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

Page concordance

< >
Scan Original
101 81
102 82
103 83
104 84
105 85
106 86
107 87
108 88
109 89
110 90
111 91
112 92
113 93
114 94
115 95
116 96
117 97
118 98
119 99
120 100
121 101
122 102
123 103
124 104
125 105
126 106
127 107
128 108
129 109
130 110
< >
page |< < (136) of 677 > >|
    <echo version="1.0RC">
      <text xml:lang="it" type="free">
        <div xml:id="echoid-div426" type="section" level="1" n="138">
          <p>
            <s xml:id="echoid-s8694" xml:space="preserve">
              <pb o="136" file="0156" n="156" rhead="GNOMONICES"/>
            tur ſinus arcus cuiuſdam, qui ex quadrante ſublatus dabit arcum, quem vocabimus Inuen-
              <lb/>
            tum primum.</s>
            <s xml:id="echoid-s8695" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8696" xml:space="preserve">DEINDE ſi fiat, vt ſinus illius arcus, quem Inuentum primum diximus, ad ſinum altitudinis
              <lb/>
            poli, ita ſinus totus ad aliud, reperietur ſinus arcus alterius, ex quo, ſi Sol fuerit borealis, habueritq́
              <lb/>
            diſtantiam à meridie maiorem, quàm hor. </s>
            <s xml:id="echoid-s8697" xml:space="preserve">6. </s>
            <s xml:id="echoid-s8698" xml:space="preserve">ſubtractus arcus complementi declinationis dabit
              <lb/>
              <note position="left" xlink:label="note-0156-01" xlink:href="note-0156-01a" xml:space="preserve">Inuen@@ ſe-
                <lb/>
              cundum.</note>
            arcum quendam, quem Inuentum ſecundum appellabimus. </s>
            <s xml:id="echoid-s8699" xml:space="preserve">Quòd ſi diſtantia Solis à meridie
              <lb/>
            minor fuerit quàm hor. </s>
            <s xml:id="echoid-s8700" xml:space="preserve">6. </s>
            <s xml:id="echoid-s8701" xml:space="preserve">in quocunque parallelo extiterit Sol, detrahendus erit arcus per Inuen-
              <lb/>
            tum primum compertus ex ſemicirculo, & </s>
            <s xml:id="echoid-s8702" xml:space="preserve">ex reliquo arcu, ſi Sol eſt borealis, ſubtrahendus rur-
              <lb/>
            ſus arcus complementi declinationis, vel ſi auſtralis Sol eſt, auferendus arcus compoſitus ex qua-
              <lb/>
            drante, & </s>
            <s xml:id="echoid-s8703" xml:space="preserve">arcu declinationis, vt arcus inueniatur, quem Inuentum ſecundum vocemus.</s>
            <s xml:id="echoid-s8704" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">10</note>
          <p>
            <s xml:id="echoid-s8705" xml:space="preserve">POSTREMO ſi fiat, vt ſinus totus ad ſinumarcus, quem ſecundum Inuentum nominaui-
              <lb/>
            mus, ita ſinus arcus, quem diximus Inuentum primum, ad aliud, inuentus erit ſinus altitudinis
              <lb/>
            Solis quæſitæ. </s>
            <s xml:id="echoid-s8706" xml:space="preserve">Quod vt planius fiat, duobus exemplis rem totam explicabimus.</s>
            <s xml:id="echoid-s8707" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8708" xml:space="preserve">PONATVR Sol in principio ♋, habere diſtantiam à meridie hor. </s>
            <s xml:id="echoid-s8709" xml:space="preserve">7. </s>
            <s xml:id="echoid-s8710" xml:space="preserve">hoc eſt, grad. </s>
            <s xml:id="echoid-s8711" xml:space="preserve">105. </s>
            <s xml:id="echoid-s8712" xml:space="preserve">ita
              <lb/>
              <note position="left" xlink:label="note-0156-03" xlink:href="note-0156-03a" xml:space="preserve">Exemplum pri-
                <lb/>
              num.</note>
            vt angulus BNQ, totidem gradus complectatur, atque adeo reliquus ex duobus rectis DNQ,
              <lb/>
            grad. </s>
            <s xml:id="echoid-s8713" xml:space="preserve">75. </s>
            <s xml:id="echoid-s8714" xml:space="preserve">Fiat ergo, vt 100000. </s>
            <s xml:id="echoid-s8715" xml:space="preserve">ſinus totus ad 96592. </s>
            <s xml:id="echoid-s8716" xml:space="preserve">ſinum anguli DNQ, ita 74314. </s>
            <s xml:id="echoid-s8717" xml:space="preserve">ſinus cõ-
              <lb/>
