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-div401" type="section" level="1" n="136">
          <p>
            <s xml:id="echoid-s7230" xml:space="preserve">
              <pb o="120" file="0140" n="140" rhead="GNOMONICES"/>
            enim erunt ſingula, quanta inuenta eſt recta E γ, Sole in ęquinoctijs exiſtente. </s>
            <s xml:id="echoid-s7231" xml:space="preserve">Hinc cognoſce-
              <lb/>
            mus eadem ſegmenta in partibus ſinus totius propriorum parallelorum, hac arte. </s>
            <s xml:id="echoid-s7232" xml:space="preserve">Fiat ut k M, ſi-
              <lb/>
            nus complementi declinationis paralleli cuiuſuis ad K M, quatenus ſinus totus proprii paralleli,
              <lb/>
            ita S T, quatenus nota in partibus ſinus totius in circulo maximo, ad aliud. </s>
            <s xml:id="echoid-s7233" xml:space="preserve">Prodibit enim nota
              <lb/>
            eadem S T, in partibus ſinus totius K M, proprii paralleli. </s>
            <s xml:id="echoid-s7234" xml:space="preserve">Vnde ſi S T, nota in partibus ſinus to-
              <lb/>
            tius proprii paralleli addatur ſinui verſo K S, arcus ſemidiurni, notus erit ſinus verſus K T, arcus
              <lb/>
            K R, compoſiti ex arcu ſemidiurno, & </s>
            <s xml:id="echoid-s7235" xml:space="preserve">arcu crepuſculi. </s>
            <s xml:id="echoid-s7236" xml:space="preserve">Quare, ut prius, ex hoc ſinu uerſo quanti-
              <lb/>
            tatem crȩpuſculi inueniemus.</s>
            <s xml:id="echoid-s7237" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7238" xml:space="preserve">HAEC autem ratio
              <unsure/>
            inueſtigandorum crepuſculorum videtur omnium facilima, & </s>
            <s xml:id="echoid-s7239" xml:space="preserve">expedi-
              <lb/>
            tiſſima, quoniam in eadem poli altitudine recta E γ, ſemel inuenta in partibus ſinus totius circu-
              <lb/>
              <note position="left" xlink:label="note-0140-01" xlink:href="note-0140-01a" xml:space="preserve">10</note>
            li maximi, eadem ſemper manet in omnibus parallelis Solis, ita vt nunquam mutetur: </s>
            <s xml:id="echoid-s7240" xml:space="preserve">cuius qui-
              <lb/>
            dem inuentio perfacilis eſt, cum in ea perueſtiganda ſinus totus uſurpetur, qui facilimam reddit
              <lb/>
            multiplicationem, ut ex demonſtratis conſtat. </s>
            <s xml:id="echoid-s7241" xml:space="preserve">Hac autem inuenta, reperitur arte proxime tradita
              <lb/>
            eadem E. </s>
            <s xml:id="echoid-s7242" xml:space="preserve">γ, uel S T, quatenus pars eſt ſinus totius proprii paralleli: </s>
            <s xml:id="echoid-s7243" xml:space="preserve">quę inuentio difficilis etiam
              <lb/>
            non eſt, propterea quòd ad eam in quirendam ſinus totus quoque adhibeatur, qui operationem
              <lb/>
            minus difficilem reddit, ut diximus. </s>
            <s xml:id="echoid-s7244" xml:space="preserve">Quod in prioribus præceptis non contingit. </s>
            <s xml:id="echoid-s7245" xml:space="preserve">Nun quam enim
              <lb/>
            in illis ſinus totus aſſumitur, ut recta K T, inueniatur. </s>
            <s xml:id="echoid-s7246" xml:space="preserve">Vnde multiplicatio difficilior aliquanto
              <lb/>
            redditur, vt pater. </s>
            <s xml:id="echoid-s7247" xml:space="preserve">Crepuſculorum ergo magnitudines, & </s>
            <s xml:id="echoid-s7248" xml:space="preserve">c. </s>
            <s xml:id="echoid-s7249" xml:space="preserve">inuenimus. </s>
            <s xml:id="echoid-s7250" xml:space="preserve">Quod faciendum erat.</s>
            <s xml:id="echoid-s7251" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div408" type="section" level="1" n="137">
          <head xml:id="echoid-head140" style="it" xml:space="preserve">SCHOLIVM.</head>
          <note position="left" xml:space="preserve">20</note>
          <p style="it">
            <s xml:id="echoid-s7252" xml:space="preserve">ALTITVDO meridiana Solis ita reperitur, vt communiter omnes tradunt. </s>
