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 contents

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[41.] COROLLARIVM.
Page: 60 (40)
[42.] SCHOLIVM.
Page: 60 (40)
[43.] THEOREMA 9. PROPOSITIO 11.
Page: 62 (42)
[44.] SCHOLIVM.
Page: 63 (43)
[45.] COROLLARIVM PRIMVM.
Page: 63 (43)
[46.] COROLLARIVM II.
Page: 63 (43)
[47.] THEOREMA 10. PROPOSITIO 12.
Page: 63 (43)
[48.] COROLLARIVM.
Page: 64 (44)
[49.] THEOREMA 11. PROPOSITIO 13.
Page: 64 (44)
[50.] THEOREMA 12. PROPOSITIO 14.
Page: 65 (45)
[51.] SCHOLIVM.
Page: 66 (46)
[52.] THEOREMA 13. PROPOSITIO 15.
Page: 66 (46)
[53.] LEMMA.
Page: 69 (49)
[54.] COROLLARIVM.
Page: 69 (49)
[55.] THEOREMA 14. PROPOSITIO 16.
Page: 69 (49)
[56.] COROLLARIVM.
Page: 70 (50)
[57.] THEOREMA 15. PROPOSITIO 17.
Page: 70 (50)
[58.] LEMMA.
Page: 72 (52)
[59.] SCHOLIVM.
Page: 72 (52)
[60.] THEOREMA 16. PROPOSITIO 18.
Page: 72 (52)
[61.] THEOREMA 17. PROPOSITIO 19.
Page: 73 (53)
[62.] SCHOLIVM.
Page: 74 (54)
[63.] THEOREMA 18. PROPOSITIO 20.
Page: 75 (55)
[64.] SCHOLIVM.
Page: 75 (55)
[65.] Linea horæ 24. ab ortu vel occaſu. Vel horizontalis linea.
Page: 76 (56)
[66.] Linea horæ 12. ab ortu vel occaſu.
Page: 76 (56)
[67.] Linea horæ ſextæ à meridie vel media nocte.
Page: 77 (57)
[68.] Linea horæ 12. à meridie vel media nocte.
Page: 77 (57)
[69.] Linea horæ 23. ab ortu vel occaſu.
Page: 81 (61)
[70.] Linea horæ 22. ab ortu vel occaſu.
Page: 81 (61)
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          <p>
            <s xml:id="echoid-s7903" xml:space="preserve">
              <pb o="128" file="0148" n="148" rhead="GNOMONICES"/>
            altitudinis Solis, & </s>
            <s xml:id="echoid-s7904" xml:space="preserve">differẽtia inter dictam medietatem, & </s>
            <s xml:id="echoid-s7905" xml:space="preserve">ſinum altitudinis meridianę
              <unsure/>
            , ita ſinus
              <lb/>
            totus ad aliud, habebitur ſinus complementi diſtantię Solis à meridie, atq; </s>
            <s xml:id="echoid-s7906" xml:space="preserve">adeo & </s>
            <s xml:id="echoid-s7907" xml:space="preserve">ipſum comple
              <lb/>
            mentum diſtantię Solis à meridie notum erit, beneficio cuius diſtantiam Solis à meridie, ac proin
              <lb/>
            de & </s>
            <s xml:id="echoid-s7908" xml:space="preserve">horam tempore obſeruationis cognoſcemus hoc modo. </s>
            <s xml:id="echoid-s7909" xml:space="preserve">Quando Sol ſeptentrionalis eſt, & </s>
            <s xml:id="echoid-s7910" xml:space="preserve">
              <lb/>
            ſinus altitudinis Solis ſuperat differentiam inter medietatem dictam, & </s>
            <s xml:id="echoid-s7911" xml:space="preserve">ſinum altitudinis meri-
              <lb/>
            dianę, vt in figura prima & </s>
            <s xml:id="echoid-s7912" xml:space="preserve">tertia apparet, ſubtrahatur complementum diſtautię Solis à meridie
              <lb/>
            inuentum ex quadrante, reman ebitq́; </s>
            <s xml:id="echoid-s7913" xml:space="preserve">Solis diſtan
              <unsure/>
            tia à meridie, quo ad gradus.</s>
            <s xml:id="echoid-s7914" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7915" xml:space="preserve">QVOD ſi ſinus altitudinis Solis fuerit ęqualis differentię inter prędictam medietatem, & </s>
            <s xml:id="echoid-s7916" xml:space="preserve">ſi-
              <lb/>
