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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          <p>
            <s xml:id="echoid-s7583" xml:space="preserve">
              <pb o="125" file="0145" n="145" rhead="LIBER PRIMVS."/>
            nus inſtrum@ta, quibus horæ depingũtur, conficienda, vt proprijs in locis explicabimus.</s>
            <s xml:id="echoid-s7584" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7585" xml:space="preserve">SINT igitur eædem figuræ, quæ in præcedenti propoſ. </s>
            <s xml:id="echoid-s7586" xml:space="preserve">ponaturq́; </s>
            <s xml:id="echoid-s7587" xml:space="preserve">Sol in puncto O, in ſuo pa
              <lb/>
            rallelo, ducaturq́; </s>
            <s xml:id="echoid-s7588" xml:space="preserve">ex O, ad K L, diametrum paralleli perpendicularis O R, & </s>
            <s xml:id="echoid-s7589" xml:space="preserve">per R, diametro Ho
              <lb/>
              <figure xlink:label="fig-0145-01" xlink:href="fig-0145-01a" number="105">
                <image file="0145-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0145-01"/>
              </figure>
              <note position="left" xlink:label="note-0145-01" xlink:href="note-0145-01a" xml:space="preserve">10</note>
              <note position="left" xlink:label="note-0145-02" xlink:href="note-0145-02a" xml:space="preserve">20</note>
              <figure xlink:label="fig-0145-02" xlink:href="fig-0145-02a" number="106">
                <image file="0145-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0145-02"/>
              </figure>
              <note position="left" xlink:label="note-0145-03" xlink:href="note-0145-03a" xml:space="preserve">30</note>
            rizontis A C, parallela agatur ſecans K N, ſinum altitudinis meridianæ in T. </s>
            <s xml:id="echoid-s7590" xml:space="preserve">Erit O R, commu-
              <lb/>
            nis ſectio paralleli Solis, & </s>
            <s xml:id="echoid-s7591" xml:space="preserve">paralleli Horizontis, in quo Sol exiſtit tempore obſeruationis. </s>
            <s xml:id="echoid-s7592" xml:space="preserve">Quia
              <lb/>
            enim vterq; </s>
            <s xml:id="echoid-s7593" xml:space="preserve">parallelus ad Meridianum rectus eſt, erit quoq; </s>
            <s xml:id="echoid-s7594" xml:space="preserve">communis eorum ſectio ad eundem
              <lb/>
              <note position="right" xlink:label="note-0145-04" xlink:href="note-0145-04a" xml:space="preserve">19. vndec.</note>
            recta, & </s>
            <s xml:id="echoid-s7595" xml:space="preserve">ob id per defin. </s>
            <s xml:id="echoid-s7596" xml:space="preserve">3. </s>
            <s xml:id="echoid-s7597" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s7598" xml:space="preserve">11. </s>
            <s xml:id="echoid-s7599" xml:space="preserve">Euclidis, ad rectam K L, perpendicularis. </s>
            <s xml:id="echoid-s7600" xml:space="preserve">Cum igitur tunc Sol
              <lb/>
            in communi illa ſectione exiſtat, ponaturq́; </s>
            <s xml:id="echoid-s7601" xml:space="preserve">in puncto O, erit O R, perpendicularis ducta ad K L,
              <lb/>
            communis ſectio dictorum parallelorum. </s>
            <s xml:id="echoid-s7602" xml:space="preserve">Quare parallelus Horizontis per centrum Solis tunc
              <lb/>
            ductus ſecabit Meridianum in R, ac proinde parallela R T, communis ſectio erit Meridiani & </s>
            <s xml:id="echoid-s7603" xml:space="preserve">pa
              <lb/>
            ralleli Horizontis. </s>
            <s xml:id="echoid-s7604" xml:space="preserve">Meridianus enim in Horizonte, & </s>
            <s xml:id="echoid-s7605" xml:space="preserve">eius parallelo quocunq; </s>
            <s xml:id="echoid-s7606" xml:space="preserve">facit duas ſectiones
              <lb/>
              <note position="right" xlink:label="note-0145-05" xlink:href="note-0145-05a" xml:space="preserve">16. vndec.</note>
            parallelas. </s>
            <s xml:id="echoid-s7607" xml:space="preserve">Erit ergo T N, ſinus rectus altitudinis Solis, hoc eſt, illius arcus, qui inter A C, & </s>
            <s xml:id="echoid-s7608" xml:space="preserve">paral-
              <lb/>
              <note position="left" xlink:label="note-0145-06" xlink:href="note-0145-06a" xml:space="preserve">40</note>
            lelam R T, interijcitur in Verticali circulo per centrum Solis ducto, pro quo accipi poteſt Meri-
              <lb/>
            dianus A B C D. </s>
            <s xml:id="echoid-s7609" xml:space="preserve">Si enim circa B D, axem Horizontis circumferatur, fungetur munere omnium
              <lb/>
            Verticalium, vt patet.</s>
            <s xml:id="echoid-s7610" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7611" xml:space="preserve">ANTE omnia igitur explorãda eſt diſtãtia Solis à meridie quo ad gradus, quã data hora quæ-
              <lb/>
              <note position="right" xlink:label="note-0145-07" xlink:href="note-0145-07a" xml:space="preserve">Diſtantia Solis
                <lb/>
              à meridie quo
                <lb/>
              ad gradus, quo
                <lb/>
              modo ex data
                <lb/>
              hora cognoſca-
                <lb/>
              tur.</note>
            cunq; </s>
            <s xml:id="echoid-s7612" xml:space="preserve">manifeſtabit hac ratione. </s>
            <s xml:id="echoid-s7613" xml:space="preserve">Si de horis aſtronomicis loquamur, diſtabit hora 1. </s>
            <s xml:id="echoid-s7614" xml:space="preserve">à meridie v. </s>
            <s xml:id="echoid-s7615" xml:space="preserve">g.
