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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        <div xml:id="echoid-div1439" type="section" level="1" n="351">
          <p>
            <s xml:id="echoid-s27979" xml:space="preserve">
              <pb o="427" file="0443" n="443" rhead="LIBER QVARTVS."/>
            cto fixo, quod animo concipimus, tranſierint ex illis 24. </s>
            <s xml:id="echoid-s27980" xml:space="preserve">quibus Sol integram reuolutionem ab
              <lb/>
            eodem puncto ad idem punctum perficit.</s>
            <s xml:id="echoid-s27981" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s27982" xml:space="preserve">VERTICALES circuli, quoniam à circulis horariis non diſcrepant, cum per polos mun-
              <lb/>
            di ducantur, deſcribentur, vt horariæ lineæ, ſtatuendo quamlibet lineam Verticalem pro commu
              <lb/>
              <note position="right" xlink:label="note-0443-01" xlink:href="note-0443-01a" xml:space="preserve">Verticales cir-
                <lb/>
              @ uli.</note>
            ni ſectione Verticalis proprii dicti, & </s>
            <s xml:id="echoid-s27983" xml:space="preserve">plani horologii, à qua cæteræ computari debent.</s>
            <s xml:id="echoid-s27984" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s27985" xml:space="preserve">PARALLELI Horizontis, & </s>
            <s xml:id="echoid-s27986" xml:space="preserve">latitudinum ciuitatum depingentur etiam, vt paralleli ſi-
              <lb/>
              <note position="right" xlink:label="note-0443-02" xlink:href="note-0443-02a" xml:space="preserve">Paralleli Hori
                <lb/>
              zonris, & lat@@
                <lb/>
              dinum ciuita-
                <lb/>
              t
                <unsure/>
              u m.</note>
            gnorum Zodiaci, ſi loco radiorum Zodiaci deſcribantur radij integri quadrantis, &</s>
            <s xml:id="echoid-s27987" xml:space="preserve">c.</s>
            <s xml:id="echoid-s27988" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s27989" xml:space="preserve">MERIDIANI figurabũtur quoque, vt lineæ horariæ, ſi prius perſpecta fuerit poſitio primi
              <lb/>
            Meridiani per Inſulas Fortunatas ducti. </s>
            <s xml:id="echoid-s27990" xml:space="preserve">Cognoſci autẽ poterit ſitus primi illius Meridiani hac ra-
              <lb/>
              <note position="right" xlink:label="note-0443-03" xlink:href="note-0443-03a" xml:space="preserve">Meridiani c
                <unsure/>
              i@-
                <lb/>
              culi.</note>
            tione. </s>
            <s xml:id="echoid-s27991" xml:space="preserve">Obſeruetur ſitus alicuius vrbis notam habentis longitudinem, quæ à loco ſub polo conſti-
              <lb/>
              <note position="left" xlink:label="note-0443-04" xlink:href="note-0443-04a" xml:space="preserve">10</note>
            tuto diſtet aliquot milliariis, & </s>
            <s xml:id="echoid-s27992" xml:space="preserve">in plano, quod Horizonti ſit parallelum, à propoſito loco ſub po-
              <lb/>
            lo ducatur linea recta verſus illam ciuitatem, cuius longitudo nota eſt, & </s>
            <s xml:id="echoid-s27993" xml:space="preserve">ex puncto in ea vt libet
              <lb/>
            aſſumpto, circulus deſcribatur. </s>
            <s xml:id="echoid-s27994" xml:space="preserve">Nam quoniam illa recta communis ſectio eſt plani horologii ho-
              <lb/>
            rizontalis, & </s>
            <s xml:id="echoid-s27995" xml:space="preserve">Meridiani per illam ciuitatem ducti, ſi ab ea verſus occidentales partes, hoc eſt, cõ-
              <lb/>
            tra ſucceſſionem ſignorum, ſecundum motum Solis diurnum, numeretur longitudo dictę ci-
              <lb/>
            uitatis, & </s>
            <s xml:id="echoid-s27996" xml:space="preserve">à fine numerationis per centrum linea recta ducatur, habebitur communis ſectio Me-
              <lb/>
            ridiani primarij, & </s>
            <s xml:id="echoid-s27997" xml:space="preserve">plani horizontalis horologii, vt patet. </s>
            <s xml:id="echoid-s27998" xml:space="preserve">Quandocunque ergo vmbra ſtyli in
              <lb/>
            hanc lineam cadet, facili negotio in aliis planis ex umbra gnomonis aliam lineam ducemus ei
              <lb/>
            reſpondentem, pro Meridiano Inſularum Fortunatarum.</s>
            <s xml:id="echoid-s27999" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s28000" xml:space="preserve">DOMVS autem cœleſtes locum in hac ſphæra non habent, propterea quod neque Meridia-
              <lb/>
              <note position="left" xlink:label="note-0443-05" xlink:href="note-0443-05a" xml:space="preserve">20</note>
              <note position="right" xlink:label="note-0443-06" xlink:href="note-0443-06a" xml:space="preserve">Domu
                <unsure/>
              s cœ
                <unsure/>
              le
                <unsure/>
              -
                <lb/>
              @es in obliquiſ
                <lb/>
              @ma ſphæra
                <lb/>
              nullæ ſunt.</note>
            nus, neque Verticalis propriè dictus per puncta veri ortus, & </s>
            <s xml:id="echoid-s28001" xml:space="preserve">occaſus incedens aſſignari poſſit,
              <lb/>
            vt diximus.</s>
            <s xml:id="echoid-s28002" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s28003" xml:space="preserve">SIGNA denique aſcendentia nulla quoque ſunt, cum perpetuo ſex ſigna ſupra Horizontem
