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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[151.] PROBLEMA 5. PROPOSITIO 5.
Page: 191 (171)
[152.] SCHOLIVM.
Page: 192 (172)
[153.] PROBLEMA 6. PROPOSITIO 6.
Page: 192 (172)
[154.] SCHOLIVM.
Page: 193 (173)
[155.] PROBLEMA 7. PROPOSITIO 7.
Page: 194 (174)
[156.] SCHOLIVM.
Page: 194 (174)
[157.] PROBLEMA 8. PROPOSITIO 8.
Page: 195 (175)
[158.] COROLLARIVM.
Page: 197 (177)
[159.] SCHOLIVM.
Page: 197 (177)
[160.] PROBLEMA. 9. PROPOSITIO 9.
Page: 197 (177)
[161.] I. Sole exiſtente in principio ♈.
Page: 198 (178)
[162.] II. Sole exiſtente in principio ♎.
Page: 198 (178)
[163.] III. Sole exiſtente in principio ♋.
Page: 198 (178)
[164.] IIII. Sole exiſtente in principio ♑.
Page: 198 (178)
[165.] Arcus ſemidiurni in initijs ſignorum, ad latitudinem grad. 42.
Page: 200 (180)
[166.] VI. Mediationes cœli, & anguli terræ, eorumq́; declinationes, orientibus 12. ſignorum Zodiaci initiis, ad latitudinem grad. 42.
Page: 201 (181)
[167.] VII. Puncta Eclipticæ in circulo horę 6. conſtituta, eorumq́ue declinationes, orientibus 12. ſignorum Zodiaci principijs, ad latitudinem grad. 42.
Page: 202 (182)
[168.] VIII. Puncta Eclipticæ in circulo horę 11. exiſtentia, eorumq́; declinationes, cum principia 12. ſignorum Zodiaci oriuntur, ad latitudinem grad. 42.
Page: 204 (184)
[169.] SCHOLIVM.
Page: 206 (186)
[170.] SEQVVNTVR TABELLÆ.
Page: 207 (187)
[171.] PROBLEMA. 10. PROPOSITIO 10.
Page: 212 (192)
[172.] SCHOLIVM.
Page: 218 (198)
[173.] PROBLEMA. 11. PROPOSITIO 11.
Page: 219 (199)
[174.] SCHOLIVM.
Page: 220 (200)
[175.] PROBLEMA 12. PROPOSITIO 12.
Page: 221 (201)
[176.] SCHOLIVM.
Page: 223 (203)
[177.] DE HOROLOGIIS VERTICALIBVS. PROBLEMA 13. PROPOSITIO 13.
Page: 224 (204)
[178.] SCHOLIVM.
Page: 227 (207)
[179.] PROBLEMA 14. PROPOSITIO 14.
Page: 231 (211)
[180.] SCHOLIVM.
Page: 237 (217)
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              <pb o="140" file="0160" n="160" rhead="GNOMONICES"/>
            M R, ſinum complementi diſtantię Solis à meridie K, ita K λ, medietas ſinus altitudinis meridianæ ad
              <lb/>
            λT, differentiam inter T N, ſinum altitudinis Solis, & </s>
            <s xml:id="echoid-s9047" xml:space="preserve">rectam λ N, medietatem ſinus altitudinis me-
              <lb/>
            ridianæ: </s>
            <s xml:id="echoid-s9048" xml:space="preserve">Sifiat vt ſinus totus adſinum complementi diſtantię Solis à meridie, ita medietas ſinus altitu-
              <lb/>
              <figure xlink:label="fig-0160-01" xlink:href="fig-0160-01a" number="117">
                <image file="0160-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0160-01"/>
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            dinis meridianæ ad aliud, inuenietur
              <lb/>
            recta, quæ addita medietati prędi-
              <lb/>
            ctę, ſi diſtantia à meridie minor eſt
              <lb/>
            quadrante, vel ab eadem medietate
              <lb/>
            ablata, ſi maior eſt diſtantia à meri
              <lb/>
            die quadrante, dabit ſinum altitudi-
              <lb/>
            nis Solis tempore obſeruationis. </s>
            <s xml:id="echoid-s9049" xml:space="preserve">Si
              <lb/>
              <note position="left" xlink:label="note-0160-01" xlink:href="note-0160-01a" xml:space="preserve">10</note>
            autem distantia Solis à meridie qua-
              <lb/>
            dranti fuerit ęqualis, erit ipſamet
              <lb/>
            medietas λ N, ſinus altitudinis So
              <lb/>
            lis tempore obſeruationis. </s>
            <s xml:id="echoid-s9050" xml:space="preserve">Rurſus
