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-div733" type="section" level="1" n="179">
          <p>
            <s xml:id="echoid-s14637" xml:space="preserve">
              <pb o="214" file="0234" n="234" rhead="GNOMONICES"/>
            lumus, vt Auſtrale horologium indicet etiam horas in facie plani boreali.) </s>
            <s xml:id="echoid-s14638" xml:space="preserve">omnia lineamenta cũ
              <lb/>
              <note position="left" xlink:label="note-0234-01" xlink:href="note-0234-01a" xml:space="preserve">@atis eſt, vt de-
                <lb/>
              ſ@ribatur horo-
                <lb/>
              logium auſtra-
                <lb/>
              le; quia portio
                <lb/>
              ſuperior abſciſ-
                <lb/>
              ſa à linea hori-
                <lb/>
              zõtali d abit ho
                <lb/>
              rologium bo-
                <lb/>
              reale, ſi omnes
                <lb/>
              eius partes in-
                <lb/>
              uertantur.</note>
            numeris inter ſe reſpondebunt, ob æqualitatem rectarum H N, H K, & </s>
            <s xml:id="echoid-s14639" xml:space="preserve">H G, H G, & </s>
            <s xml:id="echoid-s14640" xml:space="preserve">ſectionum
              <lb/>
            conicarum, &</s>
            <s xml:id="echoid-s14641" xml:space="preserve">c. </s>
            <s xml:id="echoid-s14642" xml:space="preserve">Quocirca ſatis erit, ſi horologiũ Verticale, quod ad meridiem ſpectat, delineetur,
              <lb/>
            vna cum ſignorũ parallelis. </s>
            <s xml:id="echoid-s14643" xml:space="preserve">Nam linea horizõtalis A B, abſc indet portionẽ ex parte ſuperiore, quę
              <lb/>
            horologiũ boreale referet, ſi modo talẽ ſortiatur ſitũ in facie plani boreali, vt horizontalis linea in
              <lb/>
            ſuperiori loco collocetur, & </s>
            <s xml:id="echoid-s14644" xml:space="preserve">pars dextra, quæ tunc eſt verſus A, fiat ſiniſtra, & </s>
            <s xml:id="echoid-s14645" xml:space="preserve">ſiniſtra fiat dextra.
              <lb/>
            </s>
            <s xml:id="echoid-s14646" xml:space="preserve">Hæc autẽ inuerſio ita facile fiet. </s>
            <s xml:id="echoid-s14647" xml:space="preserve">Cõuerſo ad nos horologio auſtrali (quod inuerti debet) ita vt pro-
              <lb/>
            prium ſuũ ſitum habeat, ac poſitionẽ; </s>
            <s xml:id="echoid-s14648" xml:space="preserve">ſi in facie plani oppoſita, nempe boreali, eadem lineamenta
              <lb/>
              <note position="left" xlink:label="note-0234-02" xlink:href="note-0234-02a" xml:space="preserve">Qu@ pacto in-
                <lb/>
              @e@ti debeant
                <lb/>
              partes illius por
                <lb/>
              tionis horologii
                <lb/>
              auſtralis, quam
                <lb/>
              horizontalis li-
                <lb/>
              nea abſcindit,
                <lb/>
              vt exhibeat ho-
                <lb/>
              rologiũ borea-
                <lb/>
              le.</note>
            deſcribãtur, ita vt nulla in re à lineamentis Auſtralis horologij diſcrepent, ſed eis reſpondeant ad
              <lb/>
            vnguem; </s>
            <s xml:id="echoid-s14649" xml:space="preserve">deinde horologium hoc modo in facie oppoſita deſcriptum circumuoluatur circa ſtylũ,
              <lb/>
              <note position="left" xlink:label="note-0234-03" xlink:href="note-0234-03a" xml:space="preserve">10</note>
            tanquam axem, in eadem facie oppoſita, donec pars ſuperior euadat inferior, & </s>
            <s xml:id="echoid-s14650" xml:space="preserve">contra, lineaq́; </s>
            <s xml:id="echoid-s14651" xml:space="preserve">ho
              <lb/>
            rizontalis Horizonti æquidiſtet, habebimus in oppoſita facie horologium boreale in proprio ſitu,
              <lb/>
            ac ſi Auſtrale horologiũ inuerſum fuiſſet, vt diximus; </s>
            <s xml:id="echoid-s14652" xml:space="preserve">hoc eſt, ac ſi ſuperior pars Auſtralis horolo-
              <lb/>
            gii in inferiorem, & </s>
            <s xml:id="echoid-s14653" xml:space="preserve">dextra in ſiniſtram fuiſſet commutata: </s>
            <s xml:id="echoid-s14654" xml:space="preserve">vt patet rem attente conſideranti.</s>