              <lb/>
              <note position="right" xlink:label="note-0443-07" xlink:href="note-0443-07a" xml:space="preserve">Signa aſcendẽ-
                <lb/>
              tia in eadem
                <lb/>
              ſph
                <unsure/>
              ęra obliquiſ
                <lb/>
              @ma nulla @@@.</note>
            appareant, & </s>
            <s xml:id="echoid-s28004" xml:space="preserve">ſex infra eundem abſcondantur. </s>
            <s xml:id="echoid-s28005" xml:space="preserve">Horologia igitur in ſphæra obliquiſſima, &</s>
            <s xml:id="echoid-s28006" xml:space="preserve">c. </s>
            <s xml:id="echoid-s28007" xml:space="preserve">con-
              <lb/>
            fecimus. </s>
            <s xml:id="echoid-s28008" xml:space="preserve">Quod faciendum erat.</s>
            <s xml:id="echoid-s28009" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1449" type="section" level="1" n="352">
          <head xml:id="echoid-head365" xml:space="preserve">PROBLEMA 11. PROPOSITIO 11.</head>
          <p>
            <s xml:id="echoid-s28010" xml:space="preserve">HOROLOGIA in ſphęra obliqua, in qua antarcticus polus ſu-
              <lb/>
            pra Horizontem attollitur, deſcribere.</s>
            <s xml:id="echoid-s28011" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">30</note>
          <p>
            <s xml:id="echoid-s28012" xml:space="preserve">QVONIAM omnia præcepta, quæ in 2. </s>
            <s xml:id="echoid-s28013" xml:space="preserve">& </s>
            <s xml:id="echoid-s28014" xml:space="preserve">3. </s>
            <s xml:id="echoid-s28015" xml:space="preserve">libro de horologiorum deſcriptionibus tradi
              <lb/>
            dimus, ad eam ſphęram obliquam ſpectant, quæ polum arcticum habet conſpicuum, viſum eſt
              <lb/>
            hoc problemmate paucis perſtringere, quomodo ſe gerere debeat is, qui horologia deſcribere ve-
              <lb/>
            lit in altera ſphæra obliqua, in qua antarcticus polus ſupra Horizontem eleuatur. </s>
            <s xml:id="echoid-s28016" xml:space="preserve">Hoc enim ſolũ
              <lb/>
            deeſſe videtur, vt per tradita præcepta horologia quis deſcribere in quacunque orbis terreni re-
              <lb/>
            gione poſſit: </s>
            <s xml:id="echoid-s28017" xml:space="preserve">quandoquidem hoc etiam libro regulas præſcripſimus, quibus & </s>
            <s xml:id="echoid-s28018" xml:space="preserve">in ſphæra recta,
              <lb/>
            & </s>
            <s xml:id="echoid-s28019" xml:space="preserve">in obliquiſſima, vbi polus arcticus ſupra Horizontem extollitur grad. </s>
            <s xml:id="echoid-s28020" xml:space="preserve">90. </s>
            <s xml:id="echoid-s28021" xml:space="preserve">horologia poſ-
              <lb/>
            ſint confici.</s>
            <s xml:id="echoid-s28022" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s28023" xml:space="preserve">DESCRIPTVRI igitur in hemiſphærio auſtrali horologia, vtemur iiſdem omnino præ-
              <lb/>
              <note position="left" xlink:label="note-0443-09" xlink:href="note-0443-09a" xml:space="preserve">40</note>
              <note position="right" xlink:label="note-0443-10" xlink:href="note-0443-10a" xml:space="preserve">Qua ration
                <unsure/>
              e in
                <lb/>
              ſphæra obli-
                <lb/>
              qua, quę
                <unsure/>
              c
                <unsure/>
              olu
                <unsure/>
              m
                <lb/>
              antarcticum ha
                <lb/>
              bet con pi
                <unsure/>
              e@ũ,
                <lb/>
              deſcriban
                <unsure/>
              tur.</note>
            ceptis, quæ lib. </s>
            <s xml:id="echoid-s28024" xml:space="preserve">2. </s>
            <s xml:id="echoid-s28025" xml:space="preserve">& </s>
            <s xml:id="echoid-s28026" xml:space="preserve">3. </s>
            <s xml:id="echoid-s28027" xml:space="preserve">dedimus, hac vna re animaduerſa, atque notata, vt quicquid ibi dictum eſt
              <lb/>
            de polo arctico, & </s>
            <s xml:id="echoid-s28028" xml:space="preserve">horis ante meridiem, hic intelligatur de antarctico polo, horisq́ue pomeridia-
              <lb/>
            nis. </s>
            <s xml:id="echoid-s28029" xml:space="preserve">Et quod ibidem in horologijs Verticalibus, declinantibus, inclinatis, &</s>
            <s xml:id="echoid-s28030" xml:space="preserve">c. </s>
            <s xml:id="echoid-s28031" xml:space="preserve">ſcripſimus de par-
              <lb/>
            re auſtrali, ac boreali, transferatur hic ad partem borealem, atque auſtralem. </s>
            <s xml:id="echoid-s28032" xml:space="preserve">Denique quæcunque
              <lb/>
            ibi de ſignis borealibus, auſtralibusve præcepimus, contrario modo hic de auſtralibus, boreali-
              <lb/>
            busve accipiantur eſſe dicta: </s>
            <s xml:id="echoid-s28033" xml:space="preserve">adeò vt ſi hæc commutatio polorum, horarum ante, & </s>
            <s xml:id="echoid-s28034" xml:space="preserve">poſt meridiẽ,
              <lb/>
            partis auſtralis, & </s>
            <s xml:id="echoid-s28035" xml:space="preserve">borealis, ac ſignorum borealium, auſtraliumq́ue fiat, quodlibet horologiũ lib.