            num altitudinis meridianę, diſtabit Sol quadrante i
              <unsure/>
            ntegro, ſiue ſex horis à meridie, vt in tribus
              <lb/>
            figuris prioribus manifeſtum eſſe poteſt. </s>
            <s xml:id="echoid-s7917" xml:space="preserve">Si enim λ N, differentia inter K N, ſinum altitudinis
              <lb/>
              <note position="left" xlink:label="note-0148-01" xlink:href="note-0148-01a" xml:space="preserve">10</note>
            meridianæ, & </s>
            <s xml:id="echoid-s7918" xml:space="preserve">K λ, medietatem prædictam, ponatur ſinus altitudinis Solis, ita vt λ M, ſit por-
              <lb/>
            tio diametri paralleli Horizontis per Solem tranſeuntis, dabit quadrans K P, diſtantiam Solis
              <lb/>
            à meridie.</s>
            <s xml:id="echoid-s7919" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7920" xml:space="preserve">SI vero Sole exiſtente boreali, ſinus altitudinis ſolis minor extiterit, quam differentia inter me
              <lb/>
            dietatem prędictam, & </s>
            <s xml:id="echoid-s7921" xml:space="preserve">ſinum altitudinis meridianæ, vt in ſecun da figura cõtingit, adiungatur cõ-
              <lb/>
            plementum diſtantię Solis à meridie inuentum quadranti, conflabiturq́; </s>
            <s xml:id="echoid-s7922" xml:space="preserve">diſtantia Solis à meri-
              <lb/>
            die, quo ad gradus.</s>
            <s xml:id="echoid-s7923" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7924" xml:space="preserve">SOLE deniq; </s>
            <s xml:id="echoid-s7925" xml:space="preserve">auſtrali exiſtente, complementum diſtantiæ Solis à meridie inuentum perpe-
              <lb/>
              <note position="left" xlink:label="note-0148-02" xlink:href="note-0148-02a" xml:space="preserve">Qua ratione tẽ
                <lb/>
              pore æquinoctii
                <lb/>
              hora ex altitu-
                <lb/>
              dine Solis ſu-
                <lb/>
              pra Horizontẽ
                <lb/>
              cognita depre-
                <lb/>
              hendatur.</note>
            tuo ex quadrante deducendum eſt, vt diſtantia Solis à meridie quoad gradus remaneat, vt ex figu-
              <lb/>
            ra quarta & </s>
            <s xml:id="echoid-s7926" xml:space="preserve">quinta conſtat. </s>
            <s xml:id="echoid-s7927" xml:space="preserve">Nam ſi ex quadrante K P, ſubtrahatur O P, complementum diſtantiæ
              <lb/>
              <note position="left" xlink:label="note-0148-03" xlink:href="note-0148-03a" xml:space="preserve">20</note>
            Solis à meridie, relinquetur K O, diſtantia Solis à meridie.</s>
            <s xml:id="echoid-s7928" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7929" xml:space="preserve">HANC autem diſtãtiam Solis à meridie ex altitudine Solis cognita facilius comperiemus,
              <lb/>
            Sole Æquatorem percurrente. </s>
            <s xml:id="echoid-s7930" xml:space="preserve">Vt enim ex ſexta figura liquet, eſt vt H N, ſinus complementi alti-
              <lb/>
              <note position="left" xlink:label="note-0148-04" xlink:href="note-0148-04a" xml:space="preserve">2. vel 4. ſexti</note>
            tudinis poli ad T N, ſinum altitudinis Solis tempore obſeruationis, ita H E, ſinus totus ad R E, ſi-
              <lb/>
            num complementi diſtantiæ Solis à meridie. </s>