              <lb/>
            </s>
            <s xml:id="echoid-s7616" xml:space="preserve">vel 11. </s>
            <s xml:id="echoid-s7617" xml:space="preserve">à media nocte à Meridiano ſupra Horizontẽ, hoc eſt, à meridie, grad. </s>
            <s xml:id="echoid-s7618" xml:space="preserve">15. </s>
            <s xml:id="echoid-s7619" xml:space="preserve">& </s>
            <s xml:id="echoid-s7620" xml:space="preserve">hora 2. </s>
            <s xml:id="echoid-s7621" xml:space="preserve">à meri-
              <lb/>
            die, vel 10. </s>
            <s xml:id="echoid-s7622" xml:space="preserve">à media nocte, grad. </s>
            <s xml:id="echoid-s7623" xml:space="preserve">30. </s>
            <s xml:id="echoid-s7624" xml:space="preserve">&</s>
            <s xml:id="echoid-s7625" xml:space="preserve">c. </s>
            <s xml:id="echoid-s7626" xml:space="preserve">cùm ſingulæ horę cõplectãtur grad. </s>
            <s xml:id="echoid-s7627" xml:space="preserve">15. </s>
            <s xml:id="echoid-s7628" xml:space="preserve">Si vero de horis Ita-
              <lb/>
            licis ſermo habeatur, vel Babylonicis, cognoſcendũ eſt prius tẽpus meridiei in die propoſito, vt in
              <lb/>
            cap. </s>
            <s xml:id="echoid-s7629" xml:space="preserve">3. </s>
            <s xml:id="echoid-s7630" xml:space="preserve">Sphæræ docuimus, cũ de arcubus ſemidiurnis ageremus. </s>
            <s xml:id="echoid-s7631" xml:space="preserve">Hoc namq; </s>
            <s xml:id="echoid-s7632" xml:space="preserve">cognito, non difficile
              <lb/>
            erit intelligere, quãta ſit diſtãtia horæ datæ à meridiano tẽpore. </s>
            <s xml:id="echoid-s7633" xml:space="preserve">Quãdo enim v.</s>
            <s xml:id="echoid-s7634" xml:space="preserve">g. </s>
            <s xml:id="echoid-s7635" xml:space="preserve">meridies fit hora
              <lb/>
              <note position="left" xlink:label="note-0145-08" xlink:href="note-0145-08a" xml:space="preserve">50</note>
            17 {1/2}. </s>
            <s xml:id="echoid-s7636" xml:space="preserve">ab occaſu, & </s>
            <s xml:id="echoid-s7637" xml:space="preserve">6 {1/2}. </s>
            <s xml:id="echoid-s7638" xml:space="preserve">ab ortu, quod quidẽ euenit, quãdo dies continet horas 13. </s>
            <s xml:id="echoid-s7639" xml:space="preserve">perſpicuũ eſt,
              <lb/>
            horam 20. </s>
            <s xml:id="echoid-s7640" xml:space="preserve">vel 15. </s>
            <s xml:id="echoid-s7641" xml:space="preserve">ab occaſu, & </s>
            <s xml:id="echoid-s7642" xml:space="preserve">4. </s>
            <s xml:id="echoid-s7643" xml:space="preserve">vel 9. </s>
            <s xml:id="echoid-s7644" xml:space="preserve">ab ortu, diſtare à meridie hor. </s>
            <s xml:id="echoid-s7645" xml:space="preserve">2 {1/2}. </s>
            <s xml:id="echoid-s7646" xml:space="preserve">hoc eſt, grad. </s>
            <s xml:id="echoid-s7647" xml:space="preserve">37. </s>
            <s xml:id="echoid-s7648" xml:space="preserve">Min.
