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-s16342" xml:space="preserve">
              <pb o="241" file="0259" n="259" rhead="LIBER SECVNDVS."/>
            ris lib. </s>
            <s xml:id="echoid-s16343" xml:space="preserve">erunt N L, O L, P L, Q M, R M, S M, diametri conicarum ſectionum. </s>
            <s xml:id="echoid-s16344" xml:space="preserve">Et ſi puncta
              <lb/>
            N, O, P, Q, R, S, ex puncto K, accepta transferantur hinc inde in lineam horæ ſextæ horolo-
              <lb/>
            gij ex puncto A, vbi ſtylus collocandus eſt, proijcietur vmbra ſtyli in hæc puncta, cum Sol in ini
              <lb/>
            tijs ſignorum, & </s>
            <s xml:id="echoid-s16345" xml:space="preserve">circulo A B C D, horæ ſextæ Aſtronomicæ extiterit. </s>
            <s xml:id="echoid-s16346" xml:space="preserve">Si igitur circa diametros
              <lb/>
            N L, O L, P L, &</s>
            <s xml:id="echoid-s16347" xml:space="preserve">c. </s>
            <s xml:id="echoid-s16348" xml:space="preserve">ex propoſ. </s>
            <s xml:id="echoid-s16349" xml:space="preserve">8. </s>
            <s xml:id="echoid-s16350" xml:space="preserve">ſuperioris lib. </s>
            <s xml:id="echoid-s16351" xml:space="preserve">deſcribantur in aliqua materia dura conicæ ſe-
              <lb/>
            ctiones, excindanturq́ue, ut fiant quædam quaſi regulæ inflexæ, per quas eædem ſectiones in ho-
              <lb/>
            rologio deſcribantur, ita vt per puncta N, O, P, Q, R, S, tranſeant, earumq́ue axes cum linea
              <lb/>
              <note position="right" xlink:label="note-0259-01" xlink:href="note-0259-01a" xml:space="preserve">Satis eſt, deſcri-
                <lb/>
              bantur arcus ſi-
                <lb/>
              gnorum borea-
                <lb/>
              lium duntaxat,
                <lb/>
              vel auſtralium.</note>
            D E, horæ ſextæ coniungantur, deſcripti erunt paralleli ſignorum zodiaci. </s>
            <s xml:id="echoid-s16352" xml:space="preserve">Satis eſt autem, ſi ſectio
              <lb/>
            nes conicæ Signorum Borealium, vel Auſtralium deſcribantur; </s>
            <s xml:id="echoid-s16353" xml:space="preserve">quia hæ æquales ſunt ſectionibus
              <lb/>
            oppoſitorum ſignorum, cum omnes hyperbolæ ſint, vt ex propoſ. </s>
            <s xml:id="echoid-s16354" xml:space="preserve">6. </s>
            <s xml:id="echoid-s16355" xml:space="preserve">ſuperioris lib. </s>
            <s xml:id="echoid-s16356" xml:space="preserve">conſtat. </s>
            <s xml:id="echoid-s16357" xml:space="preserve">Vnde
              <lb/>
              <note position="left" xlink:label="note-0259-02" xlink:href="note-0259-02a" xml:space="preserve">10</note>
            beneficio earundem regularũ facile in oppoſita parte horologij deſcribentur per illa puncta, quæ
              <lb/>
            in linea horæ ſextę ſunt notata.</s>
            <s xml:id="echoid-s16358" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s16359" xml:space="preserve">IN vtroque autem horologio ſigna Borealia ſunt ea, quæ infra lineam æquinoctialem ſunt de-
              <lb/>
              <note position="right" xlink:label="note-0259-03" xlink:href="note-0259-03a" xml:space="preserve">In horologiis
                <lb/>
              Meridianis ſi-
                <lb/>
              gna borealia
                <lb/>
              ſ
                <unsure/>
              unt infra lineã
                <lb/>
              æquinoctialem,
                <lb/>
              & auſtralia ſu-
                <lb/>
              pra.</note>
            ſcripta, Auſtralia vero, quæ ſupra eandem continentur, ita vt in vtroque horologio proprium ſitũ
              <lb/>
            obtinente Borealia recedant à linea æquinoctiali in Auſtrum, & </s>
            <s xml:id="echoid-s16360" xml:space="preserve">Auſtralia in Boream. </s>
            <s xml:id="echoid-s16361" xml:space="preserve">Ratio hu-
              <lb/>
            ius eſt, quòd cum ſol oritur, vel occidit in ſignis Borealibus exiſtens, vmbra ſtyli cadat in partes au
              <lb/>
            ſtrales horizontalis lineæ; </s>
            <s xml:id="echoid-s16362" xml:space="preserve">in boreales vero, cum exiſtens in ſignis auſtralibus oritur, vel occidit, vt
              <lb/>
            manifeſtum eſt.</s>
            <s xml:id="echoid-s16363" xml:space="preserve"/>
          </p>
          <figure number="182">
            <image file="0259-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0259-01"/>
          </figure>
          <note position="left" xml:space="preserve">20</note>