              <lb/>
              <note position="left" xlink:label="note-0160-02" xlink:href="note-0160-02a" xml:space="preserve">2. vel 4. ſexti</note>
            quoniam in ſecunda figura, vbi pa-
              <lb/>
            rallelus totus ſupra Horizontem ex-
              <lb/>
            tat, & </s>
            <s xml:id="echoid-s9051" xml:space="preserve">illum non tangit, eſt vt K M,
              <lb/>
            ſinus totus ad M R, ſinum complemẽ
              <lb/>
            ti diſtantiæ Solis à meridie K, ita K λ, medietas differentiæ K θ, inter ſinum maioris altitudinis meridia
              <lb/>
            næ, & </s>
            <s xml:id="echoid-s9052" xml:space="preserve">ſinum minoris altitudinis meridianæ ad λ T, differentiam inter T N, ſinum altitudinis Solis, & </s>
            <s xml:id="echoid-s9053" xml:space="preserve">
              <lb/>
              <note position="left" xlink:label="note-0160-03" xlink:href="note-0160-03a" xml:space="preserve">20</note>
            rectam λ N, compoſitam ex dictamedietate λ θ, ac ſinu θ N, minoris altitudinis meridianæ: </s>
            <s xml:id="echoid-s9054" xml:space="preserve">Si fiat,
              <lb/>
            vt ſinus totus ad ſinum complementi diſtantiæ Solis à meridie, ita medietas differentiæ inter ſinum maio-
              <lb/>
            ris altitudinis meridianę, & </s>
            <s xml:id="echoid-s9055" xml:space="preserve">ſinum minoris altitudinis meridianæ ad aliud, reperietur recta, quæ ablata
              <lb/>
            ex recta compoſita ex dicta medietate, ac ſinu minoris altitudinis meridianæ, ſi diſtantia Solis à meridie
              <lb/>
            fuerit quadrante maior, vel eidem rectæ compoſitæ addita, ſi diſtantia quadrante fuerit minor, dabit ſinũ
              <lb/>
            altitudinis Solis tempore obſeruationis, Si autem diſtantia quadranti æ qualis extiterit, erit ipſamet re-
              <lb/>
            cta compoſita ex dicta medietate, & </s>
            <s xml:id="echoid-s9056" xml:space="preserve">ſinu altitudinis meridianæ minoris, ſinus altitudinis Solis tempore
              <lb/>
            obſeruationis. </s>
            <s xml:id="echoid-s9057" xml:space="preserve">Quę omnia ex hiſce duabus appoſitis figuris facile colligi poſſunt.</s>
            <s xml:id="echoid-s9058" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s9059" xml:space="preserve">VICISSIM, ſi fiat, vt K λ, medietas ſinus altitudinis meridianæ in priori figura, vel medietas
              <lb/>
            rectæ K θ, in poſteriori, quæ differentia eſt inter ſinum maioris altitudinis meridianæ, & </s>
            <s xml:id="echoid-s9060" xml:space="preserve">ſinum minoris al-
              <lb/>
              <note position="left" xlink:label="note-0160-04" xlink:href="note-0160-04a" xml:space="preserve">30</note>
            titudinis meridianæ, ad λ T, differentiam inter ſinum altitudinis Solis, & </s>
            <s xml:id="echoid-s9061" xml:space="preserve">medietatem ſinus altitudinis
              <lb/>
            meridianæ in priori figura, vel inter ſinum altitudinis Solis, & </s>
            <s xml:id="echoid-s9062" xml:space="preserve">rectam λ N, quę componitur ex medieta-
              <lb/>
            te differentiæ inter ſinum maioris altitudinis meridianæ, & </s>
            <s xml:id="echoid-s9063" xml:space="preserve">ſinum minoris altitudinis meridianæ, atque
              <lb/>
            ſinu minoris altitudinis meridianæ, vt in poſteriori figura apparet, ita ſinus totus ad aliud, reperietur ſi-
              <lb/>
            nus complementi diſtantiæ Solis à meridie K. </s>
