
            <s xml:id="echoid-s25138" xml:space="preserve">quoniam quando æqualis aut
              <lb/>
            maior eſt arcus dictus complemento altitudinis poli, ſecabit axis mundi faciem ſuperiorem pla-
              <lb/>
            ni horologii ad partes inferiores, ſiue boreales, ita ut cum linea ſtyli in ea facie deſcripta angulum
              <lb/>
            acutum faciat uerſus polum arcticum, ſeu uerſus partes ſuperiores, quemadmodum in horologio
              <lb/>
              <note position="left" xlink:label="note-0398-07" xlink:href="note-0398-07a" xml:space="preserve">50</note>
            Verticali boreali ſolet contingere.</s>
            <s xml:id="echoid-s25139" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s25140" xml:space="preserve">HÆC eriã omnia luce clarius colligũtur ex quatuor illis Analemmatibus in propoſ. </s>
            <s xml:id="echoid-s25141" xml:space="preserve">27. </s>
            <s xml:id="echoid-s25142" xml:space="preserve">huius
              <lb/>
              <note position="left" xlink:label="note-0398-08" xlink:href="note-0398-08a" xml:space="preserve">Qua ratione ex
                <lb/>
              quatuor Ana-
                <lb/>
              lemmatibus in
                <lb/>
              propoſ. 27. hu-
                <lb/>
              ius lib. poſitis
                <lb/>
              cognoſcatur,
                <lb/>
              quando centrũ
                <lb/>
              horologii eſt in
                <lb/>
              fra lineam ęqui
                <lb/>
              noctialem, &
                <lb/>
              quando ſupra.</note>
            libri poſitis. </s>
            <s xml:id="echoid-s25143" xml:space="preserve">Si enim in prioribus duobus intelligatur ex parte boreali arcus D K, æqualis arcui Me
              <lb/>
            ridiani inter planum & </s>
            <s xml:id="echoid-s25144" xml:space="preserve">Horizontem poſito, in duobus uerò poſterioribus ex parte auſtrali ponatur
              <lb/>
            arcus B K, eidem arcui Meridiani inter planum & </s>
            <s xml:id="echoid-s25145" xml:space="preserve">Horizontem æqualis, erit recta K L, commu-
              <lb/>
            nis ſectio Meridiani, & </s>
            <s xml:id="echoid-s25146" xml:space="preserve">circuli maximi, cui horologii planũ æquidiſtat. </s>
            <s xml:id="echoid-s25147" xml:space="preserve">Igitur M N, ipſi K L, pa-
              <lb/>
            rallela communis ſectio erit Meridiani, & </s>
            <s xml:id="echoid-s25148" xml:space="preserve">plani horologii illi maximo circulo æquidiſtantis, nem-
              <lb/>
            pelinea meridiana in horologio inclinato. </s>
            <s xml:id="echoid-s25149" xml:space="preserve">Meridianus enim ſecans dictum circulum maximum,
              <lb/>
            & </s>
            <s xml:id="echoid-s25150" xml:space="preserve">planum horologii illi æquidiſtans facit ſectiones parallelas. </s>
            <s xml:id="echoid-s25151" xml:space="preserve">Vnde ubi axis mundi F G, recta
              <lb/>
              <note position="left" xlink:label="note-0398-09" xlink:href="note-0398-09a" xml:space="preserve">16. vndec.</note>
            M N, ſecat in M, ibi centrum erit horologii in linea meridiana, punctum autem N, in eadem me
              <unsure/>
              <lb/>
            ridiana linea erit illud, per quod linea æquinoctialis ducitur, cum in eo Æquator lineam </s>
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