            <s xml:id="echoid-s7931" xml:space="preserve">Quapropter ſi fiat, vt ſinus complementi altitudi-
              <lb/>
            nis poli ad ſinum altitudinis Solis tempore obſeruationis inuentæ, ita ſinus totus ad aliud,
              <lb/>
            inuenietur ſinus complementi diſtantiæ Solis à meridie, ac proinde & </s>
            <s xml:id="echoid-s7932" xml:space="preserve">ipſamet diſtantia latere
              <lb/>
            non poterit.</s>
            <s xml:id="echoid-s7933" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7934" xml:space="preserve">VNO exemplo rem explicemus. </s>
            <s xml:id="echoid-s7935" xml:space="preserve">Ponamus Sole exiſtente in principio ♊, vel ♌ nos ante meri-
              <lb/>
              <note position="left" xlink:label="note-0148-05" xlink:href="note-0148-05a" xml:space="preserve">Exemplum.</note>
            diem inueniſſe altitudinem Solis grad, 43. </s>
            <s xml:id="echoid-s7936" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s7937" xml:space="preserve">20. </s>
            <s xml:id="echoid-s7938" xml:space="preserve">ex quo exploranda ſit hora tempore illius ob-
              <lb/>
              <note position="left" xlink:label="note-0148-06" xlink:href="note-0148-06a" xml:space="preserve">30</note>
            ſeruationis. </s>
            <s xml:id="echoid-s7939" xml:space="preserve">Fiat vt 69743. </s>
            <s xml:id="echoid-s7940" xml:space="preserve">medietas rectæ cõpoſitæ ex ſinu altitudinis meridianæ, & </s>
            <s xml:id="echoid-s7941" xml:space="preserve">ſinu depreſ-
              <lb/>
            ſionis meridianæ, ad 45519 differentiam inter ſinum altitudinis Solis, & </s>
            <s xml:id="echoid-s7942" xml:space="preserve">inter differentiam præ-
              <lb/>
            dictæ medietatis, & </s>
            <s xml:id="echoid-s7943" xml:space="preserve">ſinus altitudinis meridianæ, ita 100000. </s>
            <s xml:id="echoid-s7944" xml:space="preserve">ſinus totus ad aliud. </s>
            <s xml:id="echoid-s7945" xml:space="preserve">Prodibit enim
              <lb/>
            ſinus ferè hic 65267. </s>
            <s xml:id="echoid-s7946" xml:space="preserve">complementi diſtantiæ Solis à meridie, cuius arcus grad. </s>
            <s xml:id="echoid-s7947" xml:space="preserve">40. </s>
            <s xml:id="echoid-s7948" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s7949" xml:space="preserve">45. </s>
            <s xml:id="echoid-s7950" xml:space="preserve">ſubtra
              <lb/>
            tractus ex quadrante, (quia Sol borealis eſt, & </s>
            <s xml:id="echoid-s7951" xml:space="preserve">ſinus altitudinis Solis, nempe 68624. </s>
            <s xml:id="echoid-s7952" xml:space="preserve">ſuperat diffe-
              <lb/>
            rentiã, quæ inter medietatem ſæpius dictam, & </s>
            <s xml:id="echoid-s7953" xml:space="preserve">ſinum altitudinis meridianæ reperitur, nimirum
              <lb/>
            23105.) </s>
            <s xml:id="echoid-s7954" xml:space="preserve">relinquet grad. </s>
            <s xml:id="echoid-s7955" xml:space="preserve">49. </s>
            <s xml:id="echoid-s7956" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s7957" xml:space="preserve">15. </s>
            <s xml:id="echoid-s7958" xml:space="preserve">pro diſtantia Solis à meridie, quæ complectitur horas 3.