            <s xml:id="echoid-s9064" xml:space="preserve">Quod complementum additum quadranti, quando ſinus al-
              <lb/>
            titudinis Solis minor eſt, quàm recta λ N, hoc eſt, quàm medietas ſinus altitudinis meridianæ in priori
              <lb/>
            figura, vel quàm recta compoſita ex ſinus minoris altitudinis meridianæ, & </s>
            <s xml:id="echoid-s9065" xml:space="preserve">medietate differentiæ inter ſi-
              <lb/>
            num maioris altitudinis meridianæ, & </s>
            <s xml:id="echoid-s9066" xml:space="preserve">ſinum minoris altitudinis meridianæ in figur a poſteriori, dabit di-
              <lb/>
            stantiam Solis à meridie, vt in poſteriori figura apparet. </s>
            <s xml:id="echoid-s9067" xml:space="preserve">Idem vero complementum à quadrante ſublatũ,
              <lb/>
            quando ſinus altitudinis Solis maior eſt, quàm dicta recta λ N, relinquet diſtantiam Solis à meridie.
              <lb/>
            </s>
          </p>
          <p style="it">
            <s xml:id="echoid-s9068" xml:space="preserve">SED facilius hęc res conficietur illo modo, quem vltimo loco tractauimus, antequàm problema hoc
              <lb/>
            propoſitum per triangula ſphærica explicaremus. </s>
            <s xml:id="echoid-s9069" xml:space="preserve">Nam ſi fiat, vt K M, ſinus totus ad K R, ſinum verſum
              <lb/>
            diſtantiæ Solis à meridie K, ita K λ, medietas ſinus altitudinis meridianæ in priori figura, vel in poſterio-
              <lb/>
            ri ita medietas differentiæ inter ſinum maioris altitudinis meridianę, & </s>
            <s xml:id="echoid-s9070" xml:space="preserve">ſinum minoris altitudinis meri-
              <lb/>
            dianę, ad aliud, nota euadet K T, differentia inter ſinum maioris altitudinis meridianæ, vel certe in prio-
              <lb/>
            ri figura ipſius altitudinis meridianę, & </s>
            <s xml:id="echoid-s9071" xml:space="preserve">ſinum altitudinis Solis quæſitę.</s>
            <s xml:id="echoid-s9072" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s9073" xml:space="preserve">ITEM ſi fiat, vt medietas præ dicta ad differentiam inter ſinum maioris altitudinis meridianæ, vel
              <lb/>
            certe in priori figura ipſius altitudinis meridianę, & </s>
            <s xml:id="echoid-s9074" xml:space="preserve">ſinum altitudinis Solis, ita ſinus totus ad aliud, pro-
              <lb/>
            ueniet ſinus verſus distantiæ Solis à meridie K. </s>
            <s xml:id="echoid-s9075" xml:space="preserve">Vt ex ijſdem figuris manifeſtum eſt.</s>
            <s xml:id="echoid-s9076" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s9077" xml:space="preserve">QVOD ſi polus mundi in vertice, ſeu polo Horizontis extiterit, erit in quolibet die Solis alti-
              <lb/>
              <note position="left" xlink:label="note-0160-06" xlink:href="note-0160-06a" xml:space="preserve">50</note>
            tudo perpetuo æqualis declinationi paralleli, quem tunc Sol deſcribit motu primi mo-
              <lb/>
            bilis: </s>
            <s xml:id="echoid-s9078" xml:space="preserve">Quia tunc Aequator idem est, qui Horizon, & </s>
            <s xml:id="echoid-s9079" xml:space="preserve">paralleli Hori-
              <lb/>
            zontis à parallelis Solis, vel Aequatoris non diffc-
              <lb/>
            runt, vt perſpicuum eſt.</s>
            <s xml:id="echoid-s9080" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div501" type="section" level="1" n="140">
          <head xml:id="echoid-head143" style="it" xml:space="preserve">FINIS PRIMI LIBRI.</head>
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