            plementi altitudinis poli ad aliud, inueniemusq́; </s>
            <s xml:id="echoid-s8718" xml:space="preserve">hunc propemodum ſinum 71781. </s>
            <s xml:id="echoid-s8719" xml:space="preserve">cuius arcus
              <lb/>
            grad. </s>
            <s xml:id="echoid-s8720" xml:space="preserve">45. </s>
            <s xml:id="echoid-s8721" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s8722" xml:space="preserve">52. </s>
            <s xml:id="echoid-s8723" xml:space="preserve">ex quadrante detractus relinquet arcum grad. </s>
            <s xml:id="echoid-s8724" xml:space="preserve">44. </s>
            <s xml:id="echoid-s8725" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s8726" xml:space="preserve">8. </s>
            <s xml:id="echoid-s8727" xml:space="preserve">pro Inuento primo.</s>
            <s xml:id="echoid-s8728" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8729" xml:space="preserve">RVRSVS fiat, vt 69633. </s>
            <s xml:id="echoid-s8730" xml:space="preserve">ſinus arcus Primi Inuenti ad 66913. </s>
            <s xml:id="echoid-s8731" xml:space="preserve">ſinum altitudinis poli, ita
              <lb/>
            100000. </s>
            <s xml:id="echoid-s8732" xml:space="preserve">ſinus totus ad aliud, reperiemus q́; </s>
            <s xml:id="echoid-s8733" xml:space="preserve">fere hunc ſinum 96093. </s>
            <s xml:id="echoid-s8734" xml:space="preserve">ex cuius arcu grad. </s>
            <s xml:id="echoid-s8735" xml:space="preserve">73. </s>
            <s xml:id="echoid-s8736" xml:space="preserve">Min.
              <lb/>
            </s>
            <s xml:id="echoid-s8737" xml:space="preserve">
              <note position="left" xlink:label="note-0156-04" xlink:href="note-0156-04a" xml:space="preserve">20</note>
            56. </s>
            <s xml:id="echoid-s8738" xml:space="preserve">(quoniam Sol borealis ponitur, eiuſq́; </s>
            <s xml:id="echoid-s8739" xml:space="preserve">diſtantia à meridie maior, quàm hor. </s>
            <s xml:id="echoid-s8740" xml:space="preserve">6.) </s>
            <s xml:id="echoid-s8741" xml:space="preserve">ſi detrahatur
              <lb/>
            complementum declinationis paralleli ♋, nempe grad. </s>
            <s xml:id="echoid-s8742" xml:space="preserve">66. </s>
            <s xml:id="echoid-s8743" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s8744" xml:space="preserve">30. </s>
            <s xml:id="echoid-s8745" xml:space="preserve">relinquetur arcus grad. </s>
            <s xml:id="echoid-s8746" xml:space="preserve">7.
              <lb/>
            </s>
            <s xml:id="echoid-s8747" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s8748" xml:space="preserve">26. </s>
            <s xml:id="echoid-s8749" xml:space="preserve">pro Inuento ſecundo.</s>
            <s xml:id="echoid-s8750" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8751" xml:space="preserve">TANDEM fiat, vt 100000. </s>
            <s xml:id="echoid-s8752" xml:space="preserve">ſinus totus ad 12937. </s>
            <s xml:id="echoid-s8753" xml:space="preserve">ſinum arcus Inuenti ſecundi, ita 69633.
              <lb/>
            </s>
            <s xml:id="echoid-s8754" xml:space="preserve">ſinus arcus Inuenti primi ad aliud, inuenieturq́; </s>
            <s xml:id="echoid-s8755" xml:space="preserve">hic ferme ſinus 9008. </s>
            <s xml:id="echoid-s8756" xml:space="preserve">altitudinis Solis. </s>
            <s xml:id="echoid-s8757" xml:space="preserve">Quare
              <lb/>
            altitudo Solis comprehendet grad. </s>
            <s xml:id="echoid-s8758" xml:space="preserve">5. </s>
            <s xml:id="echoid-s8759" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s8760" xml:space="preserve">10.</s>
            <s xml:id="echoid-s8761" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8762" xml:space="preserve">STATVATVR rurſus Sol in principio ♑, & </s>
            <s xml:id="echoid-s8763" xml:space="preserve">diſtantia eius à meridie hor. </s>
            <s xml:id="echoid-s8764" xml:space="preserve">2. </s>
            <s xml:id="echoid-s8765" xml:space="preserve">hoc eſt, grad.
