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-div609" type="section" level="1" n="154">
          <p style="it">
            <s xml:id="echoid-s11256" xml:space="preserve">
              <pb o="174" file="0194" n="194" rhead="GNOMONICES"/>
            quoniam Sol nondum peruenit tunc ad Meridianum Fortunatarum Inſularum, quòd earum linea meri-
              <lb/>
            diana in horologio ſit orientalior, quàm meridiana linea grad. </s>
            <s xml:id="echoid-s11257" xml:space="preserve">60. </s>
            <s xml:id="echoid-s11258" xml:space="preserve">diſtabit propterea Sol horis 4. </s>
            <s xml:id="echoid-s11259" xml:space="preserve">ante
              <lb/>
            meridiem illarum inſularum; </s>
            <s xml:id="echoid-s11260" xml:space="preserve">ac proinde erit tunc apud eaſdem hora octaua poſt mediam noctem. </s>
            <s xml:id="echoid-s11261" xml:space="preserve">Simi-
              <lb/>
            liter ſi ſcire lubet, quotatunc hora ſit in regione, cuius longitudo comprehendit grad. </s>
            <s xml:id="echoid-s11262" xml:space="preserve">300. </s>
            <s xml:id="echoid-s11263" xml:space="preserve">Aufero grad.
              <lb/>
            </s>
            <s xml:id="echoid-s11264" xml:space="preserve">300. </s>
            <s xml:id="echoid-s11265" xml:space="preserve">ex grad. </s>
            <s xml:id="echoid-s11266" xml:space="preserve">60. </s>
            <s xml:id="echoid-s11267" xml:space="preserve">adiecto prius, more Aſtronomorum, integro circulo grad. </s>
            <s xml:id="echoid-s11268" xml:space="preserve">360. </s>
            <s xml:id="echoid-s11269" xml:space="preserve">ita vt fiãt grad. </s>
            <s xml:id="echoid-s11270" xml:space="preserve">420. </s>
            <s xml:id="echoid-s11271" xml:space="preserve">re-
              <lb/>
            linquuntur{q́ue} grad. </s>
            <s xml:id="echoid-s11272" xml:space="preserve">120. </s>
            <s xml:id="echoid-s11273" xml:space="preserve">qui faciunt horas 8. </s>
            <s xml:id="echoid-s11274" xml:space="preserve">Tot ergo horis abest tunc Sol ante meridiem illius loci, ac
              <lb/>
            propterea habebunt illi tunc populi horam quartam post mediam noctem. </s>
            <s xml:id="echoid-s11275" xml:space="preserve">Rurſus idem cupio cognoſcere
              <lb/>
            in eo loco, vbi longitudo eſt grad. </s>
            <s xml:id="echoid-s11276" xml:space="preserve">110. </s>
            <s xml:id="echoid-s11277" xml:space="preserve">qualis fere eſt Calecutij in India orientali. </s>
            <s xml:id="echoid-s11278" xml:space="preserve">Demo grad. </s>
            <s xml:id="echoid-s11279" xml:space="preserve">110. </s>
            <s xml:id="echoid-s11280" xml:space="preserve">ex
              <lb/>
            grad. </s>
            <s xml:id="echoid-s11281" xml:space="preserve">60. </s>
            <s xml:id="echoid-s11282" xml:space="preserve">adiecto prius integro circulo, remanent{q́ue} grad. </s>
            <s xml:id="echoid-s11283" xml:space="preserve">310. </s>
            <s xml:id="echoid-s11284" xml:space="preserve">qui complectuntur horas 20. </s>
            <s xml:id="echoid-s11285" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s11286" xml:space="preserve">40. </s>
            <s xml:id="echoid-s11287" xml:space="preserve">atque
              <lb/>
            tot horæ deſunt in illo loco, vt ſit meridies. </s>
            <s xml:id="echoid-s11288" xml:space="preserve">Et quoniam à meridie ad meridiem effluunt horę 24. </s>
            <s xml:id="echoid-s11289" xml:space="preserve">neceſſe
              <lb/>