              <lb/>
            </s>
            <s xml:id="echoid-s7959" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s7960" xml:space="preserve">17. </s>
            <s xml:id="echoid-s7961" xml:space="preserve">Cum igitur obſeruatio fiat ante meridiem, inſtabit tunc hora 8. </s>
            <s xml:id="echoid-s7962" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s7963" xml:space="preserve">43. </s>
            <s xml:id="echoid-s7964" xml:space="preserve">poſt mediam
              <lb/>
            noctem, more Aſtronomorum. </s>
            <s xml:id="echoid-s7965" xml:space="preserve">Et ſi poſt meridiem facta eſſet obſeruatio, inſtaret hora 3. </s>
            <s xml:id="echoid-s7966" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s7967" xml:space="preserve">17. </s>
            <s xml:id="echoid-s7968" xml:space="preserve">
              <lb/>
            à meridie. </s>
            <s xml:id="echoid-s7969" xml:space="preserve">At ſecundum Italos erit hora 13. </s>
            <s xml:id="echoid-s7970" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s7971" xml:space="preserve">26. </s>
            <s xml:id="echoid-s7972" xml:space="preserve">ab occaſu, quia illo die meridies fit hora 16. </s>
            <s xml:id="echoid-s7973" xml:space="preserve">
              <lb/>
              <note position="left" xlink:label="note-0148-07" xlink:href="note-0148-07a" xml:space="preserve">40</note>
            Min. </s>
            <s xml:id="echoid-s7974" xml:space="preserve">43. </s>
            <s xml:id="echoid-s7975" xml:space="preserve">à quo meridie ſi auferatur diſtantia Solis à meridie proximè inuenta, nempe hor. </s>
            <s xml:id="echoid-s7976" xml:space="preserve">3. </s>
            <s xml:id="echoid-s7977" xml:space="preserve">Min.
              <lb/>
            </s>
            <s xml:id="echoid-s7978" xml:space="preserve">17. </s>
            <s xml:id="echoid-s7979" xml:space="preserve">remanebunt horæ 13. </s>
            <s xml:id="echoid-s7980" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s7981" xml:space="preserve">26. </s>
            <s xml:id="echoid-s7982" xml:space="preserve">Si vero obſeruatio fieret poſt meridiem, addenda eſſet hęc di-
              <lb/>
            ſtantia, vt hora ab occaſu Solis nota euaderet. </s>
            <s xml:id="echoid-s7983" xml:space="preserve">Inueniretur autem hora 20. </s>
            <s xml:id="echoid-s7984" xml:space="preserve">ab occaſu. </s>
            <s xml:id="echoid-s7985" xml:space="preserve">Secundum
              <lb/>
            denique Babylonios erit hora 4. </s>
            <s xml:id="echoid-s7986" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s7987" xml:space="preserve">o. </s>
            <s xml:id="echoid-s7988" xml:space="preserve">ab ortu Solis. </s>
            <s xml:id="echoid-s7989" xml:space="preserve">Cum enim illo die meridies fiat ſecundum
              <lb/>
            has horas, hora 7. </s>
            <s xml:id="echoid-s7990" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s7991" xml:space="preserve">17. </s>
            <s xml:id="echoid-s7992" xml:space="preserve">ſi ex hoc meridiano tempore detrahatur diſtantia Solis à meridie in-
              <lb/>
            uenta, nempe hor. </s>
            <s xml:id="echoid-s7993" xml:space="preserve">3. </s>
            <s xml:id="echoid-s7994" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s7995" xml:space="preserve">17. </s>
            <s xml:id="echoid-s7996" xml:space="preserve">remanet hora 4. </s>
            <s xml:id="echoid-s7997" xml:space="preserve">Quòd ſi obſeruatio poſt meridiem fieret, addenda
              <lb/>
            eſſet hęc diſtantia, atq; </s>
