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-div772" type="section" level="1" n="184">
          <p>
            <s xml:id="echoid-s15334" xml:space="preserve">
              <pb o="225" file="0245" n="245" rhead="LIBER SECVNDVS."/>
            tur. </s>
            <s xml:id="echoid-s15335" xml:space="preserve">Non eſt tamen neceſſarium, vt dictas rectas omnes transferamus in Verticales lineas vtrin-
              <lb/>
            que, hoc eſt, ſupra, & </s>
            <s xml:id="echoid-s15336" xml:space="preserve">infra horizontalem lineam; </s>
            <s xml:id="echoid-s15337" xml:space="preserve">quia non eſt opus tot parallelos Horizontis de-
              <lb/>
            ſcribere in horologio boreali, quot in Verticali. </s>
            <s xml:id="echoid-s15338" xml:space="preserve">Ita vides nos in Boreali deſcripſiſ@e duntaxat pa-
              <lb/>
            rall
              <unsure/>
            elum grad. </s>
            <s xml:id="echoid-s15339" xml:space="preserve">15. </s>
            <s xml:id="echoid-s15340" xml:space="preserve">quia alii caderent extra tropicum omnino, ac proinde in illos vmbra cade-
              <lb/>
            re non poſſet.</s>
            <s xml:id="echoid-s15341" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15342" xml:space="preserve">RECTE autem hac arte deſcribi parallelos Horizontis, ita demonſtrabitur. </s>
            <s xml:id="echoid-s15343" xml:space="preserve">Intelligatur in
              <lb/>
              <note position="right" xlink:label="note-0245-01" xlink:href="note-0245-01a" xml:space="preserve">Demonſtratio
                <lb/>
              poſterioris de-
                <lb/>
              ſcriptionis pa-
                <lb/>
              rallelorum Ho
                <lb/>
              rizontis.</note>
            figura præcedentis propoſ. </s>
            <s xml:id="echoid-s15344" xml:space="preserve">recta A G, quæ gnomoni ſumpta eſt æqualis, ad rectos angulos plano
              <lb/>
            horologii inſiſtere in puncto G, & </s>
            <s xml:id="echoid-s15345" xml:space="preserve">figura nuper conſtructa circa punctum A. </s>
            <s xml:id="echoid-s15346" xml:space="preserve">cum centro mundi
              <lb/>
            coniunctum circumduci, ita vt punctum A, huius figuræ à puncto A, figuræ præcedentis propoſ.
              <lb/>
            </s>
            <s xml:id="echoid-s15347" xml:space="preserve">hoc eſt, à centro mundi nunquam recedat, & </s>
            <s xml:id="echoid-s15348" xml:space="preserve">recta A C, perpetuo lineæ meridianæ H I, æquidiſtet,
              <lb/>
              <note position="left" xlink:label="note-0245-02" xlink:href="note-0245-02a" xml:space="preserve">10</note>
            hoc eſt, coniuncta ſit axi Horizontis, eiusq́ue parallelorum, ac punctum B, verſus horologium por
              <lb/>
            rigatur, & </s>
            <s xml:id="echoid-s15349" xml:space="preserve">propterea recta A B, à plano Horizontis non recedens occurrat ſemper illo motu hori-
              <lb/>
            zontali lineæ: </s>
            <s xml:id="echoid-s15350" xml:space="preserve">Cadet in hac circumductione punctum E, v. </s>
            <s xml:id="echoid-s15351" xml:space="preserve">g. </s>
            <s xml:id="echoid-s15352" xml:space="preserve">in punctum K, propterea quòd re
              <lb/>
            ctæ A K, in præcedẽti propoſ. </s>
            <s xml:id="echoid-s15353" xml:space="preserve">ſumpta eſt hic æqualis A E Eſt enim recta A K, cadens ex puncto A,
              <lb/>
            in ſublimi, nempe à vertice ſtyli, rectæ A K, in plano horologii æqualis; </s>
            <s xml:id="echoid-s15354" xml:space="preserve">Vt facile probabitur, ſi
              <lb/>
            triangulum A K G, in plano conferatur cum triangulo A K G, in ſublimi. </s>
            <s xml:id="echoid-s15355" xml:space="preserve">Cum enim latera A G,
              <lb/>
            G K, illius æqualia ſint lateribus A G, G K, huius, angulosq́; </s>
            <s xml:id="echoid-s15356" xml:space="preserve">contineant æquales, vtpote rectos; </s>
            <s xml:id="echoid-s15357" xml:space="preserve">erit
              <lb/>
            baſis A K, illius baſi A K, huius æqualis. </s>
            <s xml:id="echoid-s15358" xml:space="preserve">Cum igitur tam recta K L, quàm E F, axi Horizontis
              <lb/>
              <note position="right" xlink:label="note-0245-03" xlink:href="note-0245-03a" xml:space="preserve">4. primi.</note>
            æquidiſtet, erunt quoque K L, E F, inter ſe parallelæ; </s>
            <s xml:id="echoid-s15359" xml:space="preserve">& </s>