            <s xml:id="echoid-s7253" xml:space="preserve">Sole in borealibus
              <lb/>
              <note position="left" xlink:label="note-0140-03" xlink:href="note-0140-03a" xml:space="preserve">Meridiana alti
                <lb/>
              tudo Solis quo
                <lb/>
              pacto reperiat.</note>
            ſignis exiſtente, adijciatur eius declinatio altitudini Aequatoris, ſeu complemento altitudinis poli: </s>
            <s xml:id="echoid-s7254" xml:space="preserve">Eo-
              <lb/>
            dem verò auſtr alia per currente ſigna, dematur eius declinatio ab altitudine Aequatoris, ſcu à comple-
              <lb/>
            mento altitudinis poli. </s>
            <s xml:id="echoid-s7255" xml:space="preserve">Numerus enim ex illa additione conflatus, vel ex hac ſubtr actione relictus da-
              <lb/>
            bit altitudinem meridianam quæſitam. </s>
            <s xml:id="echoid-s7256" xml:space="preserve">Vt Sole exiſtente in principio ♋, ſi eius declinatio, quæ continet
              <lb/>
              <note position="left" xlink:label="note-0140-04" xlink:href="note-0140-04a" xml:space="preserve">Quando nume
                <lb/>
              rus conflatus ex
                <lb/>
              declinatione bo
                <lb/>
              reali & altitudi
                <lb/>
              ne Aequatoris
                <lb/>
              ſuperat gra. 90.
                <lb/>
              Quando altitu
                <lb/>
              do poli minor
                <lb/>
              eſt declinatione
                <lb/>
              borealis paralle
                <lb/>
              li Solis, verteæ
                <lb/>
              loci eſt inter pa
                <lb/>
              ralielum Solis
                <lb/>
              & Aȩquatorem,
                <lb/>
              altitudoq́; meri
                <lb/>
              diana solis eſt
                <lb/>
              borealis.</note>
            grad. </s>
            <s xml:id="echoid-s7257" xml:space="preserve">23. </s>
            <s xml:id="echoid-s7258" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s7259" xml:space="preserve">30. </s>
            <s xml:id="echoid-s7260" xml:space="preserve">addatur complemento altitudinis poli, ſiue eleuationi Aequatoris Romæ, quæ gradus
              <lb/>
            48. </s>
            <s xml:id="echoid-s7261" xml:space="preserve">complectitur, conficitur altitudo meridiana grad. </s>
            <s xml:id="echoid-s7262" xml:space="preserve">71. </s>
            <s xml:id="echoid-s7263" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s7264" xml:space="preserve">30. </s>
            <s xml:id="echoid-s7265" xml:space="preserve">ad latitudinem grad. </s>
            <s xml:id="echoid-s7266" xml:space="preserve">42. </s>
            <s xml:id="echoid-s7267" xml:space="preserve">qualis Ro-
              <lb/>
            mæreperitur. </s>
            <s xml:id="echoid-s7268" xml:space="preserve">Sole verò in principio ♑, exiſtente, ſi eius declinatio, quæ eſt grad. </s>
            <s xml:id="echoid-s7269" xml:space="preserve">23. </s>
            <s xml:id="echoid-s7270" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s7271" xml:space="preserve">30. </s>
            <s xml:id="echoid-s7272" xml:space="preserve">ab eleua-
              <lb/>
            tione Aequatoris, hoc est, à complemento altitudinis poli, nimirum à grad. </s>
            <s xml:id="echoid-s7273" xml:space="preserve">48. </s>
            <s xml:id="echoid-s7274" xml:space="preserve">detrabatur, reliqua erit
              <lb/>
              <note position="left" xlink:label="note-0140-05" xlink:href="note-0140-05a" xml:space="preserve">30</note>
            altitudo meridiana grad. </s>
            <s xml:id="echoid-s7275" xml:space="preserve">24. </s>
            <s xml:id="echoid-s7276" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s7277" xml:space="preserve">30. </s>
            <s xml:id="echoid-s7278" xml:space="preserve">Huius operationis ratio perſpicua eſt ex ſuperioribus figuris.
