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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            <s xml:id="echoid-s20873" xml:space="preserve">
              <pb o="310" file="0326" n="326" rhead="GNOMONICES"/>
            ctam H O, quæ perpendicularis est ad lineam indicis, eſſe lineam æquinoctialem eiuſdem horologii, vt ex
              <lb/>
            ſuperioribus conſtat.</s>
            <s xml:id="echoid-s20874" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s20875" xml:space="preserve">QVIA verò in æquinoctiali linea H O, recta H O, ipſi H R, ſumpta eſt æqualis, erit per ea, quæ
              <lb/>
            demonstrata ſunt, recta ex centro π, ad O, ducta axis mundi, conſtituens in π, cum linea ſtyli π H,
              <lb/>
            angulum O π H, æqualem angulo I C H, quem prior axis I C, cum linea indicis facit. </s>
            <s xml:id="echoid-s20876" xml:space="preserve">Nam idem ſem-
              <lb/>
            per est angulus altitudinis poli ſupra idem planum declinans, quem quidem axis mundi cum linea indicis
              <lb/>
            conſtituit, vt ex ſuperiorib{us} conſtat. </s>
            <s xml:id="echoid-s20877" xml:space="preserve">Quare paralleli erunt axes O π, I C; </s>
            <s xml:id="echoid-s20878" xml:space="preserve">ac proinde recta O P, quæ
              <lb/>
              <note position="left" xlink:label="note-0326-01" xlink:href="note-0326-01a" xml:space="preserve">28. primi.</note>
            ipſi I C, parallela ducta eſt, etiamſi illam non producamus vſque ad centrum π, quod aliquando nobis eſt
              <lb/>
            ignotum, erit axis mundi. </s>
            <s xml:id="echoid-s20879" xml:space="preserve">Ex quo fit rectam H Q, ad axem perpendicularem, communem ſectionem
              <lb/>
            eſſe Aequatoris, ac Meridiani proprii ipſius plani declinantis.</s>
            <s xml:id="echoid-s20880" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">10</note>
          <p style="it">
            <s xml:id="echoid-s20881" xml:space="preserve">RVRSVS cum ex R, ad lineam declinationis S R, ducta ſit perpendicularis R T, tranſibit neceſ-
              <lb/>
            ſario per T, vt ſupra oſtendimus, linea horæ 6. </s>
            <s xml:id="echoid-s20882" xml:space="preserve">ac propterea recta ex centro π, per punctum T, educta
              <lb/>
            dabit horam 6. </s>
            <s xml:id="echoid-s20883" xml:space="preserve">faciet{q́ue} in π, cum linea ſtyli angulum T π H, æqualem angulo N C H, quem minoris ho-
              <lb/>
            rologii linea horæ 6. </s>
            <s xml:id="echoid-s20884" xml:space="preserve">C N, cum indicis linea C H, constituit. </s>
            <s xml:id="echoid-s20885" xml:space="preserve">Nam circulus horæ 6. </s>
            <s xml:id="echoid-s20886" xml:space="preserve">eandem ſeruat perpe-
              <lb/>
            tuo inclinationem ad Meridianum proprium vnius eiuſdemq́, plani declinantis; </s>
            <s xml:id="echoid-s20887" xml:space="preserve">ac propterea communes
              <lb/>
            ſectiones horum circulorum, quas cum eodem plano declinante faciunt, (ſumpta quacunque longitudine
              <lb/>
            ſtyli, per cuius verticem ducuntur) eundem ſemper angulum conſtituent, qui videlicet æqualis ſit angulo,
              <lb/>
            quem eorundem circulorum ſectiones in circulo maximo, cui planum horologii ęquidiſtat, factæ conſti-
              <lb/>
            tuunt. </s>
            <s xml:id="echoid-s20888" xml:space="preserve">Nam dictæ ſectiones æquales angulos constituunt in plano horologii, & </s>
            <s xml:id="echoid-s20889" xml:space="preserve">in circulo maximo, cui
              <lb/>
            horologium ęquidistans eſt, vt prope finem huius propoſ. </s>
            <s xml:id="echoid-s20890" xml:space="preserve">demonſtr auimus de angulis, quos conſtituunt ſe-