          <note position="left" xml:space="preserve">30</note>
          <note position="left" xml:space="preserve">40</note>
          <p>
            <s xml:id="echoid-s16364" xml:space="preserve">QVONIAM autem Sole oriente, vmbra gnomonis iu horizontalem lineam A B, proijcitur
              <lb/>
              <note position="right" xlink:label="note-0259-07" xlink:href="note-0259-07a" xml:space="preserve">Portio horolo-
                <lb/>
              gii Meridiani
                <lb/>
              ſupra lineã ho-
                <lb/>
              rizontalem reſe
                <lb/>
              canda eſt, tan-
                <lb/>
              quam ſuperua-
                <lb/>
              canea.</note>
            in horologio orientali; </s>
            <s xml:id="echoid-s16365" xml:space="preserve">occidente vero eodem, in eandem horizontalem lineam proijcitur in oc-
              <lb/>
            cidentali horologio, vt ex propoſ. </s>
            <s xml:id="echoid-s16366" xml:space="preserve">11. </s>
            <s xml:id="echoid-s16367" xml:space="preserve">ſuperioris lib. </s>
            <s xml:id="echoid-s16368" xml:space="preserve">patet, fit vt toto reliquo tẽpore cuiuslibet diei,
              <lb/>
            Sole ſupra Horizontem eleuato, eadem vmbra in planum horologij infra lineam horizõtalem ca
              <lb/>
              <note position="left" xlink:label="note-0259-08" xlink:href="note-0259-08a" xml:space="preserve">50</note>
            dat. </s>
            <s xml:id="echoid-s16369" xml:space="preserve">Quocirca reſecanda eſt pars illa horologij, quæ ſupra horizontalem lineam continetur, tan-
              <lb/>
            quam ſuperuacanea, cum in illam vmbra ſtyli nunquam cadat.</s>
            <s xml:id="echoid-s16370" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s16371" xml:space="preserve">PARS tamen illa ſuperior vtriuſuis horologii abſciſſa à linea horizontali dabit horologium
              <lb/>
              <note position="right" xlink:label="note-0259-09" xlink:href="note-0259-09a" xml:space="preserve">Portio vtriuſ-
                <lb/>
              uis horologii
                <lb/>
              Meridiani ab-
                <lb/>
              ſciſſa à
                <unsure/>
              linea ho
                <lb/>
              rizontali efficic
                <unsure/>
                <lb/>
              horologium in
                <lb/>
              parte oppoſita
                <lb/>
              plani, ſi partes
                <lb/>
              immutentur, ut
                <lb/>
              ſupra dictũ eſt.</note>
            in facie plani horologij oppoſita collocandum, dummodo inuertatur, vt pars, quæ nunc ſuperior
              <lb/>
            eſt, fiat inferior, & </s>
            <s xml:id="echoid-s16372" xml:space="preserve">contra, & </s>
            <s xml:id="echoid-s16373" xml:space="preserve">quæ poſt hanc inuerſionem dextra eſt, fiat ſiniſtra, vt in ſcholio pro-
              <lb/>
            poſ. </s>
            <s xml:id="echoid-s16374" xml:space="preserve">14. </s>
            <s xml:id="echoid-s16375" xml:space="preserve">huius libri præcepimus; </s>
            <s xml:id="echoid-s16376" xml:space="preserve">horæq́ue, quæ à media nocte computabantur, numerentur à meri
              <lb/>
            die, & </s>
            <s xml:id="echoid-s16377" xml:space="preserve">è contrario; </s>
            <s xml:id="echoid-s16378" xml:space="preserve">ſigna denique borealia mutentur in auſtralia, & </s>
            <s xml:id="echoid-s16379" xml:space="preserve">auſtralia in borealia. </s>
            <s xml:id="echoid-s16380" xml:space="preserve">Cũ enim,
              <lb/>
            vt in ſcholio propoſ. </s>
            <s xml:id="echoid-s16381" xml:space="preserve">antecedentis oſtendimus, hac facta inuerſione, lineæ horariæ ſuperiotis par-
              <lb/>
            tis abſciſſæ in vtrouis horologio congruant horariis lineis horologii in facie plani oppoſita deſcri
              <lb/>
            pti, congruet etiam axis hyperbolarum ♋, & </s>
            <s xml:id="echoid-s16382" xml:space="preserve">♑, axi hyperbolarum ♋, & </s>
            <s xml:id="echoid-s16383" xml:space="preserve">♑, cum vtrobique axis
              <lb/>
            hic ſit linea horæ 6. </s>
            <s xml:id="echoid-s16384" xml:space="preserve">à meridie, vel media nocte. </s>
            <s xml:id="echoid-s16385" xml:space="preserve">Cum ergo axis tranſuerſus hyperbolarum dictarũ
              <lb/>
            in horologio orientali æqualis ſit axi tranſuerſo earundem in occidentali, propterea quòd & </s>
            <s xml:id="echoid-s16386" xml:space="preserve"/>
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