            <s xml:id="echoid-s14655" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14656" xml:space="preserve">QVOD autem portio illa
              <lb/>
              <figure xlink:label="fig-0234-01" xlink:href="fig-0234-01a" number="162">
                <image file="0234-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0234-01"/>
              </figure>
            horologii Auſtralis, quam ab-
              <lb/>
            ſcindit linea horizontalis ex par
              <lb/>
            te ſuperiore, exhibeat nobis ho-
              <lb/>
            rologium Boreale, ſi inuertatur,
              <lb/>
            vt diximus, hinc etiam perſpi-
              <lb/>
              <note position="left" xlink:label="note-0234-04" xlink:href="note-0234-04a" xml:space="preserve">20</note>
            cuum fiet. </s>
            <s xml:id="echoid-s14657" xml:space="preserve">Quoniam, vt in ſcho
              <lb/>
            lio præcedentis propoſ. </s>
            <s xml:id="echoid-s14658" xml:space="preserve">demon-
              <lb/>
            ſtrauimus, horologium Auſtra-
              <lb/>
            le conuerſum, vt ſuperiora fiant
              <lb/>
            inferiora, & </s>
            <s xml:id="echoid-s14659" xml:space="preserve">dextra euadant ſini
              <lb/>
            ſtra, & </s>
            <s xml:id="echoid-s14660" xml:space="preserve">contra, mutatur in Bo-
              <lb/>
            reale; </s>
            <s xml:id="echoid-s14661" xml:space="preserve">eſtq́ue recta A B, commu-
              <lb/>
            nis ſectio Horizontis & </s>
            <s xml:id="echoid-s14662" xml:space="preserve">horolo-
              <lb/>
            gii, vt hic oſtẽſum eſt; </s>
            <s xml:id="echoid-s14663" xml:space="preserve">fit vt pars
              <lb/>
            illa, quam horizontalis linea ab-
              <lb/>
              <note position="left" xlink:label="note-0234-05" xlink:href="note-0234-05a" xml:space="preserve">30</note>
            ſcindit verſus lineam æquino-
              <lb/>
            ctialem, hoc eſt, verſus partem
              <lb/>
            ſuperiorem in horologio Borea
              <lb/>
            li, (quod factum eſt ex illa inuer
              <lb/>
            ſione horologii Auſtralis) ſit ſu
              <lb/>
            peruacanea, cum in illam vm-
              <lb/>
            bra ſtyli cadere non poſſit. </s>
            <s xml:id="echoid-s14664" xml:space="preserve">Qua-
              <lb/>
            re portio reliqua abſciſſa erit ho
              <lb/>
            rologium Boreale; </s>
            <s xml:id="echoid-s14665" xml:space="preserve">quod ad li-
              <lb/>
            neas horarum attinet. </s>
            <s xml:id="echoid-s14666" xml:space="preserve">Quod ve-
              <lb/>
              <note position="left" xlink:label="note-0234-06" xlink:href="note-0234-06a" xml:space="preserve">40</note>
            rò ſpectat ad arcus, parallelosve
              <lb/>
            ſignorũ, mutantur arcus ſigno-
              <lb/>
            rum horologii Auſtralis in ho-
              <lb/>
            rologio boreali in arcus ſigno-
              <lb/>
            rum oppoſitorum, vt arcus ♑,
              <lb/>
            in arcum ♋, &</s>
            <s xml:id="echoid-s14667" xml:space="preserve">c. </s>
            <s xml:id="echoid-s14668" xml:space="preserve">vt perſpicuum eſt ex Analemmate huius propoſ. </s>
            <s xml:id="echoid-s14669" xml:space="preserve">ſi rectè conſiderentur coni vm-
              <lb/>
              <note position="left" xlink:label="note-0234-07" xlink:href="note-0234-07a" xml:space="preserve">Arcus ſignorũ
                <lb/>
              horologii au-
                <lb/>
              ſtralis mutan-
                <lb/>
              tur in horolo
                <lb/>
              gio boreali in
                <lb/>
              arcus ſignorum
                <lb/>
              oppoſitorum.</note>
            bre, quibus planum horologij Auſtralis occurrit, & </s>
            <s xml:id="echoid-s14670" xml:space="preserve">coni vmbræ, quibus occurrit planum Borealis
              <lb/>
            horologii. </s>
            <s xml:id="echoid-s14671" xml:space="preserve">Sunt enim huiuſmodi coni vmbræ in vtroque horologio ſignorum oppoſitorum.