              <lb/>
              <note position="left" xlink:label="note-0326-03" xlink:href="note-0326-03a" xml:space="preserve">20</note>
            ctiones, quas Meridianus proprius plani declinantis, & </s>
            <s xml:id="echoid-s20891" xml:space="preserve">Meridianus Horizontis faciunt in eodem plano
              <lb/>
            horologii, & </s>
            <s xml:id="echoid-s20892" xml:space="preserve">in maximo circulo, cui hoc planum æquidiſtat. </s>
            <s xml:id="echoid-s20893" xml:space="preserve">Quocirca parallelæ erunt lineæ T π, N C,
              <lb/>
              <note position="left" xlink:label="note-0326-04" xlink:href="note-0326-04a" xml:space="preserve">28. primi.</note>
            ac propterea recta T V, quam ipſi N C, parallelam duximus, licet ea vſque ad centrum π, quod fortaſ-
              <lb/>
            ſis in plano horologii non exiſtit, non producatur, erit linea horæ 6.</s>
            <s xml:id="echoid-s20894" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s20895" xml:space="preserve">HAEC cum ita ſint, perſpicuum eſt ex demonſtratis in priore deſcriptione huius propoſ. </s>
            <s xml:id="echoid-s20896" xml:space="preserve">lineas horæ
              <lb/>
            rias ducendas eſſe per puncta illa rectæ H O, vbi ab occultis lineis ex centro Z, prodeuntibus ſecatur,
              <lb/>
            quandoquidem diuiſio circuli ex Z, deſcripti initium habet à recta, quæ per horam vnam tranſit in æqui-
              <lb/>
            noctiali linea H O, nempe à recta Z X, quę per horam 6. </s>
            <s xml:id="echoid-s20897" xml:space="preserve">tranſit. </s>
            <s xml:id="echoid-s20898" xml:space="preserve">Eadem ratione, cum Y P, ſit communis
              <lb/>
            ſectio Aequatoris, & </s>
            <s xml:id="echoid-s20899" xml:space="preserve">proprii Meridiani ipſius plani declinantis, vt ex demonſtratis patet, quòd perpen-
              <lb/>
            dicularis ſit ad axem eundem O P, ducendę eruni horariæ lineæ per puncta æquinoctialis lineę Y V, in
              <lb/>
              <note position="left" xlink:label="note-0326-05" xlink:href="note-0326-05a" xml:space="preserve">30</note>
            quibus eam ſecant occultæ lineæ ex a, emiſſæ; </s>
            <s xml:id="echoid-s20900" xml:space="preserve">propterea quòd diuiſio circuli ex a, deſcripti initium quoque
              <lb/>
            habet à recta a V, quæ per horam 6. </s>
            <s xml:id="echoid-s20901" xml:space="preserve">ducitur in æquinoctiali linea Y V. </s>
            <s xml:id="echoid-s20902" xml:space="preserve">Rectè ergo lineæ horariæ ducun-
              <lb/>
            tur per puncta illa in rectis H O, Y V, inuenta, etiamſi centrum π, vbi omnes coirent, ſi producerentur,
              <lb/>
            ignotum nobis ſit, nempe extra planum exiſtens, vel certè remotiſſimum à puncto H. </s>
            <s xml:id="echoid-s20903" xml:space="preserve">In exemplo propo-
              <lb/>
            ſito, quia lineæ horæ 12. </s>
            <s xml:id="echoid-s20904" xml:space="preserve">& </s>
            <s xml:id="echoid-s20905" xml:space="preserve">1. </s>
            <s xml:id="echoid-s20906" xml:space="preserve">à meridie ſunt etiam deſcriptæ, perſpicuè apparet, rectas per centra Z, a,
              <lb/>
            duct{as}, quæ ad rectos angulos ſecant rectas Z X, a V, tranſeuntes per horam 6. </s>
            <s xml:id="echoid-s20907" xml:space="preserve">in vtraque æquinoctiali
              <lb/>
            linea, cadere in illa puncta linearum æquinoctialium H O, Y V, per quæ linea horæ 12. </s>
            <s xml:id="echoid-s20908" xml:space="preserve">ducitur; </s>
            <s xml:id="echoid-s20909" xml:space="preserve">ac pro-
              <lb/>
            inde eſſe ill{as}, à quib{us} diuiſiones circulorum ex Z, a, deſcriptorum inchoandę eſſent, vt ſupra docuim{us}.