              <lb/>
            </s>
            <s xml:id="echoid-s7649" xml:space="preserve">30. </s>
            <s xml:id="echoid-s7650" xml:space="preserve">&</s>
            <s xml:id="echoid-s7651" xml:space="preserve">c. </s>
            <s xml:id="echoid-s7652" xml:space="preserve">Si deniq; </s>
            <s xml:id="echoid-s7653" xml:space="preserve">horæ antiquæ, ſiue inæquales fuerint propoſitæ, diuidẽdus erit arcus diurnus per
              <lb/>
            12. </s>
            <s xml:id="echoid-s7654" xml:space="preserve">vt ſciamus quantitatem vnius horæ inæqualis. </s>
            <s xml:id="echoid-s7655" xml:space="preserve">Hinc enim facile diſtantiã Solis à meridie ex da
              <lb/>
            ta hora inæquali cognoſcemus. </s>
            <s xml:id="echoid-s7656" xml:space="preserve">Vt in principio ♋, arcus diurnus ad latitudinem grad. </s>
            <s xml:id="echoid-s7657" xml:space="preserve">42. </s>
            <s xml:id="echoid-s7658" xml:space="preserve">conti-
              <lb/>
            net horas 15. </s>
            <s xml:id="echoid-s7659" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s7660" xml:space="preserve">4. </s>
            <s xml:id="echoid-s7661" xml:space="preserve">quo diuiſo per 12. </s>
            <s xml:id="echoid-s7662" xml:space="preserve">reperiemus vnam horam inæqualẽ comprehendere hor. </s>
            <s xml:id="echoid-s7663" xml:space="preserve">
              <lb/>
            1. </s>
            <s xml:id="echoid-s7664" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s7665" xml:space="preserve">15. </s>
            <s xml:id="echoid-s7666" xml:space="preserve">Sec. </s>
            <s xml:id="echoid-s7667" xml:space="preserve">20. </s>
            <s xml:id="echoid-s7668" xml:space="preserve">ex horis æqualibus. </s>
            <s xml:id="echoid-s7669" xml:space="preserve">Quam ob rem hora 4. </s>
            <s xml:id="echoid-s7670" xml:space="preserve">inæqualis v.</s>
            <s xml:id="echoid-s7671" xml:space="preserve">g. </s>
            <s xml:id="echoid-s7672" xml:space="preserve">vel 8. </s>
            <s xml:id="echoid-s7673" xml:space="preserve">diſtabit à meri-
              <lb/>
            die, ſiue ab hora 6. </s>
            <s xml:id="echoid-s7674" xml:space="preserve">inæquali, hor. </s>
            <s xml:id="echoid-s7675" xml:space="preserve">2. </s>
            <s xml:id="echoid-s7676" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s7677" xml:space="preserve">30. </s>
            <s xml:id="echoid-s7678" xml:space="preserve">Sec. </s>
            <s xml:id="echoid-s7679" xml:space="preserve">40. </s>
            <s xml:id="echoid-s7680" xml:space="preserve">At hora 3. </s>
            <s xml:id="echoid-s7681" xml:space="preserve">inæqualis vel 9. </s>
            <s xml:id="echoid-s7682" xml:space="preserve">aberit à meridie
              <lb/>
            hor. </s>
            <s xml:id="echoid-s7683" xml:space="preserve">3. </s>
            <s xml:id="echoid-s7684" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s7685" xml:space="preserve">46. </s>
            <s xml:id="echoid-s7686" xml:space="preserve">& </s>
            <s xml:id="echoid-s7687" xml:space="preserve">ſic de cęteris. </s>
            <s xml:id="echoid-s7688" xml:space="preserve">Ex quibus horis æqualibus reperiemus diſtantiam Solis à meridie
              <lb/>
            quo ad gradus, vt prius. </s>
            <s xml:id="echoid-s7689" xml:space="preserve">Cognita porro diſtantia Solis à meridie, cognitum etiam erit eius com-
              <lb/>
            plementum, nempe differentia inter quadrantem, & </s>
            <s xml:id="echoid-s7690" xml:space="preserve">dictam diſtantiam.</s>
            <s xml:id="echoid-s7691" xml:space="preserve"/>
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