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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[121.] COROLLARIVM.
Page: 112 (92)
[122.] PROBLEMA 6. PROPOSITIO 27.
Page: 113 (93)
[123.] PROBLEMA. 7. PROPOSITIO 28.
Page: 113 (93)
[124.] SCHOLIVM I.
Page: 115 (95)
[125.] COROLLARIVM.
Page: 115 (95)
[126.] SCHOLIVM II.
Page: 116 (96)
[127.] PROBLEMA 8. PROPOSITIO 29.
Page: 119 (99)
[128.] PROBLEMA. 9. PROPOSITIO 30.
Page: 121 (101)
[129.] PROBLEMA 10. PROPOSITIO 31.
Page: 123 (103)
[130.] PROBLEMA 11. PROPOSITIO 32.
Page: 125 (105)
[131.] SCHOLIVM.
Page: 125 (105)
[132.] PROBLEMA 12. PROPOSITIO 33.
Page: 126 (106)
[133.] SCHOLIVM.
Page: 129 (109)
[134.] PROBLEMA 13. PROPOSITIO 34.
Page: 134 (114)
[135.] SCHOLIVM.
Page: 137 (117)
[136.] PROBLEMA 14. PROPOSITIO 35.
Page: 138 (118)
[137.] SCHOLIVM.
Page: 140 (120)
[138.] PROBLEMA 15. PROPOSITIO 36.
Page: 144 (124)
[139.] SCHOLIVM.
Page: 158 (138)
[140.] FINIS PRIMI LIBRI.
Page: 160 (140)
[141.] GNOMONICES LIBER SECVNDVS.
Page: 161 (141)
[142.] AVCTORE CHRISTOPHORO CLAVIO BAMBER GENSI SOCIETATIS IESV.
Page: 161 (141)
[143.] DE HOROLOGIIS HORIZONTALIBVS. PROBLEMA 1. PROPOSITIO 1.
Page: 162 (142)
[144.] SCHOLIVM.
Page: 165 (145)
[145.] PROBLEMA 2. PROPOSITIO 2.
Page: 177 (157)
[146.] SCHOLIVM.
Page: 186 (166)
[147.] PROBLEMA 3. PROPOSITIO 3.
Page: 189 (169)
[148.] SCHOLIVM.
Page: 190 (170)
[149.] PROBLEMA. 4. PROPOSITIO 4.
Page: 190 (170)
[150.] SCHOLIVM.
Page: 191 (171)
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          <p>
            <s xml:id="echoid-s7692" xml:space="preserve">QVONIAM igitur eſt, vt k M, ſinus totus ad MR, ſinũ cõplementi diſtã
              <unsure/>
            tiæ Soli
              <unsure/>
            s à meridie,
              <lb/>
              <note position="left" xlink:label="note-0146-01" xlink:href="note-0146-01a" xml:space="preserve">Altitudo Solis
                <lb/>
              ſupra Horizon-
                <lb/>
              tem quomodo
                <lb/>
              ex hora cognita
                <lb/>
              ſupputetur.</note>
            ita K λ, medieras rectæ cõpoſitæ ex ſinu altitudinis meridianæ, & </s>
            <s xml:id="echoid-s7693" xml:space="preserve">ſinu meridianæ depreſſionis, ad
              <lb/>
            rectã λ T: </s>
            <s xml:id="echoid-s7694" xml:space="preserve">Si fiat, vt ſinus totus ad ſinum cõplementi diſtãtiæ Solis à meridie, ita k λ, medietas re-
              <lb/>
              <figure xlink:label="fig-0146-01" xlink:href="fig-0146-01a" number="107">
                <image file="0146-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0146-01"/>
              </figure>
              <note position="left" xlink:label="note-0146-02" xlink:href="note-0146-02a" xml:space="preserve">10</note>
              <figure xlink:label="fig-0146-02" xlink:href="fig-0146-02a" number="108">
                <image file="0146-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0146-02"/>
              </figure>
              <note position="left" xlink:label="note-0146-03" xlink:href="note-0146-03a" xml:space="preserve">20</note>
              <note position="left" xlink:label="note-0146-04" xlink:href="note-0146-04a" xml:space="preserve">30</note>
            ctæ compoſitæ ex ſinu altitudinis meridianæ, & </s>
            <s xml:id="echoid-s7695" xml:space="preserve">ſinu depreſſionis meridianæ, ad aliud, inuenietur
              <lb/>
            recta λ T, differentia nimirum inter T N, ſinum altitudinis Solis tempore obſeruationis, & </s>
            <s xml:id="echoid-s7696" xml:space="preserve">re-
              <lb/>
            ctam λ N, quæ differentia eſt inter prædictam medietatem K λ, & </s>
            <s xml:id="echoid-s7697" xml:space="preserve">K N, ſinum altitudinis meri-