              <lb/>
            </s>
            <s xml:id="echoid-s20910" xml:space="preserve">Sed quia, vt dixim{us}, in planis, quæ nimium à Verticali declinant, neque line a horæ 12. </s>
            <s xml:id="echoid-s20911" xml:space="preserve">neque centrum
              <lb/>
            commodè notari poteſt, iuſſimus eaſdem diuiſiones inchoandas eſſe à rectis Z X, a V, &</s>
            <s xml:id="echoid-s20912" xml:space="preserve">c. </s>
            <s xml:id="echoid-s20913" xml:space="preserve">Stylum autem
              <lb/>
              <note position="left" xlink:label="note-0326-06" xlink:href="note-0326-06a" xml:space="preserve">40</note>
            eſſe Q b, eius{q́ue} locum in b, ex dictis conſtat, cum triangulum π Q H, perinde ſit conſtructum vt triangu
              <lb/>
            lum C I G, in ſuperiori figur a hui{us} propoſitionis.</s>
            <s xml:id="echoid-s20914" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s20915" xml:space="preserve">CAETERVM quodcunque horologium declinans à meridie, ſeptentrioneve in ortum, vel occa-
              <lb/>
              <note position="left" xlink:label="note-0326-07" xlink:href="note-0326-07a" xml:space="preserve">Si lineamenta
                <lb/>
              cuiuſcũque ho-
                <lb/>
              rologii declinã
                <lb/>
              tis a meridi
                <unsure/>
              e, ſe
                <lb/>
              ptẽttioneve in
                <lb/>
              or@um ita im-
                <lb/>
              mutentur, vt
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              dextra fiant ſi-
                <lb/>
              niſtra, & cõtra,
                <lb/>
              habebitur a
                <lb/>
              liud horologiũ
                <lb/>
              declinans à me
                <lb/>
              ridie ſeptentrio
                <lb/>
              neve in occasũ,
                <lb/>
              & e contrario.</note>
            ſum, ſi lineamenta ita inter ſe permutent ordinem, vt ſinistra in dextra, & </s>
            <s xml:id="echoid-s20916" xml:space="preserve">dextra in ſinistra conuertan-
              <lb/>
            tur, adeo vt talem ſitum adipiſcantur, qualem haberent lineamenta horologii, ſi in facie oppoſita plani
              <lb/>
            deſcripta eſſent, ea lege, vt ſingulæ lineę ſingulis lineis reſponderent, exhibebit nobis aliud horologium à
              <lb/>
            meridie, vel ſeptentrione declinans totidem gradib{us}, quot antea, ſed in contrariam partem; </s>
            <s xml:id="echoid-s20917" xml:space="preserve">ita vt ſi il-
              <lb/>
            lud à meridie, vel ſeptentrione in ortum deflectat, hoc à meridie quoque, vel ſeptentrione vergat in oc-
              <lb/>
            caſum, & </s>
            <s xml:id="echoid-s20918" xml:space="preserve">ſi illud declinet in occaſum, hoc in ortum ſpectet. </s>
            <s xml:id="echoid-s20919" xml:space="preserve">Commutandi autem ſunt numeri horarum
              <lb/>
            in earundem complementa vſque ad 12. </s>
            <s xml:id="echoid-s20920" xml:space="preserve">vt hora 1. </s>
            <s xml:id="echoid-s20921" xml:space="preserve">in 11. </s>
            <s xml:id="echoid-s20922" xml:space="preserve">& </s>
            <s xml:id="echoid-s20923" xml:space="preserve">2. </s>
            <s xml:id="echoid-s20924" xml:space="preserve">in 10. </s>
            <s xml:id="echoid-s20925" xml:space="preserve">&</s>
            <s xml:id="echoid-s20926" xml:space="preserve">c. </s>
            <s xml:id="echoid-s20927" xml:space="preserve">Hac arte vides in ſequenti
              <lb/>
              <note position="left" xlink:label="note-0326-08" xlink:href="note-0326-08a" xml:space="preserve">50</note>
            figura ex ſuperiore horologio declinante à meridie in ortum grad. </s>
            <s xml:id="echoid-s20928" xml:space="preserve">30. </s>
            <s xml:id="echoid-s20929" xml:space="preserve">fabricatum eſſe horologium decli-
              <lb/>
            nans à meridie in occaſum grad. </s>
            <s xml:id="echoid-s20930" xml:space="preserve">30.</s>
            <s xml:id="echoid-s20931" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s20932" xml:space="preserve">RATIO huiuſce rei obſcura non eſt, ſi attentè, & </s>
            <s xml:id="echoid-s20933" xml:space="preserve">diligenter præcepta hui{us} propoſ. </s>
            <s xml:id="echoid-s20934" xml:space="preserve">conſiderentur.
              <lb/>
            </s>
            <s xml:id="echoid-s20935" xml:space="preserve">Quoniam enim duobus horologijs à meridie, vel ſeptentrione in diuerſas partes declinantib{us}, nempe vno
              <lb/>
            in ortum, & </s>
            <s xml:id="echoid-s20936" xml:space="preserve">in occaſum altero, linea declinationis E F, in oppoſit{as} partes ducitur ex puncto E, vt di-
              <lb/>
            ctum eſt, fit vt & </s>
            <s xml:id="echoid-s20937" xml:space="preserve">linea ſtyliex centro C, in contrari{as} partes quoque protendatur, cum ea ducatur ex
              <lb/>
            C, per punctum G, in quod cadit F G, ducta ex F, puncto lineæ declinationis ad A B, perpendicularis,
              <lb/>
            & </s>
            <s xml:id="echoid-s20938" xml:space="preserve">ob id linea quoque ęquinoctialis lineam ſtyli ad angulos rectos ſecans ſit{us} contrarios obtineat. </s>
            <s xml:id="echoid-s20939" xml:space="preserve">Eo-
              <lb/>
            dem pacto linea horæ 6. </s>
            <s xml:id="echoid-s20940" xml:space="preserve">quæ ex C, ducitur per illud punctum rectę A B, in quod cadit F α, ducta ex F,
              <lb/>
            ad lineam declinationis ad angulos rectos, non poterit habere eundem ſitum in vtroque horologio, idem{q́ue}
              <lb/>
            de alijs lineis dicendum eſt. </s>
            <s xml:id="echoid-s20941" xml:space="preserve">Vnde cum lineę vni{us} horologij eaſdem inter ſe habeant diſtantias, </s>
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