              <note position="left" xlink:label="note-0194-01" xlink:href="note-0194-01a" xml:space="preserve">10</note>
            est, tunc elapſas eſſe horas 3. </s>
            <s xml:id="echoid-s11290" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s11291" xml:space="preserve">20. </s>
            <s xml:id="echoid-s11292" xml:space="preserve">poſt meridiem proximum. </s>
            <s xml:id="echoid-s11293" xml:space="preserve">Pariratione, ſi quæratur tunc
              <lb/>
            hora in eo loco, vbi longitudo continet grad. </s>
            <s xml:id="echoid-s11294" xml:space="preserve">240. </s>
            <s xml:id="echoid-s11295" xml:space="preserve">Deductis grad. </s>
            <s xml:id="echoid-s11296" xml:space="preserve">240. </s>
            <s xml:id="echoid-s11297" xml:space="preserve">ex grad. </s>
            <s xml:id="echoid-s11298" xml:space="preserve">60. </s>
            <s xml:id="echoid-s11299" xml:space="preserve">(adiecto prius
              <lb/>
            integro circulo grad. </s>
            <s xml:id="echoid-s11300" xml:space="preserve">360. </s>
            <s xml:id="echoid-s11301" xml:space="preserve">vt fiant grad. </s>
            <s xml:id="echoid-s11302" xml:space="preserve">420.) </s>
            <s xml:id="echoid-s11303" xml:space="preserve">reliqui ſunt grad. </s>
            <s xml:id="echoid-s11304" xml:space="preserve">180. </s>
            <s xml:id="echoid-s11305" xml:space="preserve">qui continent horas 12. </s>
            <s xml:id="echoid-s11306" xml:space="preserve">Di-
              <lb/>
            cam ergo, Solem distare à meridie dicti loci horis 12. </s>
            <s xml:id="echoid-s11307" xml:space="preserve">ac proinde mediam noctem tunc eſſe. </s>
            <s xml:id="echoid-s11308" xml:space="preserve">Poſtremo
              <lb/>
            ſi idem deſideretur in regione longitudinis grad. </s>
            <s xml:id="echoid-s11309" xml:space="preserve">10. </s>
            <s xml:id="echoid-s11310" xml:space="preserve">qualem habet fere Toletum Hiſpaniæ. </s>
            <s xml:id="echoid-s11311" xml:space="preserve">Aufero grad.
              <lb/>
            </s>
            <s xml:id="echoid-s11312" xml:space="preserve">10. </s>
            <s xml:id="echoid-s11313" xml:space="preserve">ex grad. </s>
            <s xml:id="echoid-s11314" xml:space="preserve">60. </s>
            <s xml:id="echoid-s11315" xml:space="preserve">relinquuntur{q́ue} grad. </s>
            <s xml:id="echoid-s11316" xml:space="preserve">50. </s>
            <s xml:id="echoid-s11317" xml:space="preserve">qui dant horas 3. </s>
            <s xml:id="echoid-s11318" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s11319" xml:space="preserve">20. </s>
            <s xml:id="echoid-s11320" xml:space="preserve">Tot ergo horis diſtat tunc Sol ante
              <lb/>
            meridiem Toleti. </s>
            <s xml:id="echoid-s11321" xml:space="preserve">Vnde eo tempore habebunt incolæ dictæ vrbis horas 8. </s>
            <s xml:id="echoid-s11322" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s11323" xml:space="preserve">40. </s>
            <s xml:id="echoid-s11324" xml:space="preserve">poſt mediam noctem. </s>
            <s xml:id="echoid-s11325" xml:space="preserve">
              <lb/>
            Idem iudicium de cæteris habendum eſt.</s>
            <s xml:id="echoid-s11326" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s11327" xml:space="preserve">IDEM quoque aſſequemur, & </s>
            <s xml:id="echoid-s11328" xml:space="preserve">fortaſſis commodius, hoc modo. </s>
            <s xml:id="echoid-s11329" xml:space="preserve">Si longitudo Meridiani, in cuius li-