              <lb/>
            </s>
            <s xml:id="echoid-s8766" xml:space="preserve">
              <note position="left" xlink:label="note-0156-05" xlink:href="note-0156-05a" xml:space="preserve">Exemplum ſe-
                <lb/>
              cundum.</note>
            30. </s>
            <s xml:id="echoid-s8767" xml:space="preserve">ita vt angulus BNQ, totidem gradus cõtineat, ac proinde reliquus ex duobus rectis DNQ,
              <lb/>
            grad. </s>
            <s xml:id="echoid-s8768" xml:space="preserve">150. </s>
            <s xml:id="echoid-s8769" xml:space="preserve">Fiat igitur, vt 100000. </s>
            <s xml:id="echoid-s8770" xml:space="preserve">ſinus totus ad 50000. </s>
            <s xml:id="echoid-s8771" xml:space="preserve">ſinum anguli DNQ, (eſt enim idem ſi-
              <lb/>
            nus arcus grad. </s>
            <s xml:id="echoid-s8772" xml:space="preserve">150. </s>
            <s xml:id="echoid-s8773" xml:space="preserve">& </s>
            <s xml:id="echoid-s8774" xml:space="preserve">arcus grad. </s>
            <s xml:id="echoid-s8775" xml:space="preserve">30. </s>
            <s xml:id="echoid-s8776" xml:space="preserve">qui cum illo ſemicirculum conficit, vt in tractatu ſinuum
              <lb/>
              <note position="left" xlink:label="note-0156-06" xlink:href="note-0156-06a" xml:space="preserve">30</note>
            docuimus) ita 74314. </s>
            <s xml:id="echoid-s8777" xml:space="preserve">ſinus complementi altitudinis poliad aliud, inuenieturq́; </s>
            <s xml:id="echoid-s8778" xml:space="preserve">ferme ſinus hic,
              <lb/>
            37157. </s>
            <s xml:id="echoid-s8779" xml:space="preserve">cuius arcus grad. </s>
            <s xml:id="echoid-s8780" xml:space="preserve">21. </s>
            <s xml:id="echoid-s8781" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s8782" xml:space="preserve">49. </s>
            <s xml:id="echoid-s8783" xml:space="preserve">ex quadrante detractus relinquet pro Inuento primo arcum
              <lb/>
            grad. </s>
            <s xml:id="echoid-s8784" xml:space="preserve">68. </s>
            <s xml:id="echoid-s8785" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s8786" xml:space="preserve">11.</s>
            <s xml:id="echoid-s8787" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8788" xml:space="preserve">DEINDE fiat, vt 92837. </s>
            <s xml:id="echoid-s8789" xml:space="preserve">ſinus arcus Primi Inuenti, ad 66913. </s>
            <s xml:id="echoid-s8790" xml:space="preserve">ſinum altitudinis poli, ita
              <lb/>
            100000. </s>
            <s xml:id="echoid-s8791" xml:space="preserve">ad aliud, inuenieturq́; </s>
            <s xml:id="echoid-s8792" xml:space="preserve">hic quaſi ſinus 72075. </s>
            <s xml:id="echoid-s8793" xml:space="preserve">cuius arcus grad. </s>
            <s xml:id="echoid-s8794" xml:space="preserve">46. </s>
            <s xml:id="echoid-s8795" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s8796" xml:space="preserve">7. </s>
            <s xml:id="echoid-s8797" xml:space="preserve">ex ſemicirculo
              <lb/>
            grad. </s>
            <s xml:id="echoid-s8798" xml:space="preserve">180. </s>
            <s xml:id="echoid-s8799" xml:space="preserve">deductus (quoniam diſtantia Solis à meridie ad hor. </s>
            <s xml:id="echoid-s8800" xml:space="preserve">6. </s>
            <s xml:id="echoid-s8801" xml:space="preserve">non peruenit) dabit arcum NQ,
              <lb/>
            grad. </s>
            <s xml:id="echoid-s8802" xml:space="preserve">133. </s>
            <s xml:id="echoid-s8803" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s8804" xml:space="preserve">53. </s>
            <s xml:id="echoid-s8805" xml:space="preserve">ex quo, quia Sol auſtralis ponitur, ſi detrahatur arcus NL, compoſitus ex ſinu
              <lb/>
            toto, & </s>
            <s xml:id="echoid-s8806" xml:space="preserve">ſinu declinationis, nempe grad. </s>
            <s xml:id="echoid-s8807" xml:space="preserve">113. </s>
            <s xml:id="echoid-s8808" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s8809" xml:space="preserve">30. </s>
            <s xml:id="echoid-s8810" xml:space="preserve">relinquetur pro Inuento ſecundo arcus grad.