              <lb/>
            dianæ. </s>
            <s xml:id="echoid-s7698" xml:space="preserve">Ex hac autem recta λ T, reperiemus ſinum altitudinis Solis T N, atque adeo & </s>
            <s xml:id="echoid-s7699" xml:space="preserve">altitudinẽ
              <lb/>
              <note position="left" xlink:label="note-0146-05" xlink:href="note-0146-05a" xml:space="preserve">Quando diſtan
                <lb/>
              tia Solis à meri
                <lb/>
              die in parallelo
                <lb/>
              boreali minor
                <lb/>
              eſt quadrante.</note>
            ipſam Solis, hoc modo. </s>
            <s xml:id="echoid-s7700" xml:space="preserve">In parallelis borealibus, quando diſtantia Solis à meridie minor eſt qua-
              <lb/>
            drante, ſeu ſex horis, addatur recta inuenta λ T, ad λ N, differentiam inter medietatem prædi-
              <lb/>
            ctam, & </s>
            <s xml:id="echoid-s7701" xml:space="preserve">ſinum altitudinis meridianæ. </s>
            <s xml:id="echoid-s7702" xml:space="preserve">Componetur enim hac ratione ſinus altitudinis Solis T N,
              <lb/>
            vt in prima figura, & </s>
            <s xml:id="echoid-s7703" xml:space="preserve">tertia apparet.</s>
            <s xml:id="echoid-s7704" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">Quando diſtan
            <lb/>
          tia Solis à meri
            <lb/>
          die in parallelo
            <lb/>
          boreali quadrãs
            <lb/>
          eſt.</note>
          <p>
            <s xml:id="echoid-s7705" xml:space="preserve">QVOD ſi diſtantia Solis à meridie contineat quadrantem, ſiue 6 horas, erit differentia inter-
              <lb/>
              <note position="left" xlink:label="note-0146-07" xlink:href="note-0146-07a" xml:space="preserve">40</note>
            dictam merietatem, & </s>
            <s xml:id="echoid-s7706" xml:space="preserve">ſinum altitudinis meridianæ, nempe recta λ N, ſinus altitudinis Solis, vt
              <lb/>
            ex eiſdem figuris patet: </s>
            <s xml:id="echoid-s7707" xml:space="preserve">quia tunc Sol in puncto P, ſui paralleli exiſtet, atq; </s>
            <s xml:id="echoid-s7708" xml:space="preserve">adeo recta λ M, erit
              <lb/>
            portio diametri paralleli Horizontis, &</s>
            <s xml:id="echoid-s7709" xml:space="preserve">c. </s>
            <s xml:id="echoid-s7710" xml:space="preserve">Vnde ſi medietas prædicta auferatur ex ſinu altitudinis
              <lb/>
            meridianæ, relinquetur ſinus altitudinis Solis.</s>
            <s xml:id="echoid-s7711" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7712" xml:space="preserve">ALITER quoq; </s>
            <s xml:id="echoid-s7713" xml:space="preserve">inueniemus altitudinem Solis, cum ſex horis à meridie abeſt. </s>
            <s xml:id="echoid-s7714" xml:space="preserve">Ductis enim
              <lb/>
            in prima ſigura ex M, F, ad A C, duabus perpendicularibus M α, F β; </s>
            <s xml:id="echoid-s7715" xml:space="preserve">quoniã eſt, vt E F, ſinus to-
              <lb/>
            tus ad F β, ſinum altitudinis poli, ita E M, ſinus declinationis ad M α, ſinum altitudinis Solis:
              <lb/>
            </s>
            <s xml:id="echoid-s7716" xml:space="preserve">
              <note position="left" xlink:label="note-0146-08" xlink:href="note-0146-08a" xml:space="preserve">4. ſexti.</note>
              <note position="left" xlink:label="note-0146-09" xlink:href="note-0146-09a" xml:space="preserve">34. primi.</note>
            (Eſt namq; </s>
            <s xml:id="echoid-s7717" xml:space="preserve">M α, æqualis ſinui altitudinis Solis λ N.) </s>