              <lb/>
            neam vmbra tempore obſeruationis cadit, minor fuerit longitudine illius loci, pro quo hora quæritur, de-
              <lb/>
              <note position="left" xlink:label="note-0194-02" xlink:href="note-0194-02a" xml:space="preserve">20</note>
            trahatur minor longitudo ex maiore. </s>
            <s xml:id="echoid-s11330" xml:space="preserve">Gradus enim reliqui ad horas reuocati dabunt tempus elapſum à
              <lb/>
            meridie dicti loci. </s>
            <s xml:id="echoid-s11331" xml:space="preserve">Vnde ſi horę pauciores fuerint, quàm 12. </s>
            <s xml:id="echoid-s11332" xml:space="preserve">cognitæ erunt horę à meridie; </s>
            <s xml:id="echoid-s11333" xml:space="preserve">ſi verò fue-
              <lb/>
            rint præcisè 12. </s>
            <s xml:id="echoid-s11334" xml:space="preserve">erunt præcisè horæ 12. </s>
            <s xml:id="echoid-s11335" xml:space="preserve">à meridie, nempe tempus mediæ noctis; </s>
            <s xml:id="echoid-s11336" xml:space="preserve">ſi denique plures fue-
              <lb/>
            rint, quàm 12. </s>
            <s xml:id="echoid-s11337" xml:space="preserve">ablatis 12. </s>
            <s xml:id="echoid-s11338" xml:space="preserve">ex ipſis, remanebunt horæ poſt mediam noctem. </s>
            <s xml:id="echoid-s11339" xml:space="preserve">Siautem longitudo Meri-
              <lb/>
            diani, in cuius lineam vmbra cadit, maior fuerit longitudine alterius loci propoſiti, detracta minore lon-
              <lb/>
            gitudine ex maiori, relinquentur gradus, qui ad horas reducti dabunt tempus ante meridiem dicti loci.
              <lb/>
            </s>
            <s xml:id="echoid-s11340" xml:space="preserve">Vnde ſi pauciores fuerint, quàm 12. </s>
            <s xml:id="echoid-s11341" xml:space="preserve">detractis illis ex 12. </s>
            <s xml:id="echoid-s11342" xml:space="preserve">remanebunt horę poſt mediam noctem; </s>
            <s xml:id="echoid-s11343" xml:space="preserve">Si ve-
              <lb/>
            rò fuerint præcisè 12. </s>
            <s xml:id="echoid-s11344" xml:space="preserve">erunt omnino horæ 12. </s>
            <s xml:id="echoid-s11345" xml:space="preserve">ante meridiem, nempe tempus mediæ noctis; </s>
            <s xml:id="echoid-s11346" xml:space="preserve">ſi denique plu-
              <lb/>
            res fuerint, quàm 12. </s>
            <s xml:id="echoid-s11347" xml:space="preserve">detractis eis ex 24. </s>
            <s xml:id="echoid-s11348" xml:space="preserve">remanebunt horæ à meridie elapſæ. </s>
            <s xml:id="echoid-s11349" xml:space="preserve">Exemplum. </s>
            <s xml:id="echoid-s11350" xml:space="preserve">Cadat rurſum
              <lb/>
            quolibet anni tempore extremitas vmbræ ſtyli in lineam meridianam grad. </s>
            <s xml:id="echoid-s11351" xml:space="preserve">60. </s>
            <s xml:id="echoid-s11352" xml:space="preserve">quanta nimirum longitu-
              <lb/>
              <note position="left" xlink:label="note-0194-03" xlink:href="note-0194-03a" xml:space="preserve">30</note>
            do est Alexandriæ Vrbis Aegypti, operæ{q́ue} pretium ſit cognoſcere, quota tunc hora ſit in eo loco, cuius
              <lb/>
            longitudo complectitur grad. </s>
            <s xml:id="echoid-s11353" xml:space="preserve">300. </s>
            <s xml:id="echoid-s11354" xml:space="preserve">Aufero minorem longitudinem ex maiore, nimirum grad. </s>
            <s xml:id="echoid-s11355" xml:space="preserve">60. </s>
            <s xml:id="echoid-s11356" xml:space="preserve">ex 300.