              <lb/>
            </s>
            <s xml:id="echoid-s8811" xml:space="preserve">20. </s>
            <s xml:id="echoid-s8812" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s8813" xml:space="preserve">23.</s>
            <s xml:id="echoid-s8814" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8815" xml:space="preserve">POSTREMO fiat, vt 100000. </s>
            <s xml:id="echoid-s8816" xml:space="preserve">ſinus totus ad 34829. </s>
            <s xml:id="echoid-s8817" xml:space="preserve">ſinum arcus Inuenti ſecundi, ita
              <lb/>
              <note position="left" xlink:label="note-0156-07" xlink:href="note-0156-07a" xml:space="preserve">40</note>
            92837. </s>
            <s xml:id="echoid-s8818" xml:space="preserve">ſinus Inuenti primi ad aliud, reperieturq́; </s>
            <s xml:id="echoid-s8819" xml:space="preserve">hic fere ſinus 32334. </s>
            <s xml:id="echoid-s8820" xml:space="preserve">altitudinis Solis, atq; </s>
            <s xml:id="echoid-s8821" xml:space="preserve">adeo
              <lb/>
            altitudo ipſa Solis complectetur grad. </s>
            <s xml:id="echoid-s8822" xml:space="preserve">18. </s>
            <s xml:id="echoid-s8823" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s8824" xml:space="preserve">52.</s>
            <s xml:id="echoid-s8825" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8826" xml:space="preserve">PORRO quando Sol exiſtit in Verticali circulo, vel abeſt à meridie horis ſex, aut denique in
              <lb/>
            Aequatore conſtitutus eſt, expediemus rem, vt paulo ante tradidimus.</s>
            <s xml:id="echoid-s8827" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8828" xml:space="preserve">AD extremum abſoluemus idem hoc proble-
              <lb/>
              <note position="left" xlink:label="note-0156-08" xlink:href="note-0156-08a" xml:space="preserve">Altitudo Solis
                <lb/>
              in ęquinoctiis,
                <lb/>
              quomodo in
                <lb/>
              ſphęra recta ex
                <lb/>
              data hora depre
                <lb/>
              hendatur.</note>
              <figure xlink:label="fig-0156-01" xlink:href="fig-0156-01a" number="113">
                <image file="0156-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0156-01"/>
              </figure>
            ma per triangula ſphærica in ſphæra recta, hac ra-
              <lb/>
            tione. </s>
            <s xml:id="echoid-s8829" xml:space="preserve">Sole Aequatorem percurrente, erit comple
              <lb/>
            mentum diſtantiæ ipſius à meridie, altitudo Solis
              <lb/>
            ſupra Horizontem: </s>
            <s xml:id="echoid-s8830" xml:space="preserve">quia in ſphæra recta Aequator
              <lb/>
            idem eſt, quod Verticalis circulus per centrum Solis
              <lb/>
              <note position="left" xlink:label="note-0156-09" xlink:href="note-0156-09a" xml:space="preserve">50</note>
            tranſiens. </s>
            <s xml:id="echoid-s8831" xml:space="preserve">Vt in ſubiecta figura, ſi poli mundi intelli
              <lb/>
            gantur B, D, erit Verticalis AEC, & </s>
            <s xml:id="echoid-s8832" xml:space="preserve">idẽ ipſe Aequa
              <lb/>
            tor. </s>
            <s xml:id="echoid-s8833" xml:space="preserve">Poſito ergo Sole in I, erit arcus AI, complemen
              <lb/>
            ti diſtantiæ Solis à meridie, arcus etiam altitudinis
              <lb/>
            Solis, vt perſpicuum eſt.</s>
            <s xml:id="echoid-s8834" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8835" xml:space="preserve">SOLE autem occupante quemcunque paral-
              <lb/>
              <note position="left" xlink:label="note-0156-10" xlink:href="note-0156-10a" xml:space="preserve">Altitudo Solis
                <lb/>
              in quocunque
                <lb/>
              parallelo exiſtẽ-
                <lb/>
              tis, quo pacto
                <lb/>
              per triangula
                <lb/>
              ſphęrica in ſphę
                <lb/>
              ra recta ex data
                <lb/>
              hora colligatur.</note>
            lelum FG, ſiue borealem, ſiue auſtralem, ita rem
              <lb/>
            exequemur. </s>
            <s xml:id="echoid-s8836" xml:space="preserve">Ponatur Sol in k, ducaturq́ Vertica-
              <lb/>
            lis EL, ex E, vertice per centrum Solis k: </s>
            <s xml:id="echoid-s8837" xml:space="preserve">Item
              <lb/>
            circulus declinationis D
              <emph style="sc">K</emph>
            B, per polos mundi, & </s>
            <s xml:id="echoid-s8838" xml:space="preserve">
              <lb/>
            per centrum Solis ductus ſit, ſecans </s>
          </p>
        </div>
      </text>
    </echo>
Impressum