            <s xml:id="echoid-s15360" xml:space="preserve">idcirco congruente puncto E, ipſi K, pun-
              <lb/>
              <note position="right" xlink:label="note-0245-04" xlink:href="note-0245-04a" xml:space="preserve">9. vndec.</note>
            cto, vt oſtendimus, congruet etiam recta E F, rectæ K L; </s>
            <s xml:id="echoid-s15361" xml:space="preserve">alias non eſſer illa huic parallela, quando-
              <lb/>
              <note position="left" xlink:label="note-0245-05" xlink:href="note-0245-05a" xml:space="preserve">20</note>
            quidem ambæ in illa circumductione conueniunt in puncto K. </s>
            <s xml:id="echoid-s15362" xml:space="preserve">Igitur cum K L, ſumpta ſit æqua-
              <lb/>
            lis rectæ E F, cadet punctum F, in punctum L, atque adeò radius paralleli Horizontis grad. </s>
            <s xml:id="echoid-s15363" xml:space="preserve">15. </s>
            <s xml:id="echoid-s15364" xml:space="preserve">pla-
              <lb/>
            no horologii occurret in L. </s>
            <s xml:id="echoid-s15365" xml:space="preserve">Per punctum ergo L, tranſibit arcus paralleli prædicti grad. </s>
            <s xml:id="echoid-s15366" xml:space="preserve">15. </s>
            <s xml:id="echoid-s15367" xml:space="preserve">cum
              <lb/>
            in illud radius dicti paralleli incidat in illa circumuolutione, vt oſtenſum eſt. </s>
            <s xml:id="echoid-s15368" xml:space="preserve">Non aliter demon-
              <lb/>
            ſtrabimus punctum M, eiuſdem radii cadere in punctum N, & </s>
            <s xml:id="echoid-s15369" xml:space="preserve">ſic de cæteris. </s>
            <s xml:id="echoid-s15370" xml:space="preserve">Parallelos igitur
              <lb/>
            Horizontis in eodem horologio Verticali deſcripſimns. </s>
            <s xml:id="echoid-s15371" xml:space="preserve">Quod erat faciendum.</s>
            <s xml:id="echoid-s15372" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div777" type="section" level="1" n="185">
          <head xml:id="echoid-head188" xml:space="preserve">PROBLEMA 18. PROPOSITIO 18.</head>
          <p>
            <s xml:id="echoid-s15373" xml:space="preserve">MERIDIANOS, ſeu circulos longitudinum ciuitatum, in eo-
              <lb/>
              <note position="left" xlink:label="note-0245-06" xlink:href="note-0245-06a" xml:space="preserve">30</note>
            dem Verticali horologio deſcribere.</s>
            <s xml:id="echoid-s15374" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15375" xml:space="preserve">HI deſcribuntur, vt lineæ horarię à meridie, vel media nocte, quemadmodum propoſ. </s>
            <s xml:id="echoid-s15376" xml:space="preserve">6. </s>
            <s xml:id="echoid-s15377" xml:space="preserve">hu-
              <lb/>
              <note position="right" xlink:label="note-0245-07" xlink:href="note-0245-07a" xml:space="preserve">Deſcriptio Me-
                <lb/>
              ridianorum in
                <lb/>
              eodem horolo-
                <lb/>
              gio Verticali.</note>
            ius libri diximus, dummodo circulus ex E, deſcriptus initium diuiſionis habeat à Meridiano inſu
              <lb/>
            larum Fortunatarum, qui habetur, ſi longitudo loci numeretur ab N, in horologio quidem auſtra-
              <lb/>
            li propoſ. </s>
            <s xml:id="echoid-s15378" xml:space="preserve">13. </s>
            <s xml:id="echoid-s15379" xml:space="preserve">huius libri deſcripto verſus ſiniſtram, in boreali verò verſus dextram, nempe ad par
              <lb/>
            tes ſemper occidentales, vt ratio poſtulat. </s>
            <s xml:id="echoid-s15380" xml:space="preserve">Quod quidem facile intelligetur, ſi in vtroque horolo-
              <lb/>
            gio circulus ex E, deſcriptus circumuertatur circa lineam æquinoctialem, donec propriam adipi-
              <lb/>
            ſcatur poſitionem, nempe in plano Aequatoris ſit conſtitutus, &</s>
            <s xml:id="echoid-s15381" xml:space="preserve">c. </s>
            <s xml:id="echoid-s15382" xml:space="preserve">Itaque Meridianos, ſeu circu-
              <lb/>
              <note position="left" xlink:label="note-0245-08" xlink:href="note-0245-08a" xml:space="preserve">40</note>
            los longitudinum ciuitatum in eodem Verticali horologio deſcripſimus. </s>
            <s xml:id="echoid-s15383" xml:space="preserve">Quod faciendum erat.</s>
            <s xml:id="echoid-s15384" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div780" type="section" level="1" n="186">
          <head xml:id="echoid-head189" style="it" xml:space="preserve">SCHOLIVM.</head>
          <p style="it">