              <lb/>
            </s>
            <s xml:id="echoid-s11357" xml:space="preserve">& </s>
            <s xml:id="echoid-s11358" xml:space="preserve">reliquos grad. </s>
            <s xml:id="echoid-s11359" xml:space="preserve">240. </s>
            <s xml:id="echoid-s11360" xml:space="preserve">reduco ad horas 16. </s>
            <s xml:id="echoid-s11361" xml:space="preserve">quæ elapſæ ſunt à meridie illius loci. </s>
            <s xml:id="echoid-s11362" xml:space="preserve">Vnde inſtat tunc hora
              <lb/>
            quarta poſt mediam noctem. </s>
            <s xml:id="echoid-s11363" xml:space="preserve">Rurſus idem inuestigetur in ciuitate longitudinis grad. </s>
            <s xml:id="echoid-s11364" xml:space="preserve">240. </s>
            <s xml:id="echoid-s11365" xml:space="preserve">Detractis grad. </s>
            <s xml:id="echoid-s11366" xml:space="preserve">
              <lb/>
            60. </s>
            <s xml:id="echoid-s11367" xml:space="preserve">ex grad. </s>
            <s xml:id="echoid-s11368" xml:space="preserve">240. </s>
            <s xml:id="echoid-s11369" xml:space="preserve">remanent grad. </s>
            <s xml:id="echoid-s11370" xml:space="preserve">180. </s>
            <s xml:id="echoid-s11371" xml:space="preserve">qui faciunt horas 12. </s>
            <s xml:id="echoid-s11372" xml:space="preserve">à meridie elapſas. </s>
            <s xml:id="echoid-s11373" xml:space="preserve">Eſt ergo pręcisè tunc tem
              <lb/>
            pus mediæ noctis. </s>
            <s xml:id="echoid-s11374" xml:space="preserve">Adhuc deſiderat quis idem noſſe in eo loco, qui ab Inſulis Fortunatis recedit grad. </s>
            <s xml:id="echoid-s11375" xml:space="preserve">
              <lb/>
            110. </s>
            <s xml:id="echoid-s11376" xml:space="preserve">verſus orientem, cuiuſmodi eſt Calecutium emporium Indiæ orientalis. </s>
            <s xml:id="echoid-s11377" xml:space="preserve">Subductis grad. </s>
            <s xml:id="echoid-s11378" xml:space="preserve">60. </s>
            <s xml:id="echoid-s11379" xml:space="preserve">ex
              <lb/>
            grad. </s>
            <s xml:id="echoid-s11380" xml:space="preserve">110. </s>
            <s xml:id="echoid-s11381" xml:space="preserve">reliqui fiunt grad. </s>
            <s xml:id="echoid-s11382" xml:space="preserve">50. </s>
            <s xml:id="echoid-s11383" xml:space="preserve">qui exhibent horas 3. </s>
            <s xml:id="echoid-s11384" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s11385" xml:space="preserve">20. </s>
            <s xml:id="echoid-s11386" xml:space="preserve">poſt meridiem tranſactas. </s>
            <s xml:id="echoid-s11387" xml:space="preserve">Ad extremum
              <lb/>
            ſi optemus idem cognoſcere in loco, quilongitudinem habeat grad. </s>
            <s xml:id="echoid-s11388" xml:space="preserve">10. </s>
            <s xml:id="echoid-s11389" xml:space="preserve">ſubtrahemus grad. </s>
            <s xml:id="echoid-s11390" xml:space="preserve">10. </s>
            <s xml:id="echoid-s11391" xml:space="preserve">ex grad. </s>
            <s xml:id="echoid-s11392" xml:space="preserve">60. </s>
            <s xml:id="echoid-s11393" xml:space="preserve">
              <lb/>
            Nam reliq@i grad. </s>
            <s xml:id="echoid-s11394" xml:space="preserve">50. </s>
            <s xml:id="echoid-s11395" xml:space="preserve">dabunt horas 3. </s>
            <s xml:id="echoid-s11396" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s11397" xml:space="preserve">20. </s>
            <s xml:id="echoid-s11398" xml:space="preserve">ante meridiem illius loci, hoc eſt, horas 8. </s>
            <s xml:id="echoid-s11399" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s11400" xml:space="preserve">40. </s>
            <s xml:id="echoid-s11401" xml:space="preserve">
              <lb/>
              <note position="left" xlink:label="note-0194-04" xlink:href="note-0194-04a" xml:space="preserve">40</note>
            poſt mediam noctem, &</s>
