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

Table of Notes

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          <pb o="131" file="0151" n="151" rhead="LIBER PRIMVS."/>
          <p>
            <s xml:id="echoid-s8164" xml:space="preserve">SED inter omnes modos fortaſſe commodiſſimus hic erit. </s>
            <s xml:id="echoid-s8165" xml:space="preserve">Quoniam in prioribus quinque
              <lb/>
            figuris ad initiũ huius propoſ. </s>
            <s xml:id="echoid-s8166" xml:space="preserve">poſitis eſt, vt k M, ſinus totus in parallelo Solis ad K R, ita K λ, me-
              <lb/>
              <note position="right" xlink:label="note-0151-01" xlink:href="note-0151-01a" xml:space="preserve">2. vel 4. ſexti</note>
            dietas rectę compoſitę ex ſinu altitudinis meridianę, & </s>
            <s xml:id="echoid-s8167" xml:space="preserve">ſinu depreſſionis meridianæ ad
              <emph style="sc">K</emph>
            T: </s>
            <s xml:id="echoid-s8168" xml:space="preserve">Et
              <lb/>
            vt k R, ad R S, differentiam inter K S, ſinum verſum arcus ſemidiurni, & </s>
            <s xml:id="echoid-s8169" xml:space="preserve">K R, ſinum verſum di-
              <lb/>
              <note position="right" xlink:label="note-0151-02" xlink:href="note-0151-02a" xml:space="preserve">2. ſexti.</note>
            ſtantię Solis à meridie, ita K T, ad T N, ſinum rectum altitudinis Solis; </s>
            <s xml:id="echoid-s8170" xml:space="preserve">Erit ex æquo, vt
              <emph style="sc">K</emph>
            M, ſinus
              <lb/>
            totus in parallelo Solis ad R S, differentiam inter ſinum verſum arcus ſemidiurni, & </s>
            <s xml:id="echoid-s8171" xml:space="preserve">ſinũ verſum
              <lb/>
            diſtantię Solis à meridie, ita K λ, medietas rectę compoſitę ex ſinu altitudinis meridianæ, & </s>
            <s xml:id="echoid-s8172" xml:space="preserve">ſinu
              <lb/>
            depreſſionis meridianę ad T N, ſinum rectum altitudinis Solis. </s>
            <s xml:id="echoid-s8173" xml:space="preserve">Quapropter ſi fiat, vt ſinus totus
              <lb/>
              <note position="right" xlink:label="note-0151-03" xlink:href="note-0151-03a" xml:space="preserve">Altitudo Solis
                <lb/>
              quo pacto ex ho
                <lb/>
              ra aliter inue-
                <lb/>
              nienda.</note>
            ad differentiam inter ſinum verſum arcus ſemidiurni, & </s>
            <s xml:id="echoid-s8174" xml:space="preserve">ſinum verſum diſtantiæ Solis à meridie,
              <lb/>
            ita medietas rectæ compoſitę ex ſinu altitudinis meridianę, & </s>
            <s xml:id="echoid-s8175" xml:space="preserve">ſinu depreſſionis meridianę, ad
              <lb/>
              <note position="left" xlink:label="note-0151-04" xlink:href="note-0151-04a" xml:space="preserve">10</note>
            aliud, inuentus erit ſinus rectus altitudinis Solis, qui inquiritur; </s>
            <s xml:id="echoid-s8176" xml:space="preserve">atque adeo altitudo ipſa no-
              <lb/>
            ta euadet.</s>
            <s xml:id="echoid-s8177" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8178" xml:space="preserve">QVOD ſi viciſſim fiat, vt K λ, medietas prędicta ad T N, ſinum altitudinis Solis, ita
              <emph style="sc">K</emph>
            M, ſinus
              <lb/>
              <note position="right" xlink:label="note-0151-05" xlink:href="note-0151-05a" xml:space="preserve">Quomodo ho-
                <lb/>
              ra ex altitudine
                <lb/>
              Solis ſupputan
                <lb/>
              da ſit aliter ꝗ̃
                <lb/>
              ſupra traditum
                <lb/>
              eſt.</note>
            totus ad aliud, inuenietur R S, differentia inter ſinum verſum arcus ſemidiurni, & </s>
            <s xml:id="echoid-s8179" xml:space="preserve">ſinum verſum
              <lb/>
            diſtantię Solis à meridie; </s>
            <s xml:id="echoid-s8180" xml:space="preserve">qua differentia ſublata à ſinu verſo arcus ſemidiurni, reliquus erit k R,
              <lb/>
            ſinus verſus diſtantię Solis à meridie, &</s>
            <s xml:id="echoid-s8181" xml:space="preserve">c.</s>
            <s xml:id="echoid-s8182" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8183" xml:space="preserve">AVT certe hoc modo (qui mihi magis probatur) idem negotium conficiemus. </s>
            <s xml:id="echoid-s8184" xml:space="preserve">Quoniam eſt