              <lb/>
            </s>
            <s xml:id="echoid-s7279" xml:space="preserve">Nam in prima, vbi parallelus diametri K L, borealis eſt, componitur altitudo meridiana A K, ex de-
              <lb/>
            clinatione K H, & </s>
            <s xml:id="echoid-s7280" xml:space="preserve">altitudine Aequatoris H A. </s>
            <s xml:id="echoid-s7281" xml:space="preserve">In alijs verò, in quibus parallelus diametri K L, au-
              <lb/>
            ſtralis eſt, prouenit altitudo meridiana A K, ſi declinatio K H, ab altitudine Aequatoris H A,
              <lb/>
            deducatur.</s>
            <s xml:id="echoid-s7282" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s7283" xml:space="preserve">SED hic nonulla obſeruanda ſunt. </s>
            <s xml:id="echoid-s7284" xml:space="preserve">Primum, quando in ſignis borealibus ex additione declina-
              <lb/>
            tionis ad eleuationem Aequatoris maior numerus conflatur, quàm grad. </s>
            <s xml:id="echoid-s7285" xml:space="preserve">90. </s>
            <s xml:id="echoid-s7286" xml:space="preserve">auferendus eſt numer us
              <lb/>
              <note position="left" xlink:label="note-0140-06" xlink:href="note-0140-06a" xml:space="preserve">Quando altitu-
                <lb/>
              do poli æqualis
                <lb/>
              eſt declinationi
                <lb/>
              borealis paralle
                <lb/>
              li Solis, tangit
                <lb/>
              parallelus Solis
                <lb/>
              Verticalem cir-
                <lb/>
              culum in B, uer
                <lb/>
              tice, altitudoq́ue
                <lb/>
              meridiana Solis
                <lb/>
              eſt quadrans.</note>
            conflatus ex ſemicir culo, vt altitudo meridiana babeatur. </s>
            <s xml:id="echoid-s7287" xml:space="preserve">Tunc enim Sol inter verticem B, & </s>
            <s xml:id="echoid-s7288" xml:space="preserve">polum
              <lb/>
            arcticum F, exiſtet, vel (quod idem eſt) vertex B, inter Solem & </s>
            <s xml:id="echoid-s7289" xml:space="preserve">Aequatorem: </s>
            <s xml:id="echoid-s7290" xml:space="preserve">vt in priori figura hu-
              <lb/>
            ius ſcholij cernitur, vbi arcus A K, inter Horizontem, & </s>
            <s xml:id="echoid-s7291" xml:space="preserve">parallelum borealem, quadr antem A B, ſupe-
              <lb/>
              <note position="left" xlink:label="note-0140-07" xlink:href="note-0140-07a" xml:space="preserve">40</note>
            rat, & </s>
            <s xml:id="echoid-s7292" xml:space="preserve">altitudo meridiana eſt arcus C k, ex parte boreali, vertex{q́ue}, B, inter parallelum Solis, & </s>
            <s xml:id="echoid-s7293" xml:space="preserve">Ae-
              <lb/>
            quatorem conſtitutus eſt. </s>
            <s xml:id="echoid-s7294" xml:space="preserve">Quod quidem accidit, cum altitudo poli minor eſt declinatione propoſiti pa-
              <lb/>
            ralleli, vt bic contingit. </s>
            <s xml:id="echoid-s7295" xml:space="preserve">Arcus enim B H, qui arcui altitudinis poli C F, ęqualis eſt, vt in ſphæra ostendi-
              <lb/>
            mus, & </s>
            <s xml:id="echoid-s7296" xml:space="preserve">ex fig ur a facile colligitur, (Nam ſi ex ęqualibus quadr antibus C B, F H, dematur communis
              <lb/>
              <note position="left" xlink:label="note-0140-08" xlink:href="note-0140-08a" xml:space="preserve">Quando com-
                <lb/>
              plemen tum al-
                <lb/>
              titudinis poli
                <lb/>
              minus eſt decli-
                <lb/>
              natione borea-
                <lb/>
              lis paralleli So-
                <lb/>
              lis, extat totus
                <lb/>
              parallelus ſupra
                <lb/>
              Horizontẽ, nul
                <lb/>
              lumq́; crepuſcu
                <lb/>
              lunt ht. Sol au-
                <lb/>
              tem duas habet
                <lb/>
