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.
[152.] SCHOLIVM.
[153.] PROBLEMA 6. PROPOSITIO 6.
[154.] SCHOLIVM.
[155.] PROBLEMA 7. PROPOSITIO 7.
[156.] SCHOLIVM.
[157.] PROBLEMA 8. PROPOSITIO 8.
[158.] COROLLARIVM.
[159.] SCHOLIVM.
[160.] PROBLEMA. 9. PROPOSITIO 9.
[161.] I. Sole exiſtente in principio ♈.
[162.] II. Sole exiſtente in principio ♎.
[163.] III. Sole exiſtente in principio ♋.
[164.] IIII. Sole exiſtente in principio ♑.
[165.] Arcus ſemidiurni in initijs ſignorum, ad latitudinem grad. 42.
[166.] VI. Mediationes cœli, & anguli terræ, eorumq́; declinationes, orientibus 12. ſignorum Zodiaci initiis, ad latitudinem grad. 42.
[167.] VII. Puncta Eclipticæ in circulo horę 6. conſtituta, eorumq́ue declinationes, orientibus 12. ſignorum Zodiaci principijs, ad latitudinem grad. 42.
[168.] VIII. Puncta Eclipticæ in circulo horę 11. exiſtentia, eorumq́; declinationes, cum principia 12. ſignorum Zodiaci oriuntur, ad latitudinem grad. 42.
[169.] SCHOLIVM.
[170.] SEQVVNTVR TABELLÆ.
[171.] PROBLEMA. 10. PROPOSITIO 10.
[172.] SCHOLIVM.
[173.] PROBLEMA. 11. PROPOSITIO 11.
[174.] SCHOLIVM.
[175.] PROBLEMA 12. PROPOSITIO 12.
[176.] SCHOLIVM.
[177.] DE HOROLOGIIS VERTICALIBVS. PROBLEMA 13. PROPOSITIO 13.
[178.] SCHOLIVM.
[179.] PROBLEMA 14. PROPOSITIO 14.
[180.] SCHOLIVM.
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          <p>
            <s xml:id="echoid-s11610" xml:space="preserve">
              <pb o="178" file="0198" n="198" rhead="GNOMONICES"/>
            mus ex doctrina ſinuum) grad. </s>
            <s xml:id="echoid-s11611" xml:space="preserve">66, min, 57. </s>
            <s xml:id="echoid-s11612" xml:space="preserve">quæ ad horas reducta continet horas 4. </s>
            <s xml:id="echoid-s11613" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s11614" xml:space="preserve">28. </s>
            <s xml:id="echoid-s11615" xml:space="preserve">Hæ
              <lb/>
            autem ſubtractæ ex horis 6. </s>
            <s xml:id="echoid-s11616" xml:space="preserve">hoc eſt, ex arcu ſemidiurno, relinquunt hor. </s>
            <s xml:id="echoid-s11617" xml:space="preserve">1. </s>
            <s xml:id="echoid-s11618" xml:space="preserve">min. </s>
            <s xml:id="echoid-s11619" xml:space="preserve">32. </s>
            <s xml:id="echoid-s11620" xml:space="preserve">ante meridiẽ.