            <s xml:id="echoid-s7998" xml:space="preserve">ita inueniretur hora 10. </s>
            <s xml:id="echoid-s7999" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s8000" xml:space="preserve">43. </s>
            <s xml:id="echoid-s8001" xml:space="preserve">ab ortu Solis. </s>
            <s xml:id="echoid-s8002" xml:space="preserve">Ex hoc exemplo cętera ſine
              <lb/>
            labore intelligentur.</s>
            <s xml:id="echoid-s8003" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8004" xml:space="preserve">IN Verticali ci@culo Sole exiſtente, ita quoque pręter artem hactenus traditam ex eius altitu-
              <lb/>
              <note position="left" xlink:label="note-0148-08" xlink:href="note-0148-08a" xml:space="preserve">Hora quanta
                <lb/>
              ſit, cum @ol in
                <lb/>
              Verticali circu
                <lb/>
              lo @xiſtit, qua
                <lb/>
              ratione explorã
                <lb/>
              dum.</note>
            dine horam offendemus. </s>
            <s xml:id="echoid-s8005" xml:space="preserve">Ducta in quarta figura ex puncto Z, vbi parallelus Solis Verticalẽ inter-
              <lb/>
              <note position="left" xlink:label="note-0148-09" xlink:href="note-0148-09a" xml:space="preserve">50</note>
            ſecat, ad V X, perpendiculari Z β, vſque ad circunferentiam paralleli Solis ex centro Y, deſcripti
              <lb/>
            circa diametrum V X, erit Z β, cõmunis ſectio paralleli Solis, & </s>
            <s xml:id="echoid-s8006" xml:space="preserve">paralleli Horizontis, cuius dia-
              <lb/>
            meter μ Z: </s>
            <s xml:id="echoid-s8007" xml:space="preserve">quod ita perſpicuũ fiet. </s>
            <s xml:id="echoid-s8008" xml:space="preserve">Quoniã vterq; </s>
            <s xml:id="echoid-s8009" xml:space="preserve">parallelus ad Meridianũ rectus eſt, erit & </s>
            <s xml:id="echoid-s8010" xml:space="preserve">eorũ
              <lb/>
              <note position="left" xlink:label="note-0148-10" xlink:href="note-0148-10a" xml:space="preserve">19. vndec.</note>
            cõmunis ſectio ad eandẽ recta, ac proinde per defin. </s>
            <s xml:id="echoid-s8011" xml:space="preserve">3. </s>
            <s xml:id="echoid-s8012" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s8013" xml:space="preserve">11. </s>
            <s xml:id="echoid-s8014" xml:space="preserve">Euclidis, ad V X, perpendicularis in
              <lb/>
            Z, puncto, vbi ſe mutuo ſecant dicti paralleli in Meridiano. </s>
            <s xml:id="echoid-s8015" xml:space="preserve">Igitur Z β, perpendicularis ad V X, in
              <lb/>
            Z, communis ſectio erit illorum parallelorum. </s>
            <s xml:id="echoid-s8016" xml:space="preserve">Ex quo ſequitur, cum Z, ſit centrum paralleli Ho
              <lb/>
            rizontis, cuius diameter μ Z, rectam Z β, ę
              <unsure/>
            qualem eſſe ſemidiametro μ Z, quan
              <unsure/>
            doquidem om-
              <lb/>
            nes lineæ ductæ ex Z, ad circunferentiam paralleli, cuius diameter μ Z, (qualis etiam eſt Z β,
              <lb/>
            communis eius ſectio cum parallelo Solis, vt oſtenſum eſt) ęquales ſunt ſemidiametro μ Z. </s>
            <s xml:id="echoid-s8017" xml:space="preserve">Quo-
              <lb/>
            niam verò μ Z, ſinus eſt complementi altitudinis Solis in Verticali circulo exiſtentis, nempe ſi-
              <lb/>
            nus arcus B μ, erit vt V Y, ſinus complementi declinationis paralleli V X, (quatenus </s>
          </p>
        </div>
      </text>
    </echo>
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