            <s xml:id="echoid-s11402" xml:space="preserve">c.</s>
            <s xml:id="echoid-s11403" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div613" type="section" level="1" n="155">
          <head xml:id="echoid-head158" xml:space="preserve">PROBLEMA 7. PROPOSITIO 7.</head>
          <p>
            <s xml:id="echoid-s11404" xml:space="preserve">PARALLELOS ciuitatum, hoc eſt, circulos latitudinum, in eo-
              <lb/>
            dem horologio horizontali deſcribere.</s>
            <s xml:id="echoid-s11405" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11406" xml:space="preserve">HORVM deſcriptio à deſcriptione parallelorum Zodiaci, quam propoſ. </s>
            <s xml:id="echoid-s11407" xml:space="preserve">2. </s>
            <s xml:id="echoid-s11408" xml:space="preserve">huius libri tra-
              <lb/>
              <note position="left" xlink:label="note-0194-05" xlink:href="note-0194-05a" xml:space="preserve">Deſcriptio pa-
                <lb/>
              rallelorum ciui
                <lb/>
              ta um, ſiue cir
                <lb/>
              culorum latitu-
                <lb/>
              dinum, in eodẽ
                <lb/>
              horizontali ho-
                <lb/>
              rologio.</note>
            didimus, non differt, cum tam hi, quàm illi æquidiſtent Aequatori; </s>
            <s xml:id="echoid-s11409" xml:space="preserve">ſi modo loco declinationum
              <lb/>
              <note position="left" xlink:label="note-0194-06" xlink:href="note-0194-06a" xml:space="preserve">50</note>
            ſignorum, quas ibi vſurpauimus, aſſumantur hic declinationes parallelorum, qui per vertices ci-
              <lb/>
            uitatum ducuntur, nempe ipſæmet latitudines ciuitatum. </s>
            <s xml:id="echoid-s11410" xml:space="preserve">Immo & </s>
            <s xml:id="echoid-s11411" xml:space="preserve">paralleli ſignorum ſupra de-
              <lb/>
            ſcripti, circuli etiam ſunt latitudinum ciuitatum, vt tropicus ♋, eſt circulus latitudinis ciuitatum,
              <lb/>
            quæ ab Aequatore boream verſus abſunt grad. </s>
            <s xml:id="echoid-s11412" xml:space="preserve">23. </s>
            <s xml:id="echoid-s11413" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s11414" xml:space="preserve">30. </s>
            <s xml:id="echoid-s11415" xml:space="preserve">qualis eſt Syene vrbs Aegypti, &</s>
            <s xml:id="echoid-s11416" xml:space="preserve">c. </s>
            <s xml:id="echoid-s11417" xml:space="preserve">Pa-
              <lb/>
            rallelos ergo ciuitatum, &</s>
            <s xml:id="echoid-s11418" xml:space="preserve">c. </s>
            <s xml:id="echoid-s11419" xml:space="preserve">deſcripſimus. </s>
            <s xml:id="echoid-s11420" xml:space="preserve">Quod erat faciendum.</s>
            <s xml:id="echoid-s11421" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">Paralleli ciuita
            <lb/>
          tum. ſeu circuli
            <lb/>
          latitudinum in
            <lb/>
          horologio de-
            <lb/>
          ſctipti indicãt,
            <lb/>
          quæ gentes So-
            <lb/>
          lem habeant in
            <lb/>
          vertice capitis
            <lb/>
          tempore meri-
            <lb/>
          diano.</note>
        </div>
        <div xml:id="echoid-div615" type="section" level="1" n="156">
          <head xml:id="echoid-head159" style="it" xml:space="preserve">SCHOLIVM.</head>
          <p style="it">
            <s xml:id="echoid-s11422" xml:space="preserve">CIRCVLI latitudinum, ſeu paralleli ciuitatum hanc nobis afferunt vtilitatem, vt eorum benefi-
              <lb/>
            cio intelligamus, quinam populi Solem habeant in vertice capitis tempore meridiano. </s>
            <s xml:id="echoid-s11423" xml:space="preserve">Nam cum @ vmbra
              <lb/>
            gnomonis in aliquem horum parallelorum cadit, tranſibit illa die Sol per verticem omnium locorum, </s>
          </p>
        </div>
      </text>
    </echo>
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