              <lb/>
            vt K M, ſinus totus in parallelo Solis, ad K R, ſinum verſum diſtantię Solis à meridie, ita K λ, me-
              <lb/>
              <note position="right" xlink:label="note-0151-06" xlink:href="note-0151-06a" xml:space="preserve">2. vel 4. ſexti</note>
            dietas rectę compoſitę ex ſinu altitudinis meridianę, & </s>
            <s xml:id="echoid-s8185" xml:space="preserve">ſinu depreſſionis meridianę ad K T, diffe-
              <lb/>
            rentiam inter k N, ſinum altitudinis meridianæ, & </s>
            <s xml:id="echoid-s8186" xml:space="preserve">T N, ſinum altitudinis Solis tempore obſerua-
              <lb/>
              <note position="left" xlink:label="note-0151-07" xlink:href="note-0151-07a" xml:space="preserve">20</note>
            tionis: </s>
            <s xml:id="echoid-s8187" xml:space="preserve">Si fiat vt ſinus totus ad ſinum verſum diſtantię Solis à meridie, ita medietas rectæ compo-
              <lb/>
              <note position="right" xlink:label="note-0151-08" xlink:href="note-0151-08a" xml:space="preserve">Altitudo Solis
                <lb/>
              qua ratione ex
                <lb/>
              hora aliter inue
                <lb/>
              nienda.</note>
            ſitę ex ſinu altitudinis meridianę, & </s>
            <s xml:id="echoid-s8188" xml:space="preserve">ſinu depreſſionis meridianæ ad aliud, reperietur numerus
              <lb/>
            rectę k T, qui ex ſinu altitudinis meridianæ detractus relinquet ſinum altitudinis Solis.</s>
            <s xml:id="echoid-s8189" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8190" xml:space="preserve">ITEM, ſi viciſſim fiat, vt k λ, medietas prædicta ad K T, differentiam inter ſinum altitudinis
              <lb/>
              <note position="right" xlink:label="note-0151-09" xlink:href="note-0151-09a" xml:space="preserve">Hora qua ratio
                <lb/>
              ne aliter ex alti
                <lb/>
              tudine Solis nu
                <lb/>
              meranda.</note>
            meridianę, & </s>
            <s xml:id="echoid-s8191" xml:space="preserve">ſinum altitudinis Solis, quę nota ponitur, ita k M, ſinus totus ad aliud, cognitus erit
              <lb/>
            K R, ſinus verſus diſtantiæ Solis à meridie, &</s>
            <s xml:id="echoid-s8192" xml:space="preserve">c.</s>
            <s xml:id="echoid-s8193" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8194" xml:space="preserve">HIC modus poſtremus latiſſime patet. </s>
            <s xml:id="echoid-s8195" xml:space="preserve">Pertinet enim etiam ad illum parallelum Solis, qui
              <lb/>
              <note position="right" xlink:label="note-0151-10" xlink:href="note-0151-10a" xml:space="preserve">Quis modus
                <lb/>
              inuenieudæ al-
                <lb/>
              titudinis Solis
                <lb/>
              ſit præſtantior.</note>
            vel Horizontem tangit, vel totus ſupra eundem extat, vt ad finem ſcholij huius propoſ. </s>
            <s xml:id="echoid-s8196" xml:space="preserve">dicemus.
              <lb/>
            </s>
            <s xml:id="echoid-s8197" xml:space="preserve">Adde quòd conuenit non ſolum in Horizontem, ſed in alia etiã omnia plana, quæ vel recta ſint ad
              <lb/>
            Horizontem, vel inclinata, vt ex propoſ. </s>
            <s xml:id="echoid-s8198" xml:space="preserve">1. </s>
            <s xml:id="echoid-s8199" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s8200" xml:space="preserve">4. </s>
            <s xml:id="echoid-s8201" xml:space="preserve">perſpicuum erit. </s>
            <s xml:id="echoid-s8202" xml:space="preserve">Ibi enim eadem hac rationealti-
              <lb/>
              <note position="left" xlink:label="note-0151-11" xlink:href="note-0151-11a" xml:space="preserve">30</note>
            iudinem Solis ſupra quodcunque planum ex data hora inueſtigabimus. </s>
            <s xml:id="echoid-s8203" xml:space="preserve">Quare præ cæter is omni-
              <lb/>
            bus modus hic memorię commendandus erit.</s>
            <s xml:id="echoid-s8204" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8205" xml:space="preserve">LIBET iam per triangula ſphęrica idem hoc problema explicare. </s>
            <s xml:id="echoid-s8206" xml:space="preserve">Sit ergo Horizon ABCD;
              <lb/>
            </s>
            <s xml:id="echoid-s8207" xml:space="preserve">
              <note position="right" xlink:label="note-0151-12" xlink:href="note-0151-12a" xml:space="preserve">Altitudo Solis