              altitudines me-
                <lb/>
              ridianas in eo
                <lb/>
              parallelo.</note>
            arous F B, æquales remanent arcus C F, B H,) minor est declinatione H K. </s>
            <s xml:id="echoid-s7297" xml:space="preserve">Quòd ſi altitudo poli
              <lb/>
            B H, æqualis quandoque fuerit declinationi paralleli, tanget parallelus Verticalem in B, vertice, erit{q́ue}
              <lb/>
            altitudo meridiana quadrans, nempe C B, vel A B, grad. </s>
            <s xml:id="echoid-s7298" xml:space="preserve">90.</s>
            <s xml:id="echoid-s7299" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s7300" xml:space="preserve">DEINDE, quando complementum altitudinis poli minus eſt declinatione paralleli borealis, exta-
              <lb/>
            bit parallelus totus ſupra Horizontem, habebitq́, duas altitudines meridianas, auſtralem vnam, quæ ma-
              <lb/>
            ior cſt, & </s>
            <s xml:id="echoid-s7301" xml:space="preserve">alteram Septentrionalem, quæ minor eſt. </s>
            <s xml:id="echoid-s7302" xml:space="preserve">Prior inuenitur per regulam ſupra traditam; </s>
            <s xml:id="echoid-s7303" xml:space="preserve">poſte-
              <lb/>
              <note position="left" xlink:label="note-0140-09" xlink:href="note-0140-09a" xml:space="preserve">50</note>
            rior autem babetur, ſi complementum altitudinis poli ex declinatione dematur. </s>
            <s xml:id="echoid-s7304" xml:space="preserve">Perſpicuum hoc eſt in
              <lb/>
            ſecunda figura huius ſcholij, vbi C I, complementum altitudinis poli minus eſt declinatione I L, & </s>
            <s xml:id="echoid-s7305" xml:space="preserve">pa-
              <lb/>
            rallelus borealis K L, totus eſt ſupra Horizontem; </s>
            <s xml:id="echoid-s7306" xml:space="preserve">altitudo meridiana auſtr alis & </s>
            <s xml:id="echoid-s7307" xml:space="preserve">maior, arcus A K;
              <lb/>
            </s>
            <s xml:id="echoid-s7308" xml:space="preserve">
              <note position="left" xlink:label="note-0140-10" xlink:href="note-0140-10a" xml:space="preserve">Quando com-
                <lb/>
              plementũ altitu
                <lb/>
              dinis poli æqua
                <lb/>
              le eſt declinatio
                <lb/>
              ni borealis pa-
                <lb/>
              ralleli Solis, tan
                <lb/>
              git parallelus
                <lb/>
              Horizontẽ, nul
                <lb/>
              lumq́; eſt crepu
                <lb/>
              ſculum.</note>
            borealis verò & </s>
            <s xml:id="echoid-s7309" xml:space="preserve">minor, arcus C L, quæ babetur, ſi ex declinatione I L, auferatur complementum altitu-
              <lb/>
            dinis poli I C. </s>
            <s xml:id="echoid-s7310" xml:space="preserve">Sole autem in hoc parallelo exiſtente nullum crepuſculum eſt, cum continua dies exiſtat.
              <lb/>
            </s>
            <s xml:id="echoid-s7311" xml:space="preserve">Quòd ſi complementum altitudinis poli I C, fuerit quandoque ęquale declinationi paralleli, tanget pa-
              <lb/>
            rallelus Horizontem in C, totusq́, ſupra Horizontem extabit, vnde nec tunc crepuſculum quæren-
              <lb/>
            dum erit.</s>
            <s xml:id="echoid-s7312" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s7313" xml:space="preserve">TERTIO quando in ſignis austr alibus declinatio paralleli alicuius maior fuerit complemento
              <lb/>
            altitudinis poli, & </s>
            <s xml:id="echoid-s7314" xml:space="preserve">propterea auferri non poſſit à dicto complemento, vt altitudo meridiana habeatur,
              <lb/>
              <note position="left" xlink:label="note-0140-11" xlink:href="note-0140-11a" xml:space="preserve">Quando decli-
                <lb/>
              nauo paralleli</note>
            nullam habebit Sol in illo parallelo altitudinem meridianam, ſed totus parallelus ſub Horizonte </s>
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