            <s xml:id="echoid-s15385" xml:space="preserve">SI circuli Meridiani, vel potius communes eorum, & </s>
            <s xml:id="echoid-s15386" xml:space="preserve">plani horologii ſectiones in auſtrali horologio
              <lb/>
              <note position="right" xlink:label="note-0245-09" xlink:href="note-0245-09a" xml:space="preserve">Quomodo Me-
                <lb/>
              ridiani auſtra-
                <lb/>
              lis horologii vl-
                <lb/>
              tra lineam hori
                <lb/>
              zontalem pro-
                <lb/>
              ducti præbeant
                <lb/>
              eoſdem Meri-
                <lb/>
              dianos in horo
                <lb/>
              logio boreali.</note>
            producantur vltra lineam horizontalem, & </s>
            <s xml:id="echoid-s15387" xml:space="preserve">centrum H, habebuntur quoque iidem Meridiani circuli in
              <lb/>
            horologio boreali, quod quidem linea horizontalis abſcindit, dummodo memor ſis, totum horologium de-
              <lb/>
            bere inuerti, ita vt ſuperiora fiant inferiora, & </s>
            <s xml:id="echoid-s15388" xml:space="preserve">dextra euadant ſiniſtra, vt in ſcholio propoſ. </s>
            <s xml:id="echoid-s15389" xml:space="preserve">14. </s>
            <s xml:id="echoid-s15390" xml:space="preserve">huius
              <lb/>
            libri oſtenſum eſt: </s>
            <s xml:id="echoid-s15391" xml:space="preserve">Item has ſectiones Meridianorum, & </s>
            <s xml:id="echoid-s15392" xml:space="preserve">plani horologii auſtralis referre in borcali ho-
              <lb/>
            rologio ſectiones ſemicir culorum Meridianorum oppoſitorum, ita vt habeant numeros, qui conficiuntur
              <lb/>
              <note position="left" xlink:label="note-0245-10" xlink:href="note-0245-10a" xml:space="preserve">50</note>
            ex additione graduum 180. </s>
            <s xml:id="echoid-s15393" xml:space="preserve">ad numeros, quos habent in horologio auſtrali, (abiectis tamen grad. </s>
            <s xml:id="echoid-s15394" xml:space="preserve">360.
              <lb/>
            </s>
            <s xml:id="echoid-s15395" xml:space="preserve">ſi ex illa additione fiat maior numerus, quàm grad. </s>
            <s xml:id="echoid-s15396" xml:space="preserve">360.) </s>
            <s xml:id="echoid-s15397" xml:space="preserve">vel certè qui in circulo ex E, deſcripto per
              <lb/>
            diametrum opponuntur numeris illis, quos dictæ ſectiones habent in horologio auſtrali. </s>
            <s xml:id="echoid-s15398" xml:space="preserve">Veruntamen li-
              <lb/>
            neæ auſtralis horologii vltra centrum H, protractæ habebunt in boreali iterum eoſdem omnino numeros,
              <lb/>
            quos in auſtrali horologio, propterea quòd illæ in horologio boreali ſint iterum ſectiones ſemicir culorum
              <lb/>
            oppoſitorum, quemadmodum de lineis horariis à meridie, vel media nocte dictum est. </s>
            <s xml:id="echoid-s15399" xml:space="preserve">I
              <unsure/>
            bi enim linea
              <lb/>
            v. </s>
            <s xml:id="echoid-s15400" xml:space="preserve">g. </s>
            <s xml:id="echoid-s15401" xml:space="preserve">horę 7. </s>
            <s xml:id="echoid-s15402" xml:space="preserve">à media nocte in auſtrali horologio producta vltra lineam horizontalem, antequam ad cen-
              <lb/>
            trum H, perueniat, indicat in horeali horologio (ſi fiat inuerſio ſupradicta horologii) horam 7. </s>
            <s xml:id="echoid-s15403" xml:space="preserve">à meri-
              <lb/>
            di@, hoc eſt, communis ſectio eſt plani horologii, & </s>
            <s xml:id="echoid-s15404" xml:space="preserve">ſemicirculi horæ 7. </s>
            <s xml:id="echoid-s15405" xml:space="preserve">à meridie, & </s>
            <s xml:id="echoid-s15406" xml:space="preserve">non à media nocte,
              <lb/>
            vt in auſtrali horologio: </s>
            <s xml:id="echoid-s15407" xml:space="preserve">producta verò vltra centrum H, oſtendet iterum horam 7. </s>
            <s xml:id="echoid-s15408" xml:space="preserve">à media nocte, vt
              <lb/>
            in horologio auſtrali. </s>
            <s xml:id="echoid-s15409" xml:space="preserve">Eadem{q́ue}
              <unsure/>
            ratio de cæteris habenda eſt, vt perſpicuum eſt ex horologio propoſ. </s>
            <s xml:id="echoid-s15410" xml:space="preserve">14.</s>
            <s xml:id="echoid-s15411" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
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