                <lb/>
              qua uia ex co-
                <lb/>
              gn@a hora per
                <lb/>
              triangula ſphæ-
                <lb/>
              rica ſit explotã-
                <lb/>
              da, Sole in quo-
                <lb/>
              cunque pa@all@
                <lb/>
              lo exiſtente.</note>
            Meridianus B E D; </s>
            <s xml:id="echoid-s8208" xml:space="preserve">Aequator AFC; </s>
            <s xml:id="echoid-s8209" xml:space="preserve">Verticalis A E C; </s>
            <s xml:id="echoid-s8210" xml:space="preserve">parallelus Solis ſiue borealis, ſiue auſtralis
              <lb/>
            G H I, ita vt borealis Verticalem ſecet in K; </s>
            <s xml:id="echoid-s8211" xml:space="preserve">quod quidem contingit, quando arcus F H, declina-
              <lb/>
              <figure xlink:label="fig-0151-01" xlink:href="fig-0151-01a" number="110">
                <image file="0151-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0151-01"/>
              </figure>
              <note position="left" xlink:label="note-0151-13" xlink:href="note-0151-13a" xml:space="preserve">40</note>
            tionis parallelli minor fuerit arcu E F, altitudinis poli, qui inter verticem, & </s>
            <s xml:id="echoid-s8212" xml:space="preserve">Aequatorem interpo
              <lb/>
              <note position="left" xlink:label="note-0151-14" xlink:href="note-0151-14a" xml:space="preserve">50</note>
            nitur; </s>
            <s xml:id="echoid-s8213" xml:space="preserve">ponaturq́; </s>
            <s xml:id="echoid-s8214" xml:space="preserve">Sol in puncto L, ſui paralleli, ita vt H L, ſit diſtantia Solis à meridie, cui ſimilis
              <lb/>
            erit arcus Aequatoris F M, per propoſ. </s>
            <s xml:id="echoid-s8215" xml:space="preserve">10. </s>
            <s xml:id="echoid-s8216" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s8217" xml:space="preserve">2. </s>
            <s xml:id="echoid-s8218" xml:space="preserve">Theodoſii, quem aufert circulus declinationis ex
              <lb/>
            polo N, per centrum Solis L, ductus. </s>
            <s xml:id="echoid-s8219" xml:space="preserve">Ex vertice E, per Solem L, deſcendat Verticalis E L O, ita vt
              <lb/>
            arcus altitudinis Solis ſit L O, quem inueſtigare oportet, ſi diſtantia Solis à meridie ex hora data
              <lb/>
            cognita ſit, vt prior pars problematis pręcipit. </s>
            <s xml:id="echoid-s8220" xml:space="preserve">Deſcribatur alius circulus maximus per A, polum
              <lb/>
            Meridiani, & </s>
            <s xml:id="echoid-s8221" xml:space="preserve">per Solem in L, conſtitutum, ſecans Meridianum in P.</s>
            <s xml:id="echoid-s8222" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8223" xml:space="preserve">QVONIAM igitur in triangulo ſphęrico A L M, priorum quatuor figurarum, angulus M,
              <lb/>
            rectus eſt, per propoſ. </s>
            <s xml:id="echoid-s8224" xml:space="preserve">15. </s>
            <s xml:id="echoid-s8225" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s8226" xml:space="preserve">1. </s>
            <s xml:id="echoid-s8227" xml:space="preserve">Theodoſii, cum circulus maximus N M, per N, polum Aequatoris
              <lb/>
            A F C, ductus ſit; </s>
            <s xml:id="echoid-s8228" xml:space="preserve">erit per propoſ. </s>
            <s xml:id="echoid-s8229" xml:space="preserve">19. </s>
            <s xml:id="echoid-s8230" xml:space="preserve">lib: </s>
            <s xml:id="echoid-s8231" xml:space="preserve">4. </s>
            <s xml:id="echoid-s8232" xml:space="preserve">Ioan. </s>
            <s xml:id="echoid-s8233" xml:space="preserve">Regiom. </s>
            <s xml:id="echoid-s8234" xml:space="preserve">de triangulis, uel per propoſ. </s>
            <s xml:id="echoid-s8235" xml:space="preserve">15. </s>
            <s xml:id="echoid-s8236" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s8237" xml:space="preserve">1.
              <lb/>
            </s>
            <s xml:id="echoid-s8238" xml:space="preserve">Gebri, uel per propoſ. </s>
            <s xml:id="echoid-s8239" xml:space="preserve">43. </s>
            <s xml:id="echoid-s8240" xml:space="preserve">noſtrorum triangulorum ſphęricorum, ut ſinus complementiarcus
              <lb/>
            A M, hoc eſt, ut ſinus diſtantię Solis à meridie (eſt enim F M, diſtantia Solis à meridie, </s>
          </p>
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