              <lb/>
            </s>
            <s xml:id="echoid-s14672" xml:space="preserve">Vt quemadmodum conus vmbræ, Sole exiſtente in principio ♑, abrumpitur in Auſtrali horolo-
              <lb/>
            gio in puncto N, & </s>
            <s xml:id="echoid-s14673" xml:space="preserve">prope locum ſtyli G, ita in horologio Boreali conus vmbræ, Sole exiſtente in
              <lb/>
              <note position="left" xlink:label="note-0234-08" xlink:href="note-0234-08a" xml:space="preserve">50</note>
            principio ♋, abrumpitur in puncto K, prope locum etiã ſtyli G, &</s>
            <s xml:id="echoid-s14674" xml:space="preserve">c. </s>
            <s xml:id="echoid-s14675" xml:space="preserve">Idem intelligendũ eſt de arcu
              <lb/>
              <note position="left" xlink:label="note-0234-09" xlink:href="note-0234-09a" xml:space="preserve">Arcus quoque
                <lb/>
              diurni horolo-
                <lb/>
              gii auſtralis mu
                <lb/>
              tantur in borea
                <lb/>
              li horologio in
                <lb/>
              arcus diurnos
                <lb/>
              oppoſitos.</note>
            bus diurnis, de quibus in ſequenti propoſ. </s>
            <s xml:id="echoid-s14676" xml:space="preserve">agemus. </s>
            <s xml:id="echoid-s14677" xml:space="preserve">Mutantur enim & </s>
            <s xml:id="echoid-s14678" xml:space="preserve">hi in arcus diurnos oppoſi-
              <lb/>
            tos in horologio boreali. </s>
            <s xml:id="echoid-s14679" xml:space="preserve">Vt arcus diurnus horarũ 10. </s>
            <s xml:id="echoid-s14680" xml:space="preserve">Auſtralis horologii mutatur in horologio
              <lb/>
            boreali in arcũ diurnũ horarum 14. </s>
            <s xml:id="echoid-s14681" xml:space="preserve">&</s>
            <s xml:id="echoid-s14682" xml:space="preserve">c. </s>
            <s xml:id="echoid-s14683" xml:space="preserve">Sed huius rei aliã cauſam afferemus propoſ. </s>
            <s xml:id="echoid-s14684" xml:space="preserve">21. </s>
            <s xml:id="echoid-s14685" xml:space="preserve">huius lib.</s>
            <s xml:id="echoid-s14686" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14687" xml:space="preserve">PORRO horizontalis linea pulchrè demonſtrat, quanam hora Sol in quolibet parallelo exi-
              <lb/>
            ſtens oriatur, aut occidat. </s>
            <s xml:id="echoid-s14688" xml:space="preserve">Nam vbi ſectiones conicæ ſecant lineam horizontalem, ibi Sol oritur
              <lb/>
              <note position="left" xlink:label="note-0234-10" xlink:href="note-0234-10a" xml:space="preserve">Horizontalis li
                <lb/>
              nea indicat, qua
                <lb/>
              hora Sol otia-
                <lb/>
              @ur, vel occidat.</note>
            vel occidit exiſtens in illis parallelis, quos dictæ ſectiones referunt. </s>
            <s xml:id="echoid-s14689" xml:space="preserve">Si igitur per illa puncta, vbi
              <lb/>
            ſe mutuo ſecant linea horizontalis, & </s>
            <s xml:id="echoid-s14690" xml:space="preserve">ſectiones conicę, lineæ horariæ ducantur indicabunt hæ tem
              <lb/>
            pus ortus & </s>
            <s xml:id="echoid-s14691" xml:space="preserve">occaſus Solis, &</s>
            <s xml:id="echoid-s14692" xml:space="preserve">c. </s>
            <s xml:id="echoid-s14693" xml:space="preserve">Ita vides in horologio Auſtrali, Solem exiſtentẽ in principio ♑, ori-
              <lb/>
            ri circa horam 7 {1/2}. </s>
            <s xml:id="echoid-s14694" xml:space="preserve">à media nocte, & </s>
            <s xml:id="echoid-s14695" xml:space="preserve">occidere circ a horam 4 {1/2}. </s>
            <s xml:id="echoid-s14696" xml:space="preserve">à meridie. </s>
            <s xml:id="echoid-s14697" xml:space="preserve">In ♒, verò & </s>
            <s xml:id="echoid-s14698" xml:space="preserve">♐, eun-
              <lb/>
            dem oriri paulo ante horam 7 {1/2}. </s>
            <s xml:id="echoid-s14699" xml:space="preserve">à media nocte, & </s>
            <s xml:id="echoid-s14700" xml:space="preserve">occidere paulo poſt horam 4 {1/2}. </s>
            <s xml:id="echoid-s14701" xml:space="preserve">à meridie.</s>
            <s xml:id="echoid-s14702" xml:space="preserve"/>
          </p>
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