              <lb/>
            </s>
            <s xml:id="echoid-s28036" xml:space="preserve">2. </s>
            <s xml:id="echoid-s28037" xml:space="preserve">& </s>
            <s xml:id="echoid-s28038" xml:space="preserve">3. </s>
            <s xml:id="echoid-s28039" xml:space="preserve">delineatum, verbi gratia, ad latitudinem grad. </s>
            <s xml:id="echoid-s28040" xml:space="preserve">42. </s>
            <s xml:id="echoid-s28041" xml:space="preserve">in hemiſphærio borali, exhibeat quoque
              <lb/>
            horologium in auſtrali hemiſphærio ad latitudinem grad. </s>
            <s xml:id="echoid-s28042" xml:space="preserve">42. </s>
            <s xml:id="echoid-s28043" xml:space="preserve">fabricatum. </s>
            <s xml:id="echoid-s28044" xml:space="preserve">Quod vt planius fiat,
              <lb/>
            per varia horologia in ſuperioribus libris deſcripta breuiter percurremus, declarantes in vnoquo-
              <lb/>
              <note position="left" xlink:label="note-0443-11" xlink:href="note-0443-11a" xml:space="preserve">50</note>
            que, quomodo in auſtrali hemiſphærio collocandum, quidque in eo immutandum ſit, vt ho-
              <lb/>
            ras commonſtret.</s>
            <s xml:id="echoid-s28045" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s28046" xml:space="preserve">HORIZONTALE ergo horologium in ſphæra obliqua, vbi polus antarcticus ſupra
              <lb/>
              <note position="right" xlink:label="note-0443-12" xlink:href="note-0443-12a" xml:space="preserve">Quomodo he-
                <lb/>
              rologium hoti
                <lb/>
              zontale pro
                <lb/>
              ſphæra obliqua
                <lb/>
              boreali fabrica
                <lb/>
              tum collocan-
                <lb/>
              dũ ſit in ſphæ-
                <lb/>
              ra obliqua au-
                <lb/>
              ſt@ali, & qua ra
                <lb/>
              tione numeri
                <lb/>
              horarum ſins
                <unsure/>
                <lb/>
              mu andi.</note>
            Horizontem eleuatur, ita collocandum eſt, vt centrum ipſius in boream, & </s>
            <s xml:id="echoid-s28047" xml:space="preserve">linea æquinoctialis in
              <lb/>
            auſtrum vergat, quia hac ratione axis mundi per centrum horologii, & </s>
            <s xml:id="echoid-s28048" xml:space="preserve">verticem gnomonis tran-
              <lb/>
            ſiens proprium ſitum habebit, hoc eſt, per polos mundi incedet. </s>
            <s xml:id="echoid-s28049" xml:space="preserve">Arcus quoque ſignorum borea
              <lb/>
            lium mutandi ſunt in arcus ſignorum auſtralium, & </s>
            <s xml:id="echoid-s28050" xml:space="preserve">arcus auſtralium in arcus borealium, ita vt
              <lb/>
            ſigna inter centrum, & </s>
            <s xml:id="echoid-s28051" xml:space="preserve">æquinoctialem lineam pertineant ad ſigna auſtralia, & </s>
            <s xml:id="echoid-s28052" xml:space="preserve">reliqua ad borealia@
              <lb/>
            quoniam ibi principium ♑, in meridie maximè ad Zenith accedit, principium vero ♋, ab eo-
              <lb/>
            d
              <unsure/>
            em maximè recedit. </s>
            <s xml:id="echoid-s28053" xml:space="preserve">Horæ denique mutandę ſunt in earum complementa vſque ad 12. </s>
            <s xml:id="echoid-s28054" xml:space="preserve">ſi à </s>
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