            <s xml:id="echoid-s7718" xml:space="preserve">Si fiat, vt ſinus totus ad ſinum altitudinis
              <lb/>
            poli, ita ſinus declinationis ad aliud, inuenietur ſinus altitudinis Solis.</s>
            <s xml:id="echoid-s7719" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7720" xml:space="preserve">SI autẽ diſtantia Solis à meridie quadrantẽ vel 6. </s>
            <s xml:id="echoid-s7721" xml:space="preserve">horas ſuperet, vt in ſecunda figura cernitur,
              <lb/>
              <note position="left" xlink:label="note-0146-10" xlink:href="note-0146-10a" xml:space="preserve">Quando diſtan
                <lb/>
              tia Solis à meri
                <lb/>
              die in parallelo
                <lb/>
              boreali maior
                <lb/>
              eſt quadrante.</note>
              <note position="left" xlink:label="note-0146-11" xlink:href="note-0146-11a" xml:space="preserve">50</note>
            auferenda eſt recta inuenta λ T, ex λ N, differentia inter dictam medietatem, & </s>
            <s xml:id="echoid-s7722" xml:space="preserve">ſinum altitudi-
              <lb/>
            nis meridianæ, vt habeatur T N, ſinus altitudinis Solis.</s>
            <s xml:id="echoid-s7723" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7724" xml:space="preserve">IN ſignis deniq; </s>
            <s xml:id="echoid-s7725" xml:space="preserve">auſtralibus ſemper auferenda eſt differentia inter medietatem dictam, & </s>
            <s xml:id="echoid-s7726" xml:space="preserve">ſi-
              <lb/>
              <note position="left" xlink:label="note-0146-12" xlink:href="note-0146-12a" xml:space="preserve">Qua
                <unsure/>
              ndo Solin
                <lb/>
              parallelo auſtra
                <lb/>
              li exiſtit.</note>
            num altitudinis meridianæ, hoc eſt, recta λ N, ex recta λ T, inuenta, vt relinquatur T N, ſinus
              <lb/>
            altitudinis Solis, vt perſpicuum eſt ex figura quarta, & </s>
            <s xml:id="echoid-s7727" xml:space="preserve">quinta.</s>
            <s xml:id="echoid-s7728" xml:space="preserve">
              <unsure/>
            </s>
          </p>
          <p>
            <s xml:id="echoid-s7729" xml:space="preserve">CÆTERVM Sole exiſtente in æquinoctijs, multo breuius altitudinem Solis conſequemur
              <lb/>
              <note position="left" xlink:label="note-0146-13" xlink:href="note-0146-13a" xml:space="preserve">Altitudo Solis
                <lb/>
              ſupra Horizon
                <lb/>
              tem quomodo
                <lb/>
              in æquinoctiis
                <lb/>
              ex data hora nu
                <lb/>
              meranda ſit.</note>
            ex data hora. </s>
            <s xml:id="echoid-s7730" xml:space="preserve">Quoniam enim in ſexta figura eſt, vt H E, ſinus totus ad R E, ſinum cõplementi di-
              <lb/>
            ſtantiæ Solis à meridie, ita H N, ſinus complementi altitudinis poli ad T N, ſinum altitudinis So-
              <lb/>
            lis: </s>
            <s xml:id="echoid-s7731" xml:space="preserve">Si fiat vt ſinus totus ad ſinum complementi diſtantiæ Solis à meridie, ita ſinus complementi
              <lb/>
            altitudinis poliad aliud, habebitur ſinus altitudinis Solis tempore obſeruationis.</s>
            <s xml:id="echoid-s7732" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">2. vel 4. ſexti</note>
          <p>
            <s xml:id="echoid-s7733" xml:space="preserve">SIMILITER altitudinem Solis in Verticali circulo proprie dicto exiſtentis, ſine magno </s>
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