              <lb/>
            </s>
            <s xml:id="echoid-s11621" xml:space="preserve">Hac ergo hora principium ♋, aſcendit ſupra Horizontem, Sole in principio ♈, exiſtente; </s>
            <s xml:id="echoid-s11622" xml:space="preserve">quæ
              <lb/>
            quidem reſpondet horis 10. </s>
            <s xml:id="echoid-s11623" xml:space="preserve">min. </s>
            <s xml:id="echoid-s11624" xml:space="preserve">28. </s>
            <s xml:id="echoid-s11625" xml:space="preserve">poſt mediam noctem. </s>
            <s xml:id="echoid-s11626" xml:space="preserve">Rurſus Sole poſſidente principium
              <lb/>
            ♋, arcus ſemidiurnus ad eleuationem grad. </s>
            <s xml:id="echoid-s11627" xml:space="preserve">42. </s>
            <s xml:id="echoid-s11628" xml:space="preserve">complectitur horas 7. </s>
            <s xml:id="echoid-s11629" xml:space="preserve">min. </s>
            <s xml:id="echoid-s11630" xml:space="preserve">32. </s>
            <s xml:id="echoid-s11631" xml:space="preserve">quæriturq́;</s>
            <s xml:id="echoid-s11632" xml:space="preserve">, qua
              <lb/>
            hora principium ♐, ſupra Horizontem aſcendat. </s>
            <s xml:id="echoid-s11633" xml:space="preserve">Aſcenſio obliqua arcus inter principium ♋,
              <lb/>
            & </s>
            <s xml:id="echoid-s11634" xml:space="preserve">primum gradum ♐, interiecti continet grad. </s>
            <s xml:id="echoid-s11635" xml:space="preserve">190. </s>
            <s xml:id="echoid-s11636" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s11637" xml:space="preserve">12. </s>
            <s xml:id="echoid-s11638" xml:space="preserve">quæ in horas conuerſa facit horas
              <lb/>
            12, min. </s>
            <s xml:id="echoid-s11639" xml:space="preserve">41. </s>
            <s xml:id="echoid-s11640" xml:space="preserve">a quibus ſi auferatur arcus ſemidiurnus horarum 7. </s>
            <s xml:id="echoid-s11641" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s11642" xml:space="preserve">32. </s>
            <s xml:id="echoid-s11643" xml:space="preserve">relinquitur hora quinta
              <lb/>
            min. </s>
            <s xml:id="echoid-s11644" xml:space="preserve">9. </s>
            <s xml:id="echoid-s11645" xml:space="preserve">poſt meridiem, qua ſcilicet initium ♐, ſupra Horizontem tunc emergit. </s>
            <s xml:id="echoid-s11646" xml:space="preserve">Et ſic de cæt
              <unsure/>
            eris. </s>
            <s xml:id="echoid-s11647" xml:space="preserve">
              <lb/>
            Hac ratione ſequentes quatuor tabellas compoſuimus, in quibus horæ continentur, quibus ſigno-
              <lb/>
              <note position="left" xlink:label="note-0198-01" xlink:href="note-0198-01a" xml:space="preserve">10</note>
            rum initia oriuntur in Horizonte Romano grad. </s>
            <s xml:id="echoid-s11648" xml:space="preserve">42.</s>
            <s xml:id="echoid-s11649" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div629" type="section" level="1" n="161">
          <head xml:id="echoid-head164" xml:space="preserve">I. Sole exiſtente in principio ♈.</head>
          <note position="right" xml:space="preserve">
            <lb/>
          ♈ # ♉ # ♊ # ♋ # ♌ # ♍ # ♎ # ♏ # ♐ # ♑ # ♒ # ♓ Ante \\ mer. # Ante \\ mer. # Ante \\ mer. # Ante \\ mer. # Poſt \\ mer. # Poſt \\ mer. # Poſt \\ mer. # Poſt \\ mer. # Poſt \\ mer. # Ante \\ mer. # Ante \\ mer. # Ante \\ mer. H. M # H. M. # H. M. # H. M # H. M # H. M. # H. M. # H. M. # H. M. # H. M. # H. M # H. M. 6. 0 # 4. 51. # 5. 26. # 1. 32. # 0. 51. # 3. 26. # 6. 0. # 8. 34. # 11. 9. # 10. 28. # 8. 34. # 7. 9.</note>
          <note position="left" xml:space="preserve">20</note>
        </div>
        <div xml:id="echoid-div630" type="section" level="1" n="162">
          <head xml:id="echoid-head165" xml:space="preserve">II. Sole exiſtente in principio ♎.</head>
          <note position="right" xml:space="preserve">
            <lb/>
          ♎ # ♏ # ♐ # ♑ # ♒ # ♓ # ♈ # ♉ # ♊ # ♋ # ♌ # ♍ Ante \\ mer. # Ante \\ mer. # Ante \\ mer. # Poſt \\ mer. # Poſt \\ mer. # Poſt \\ mer. # Poſt \\ mer. # Poſt \\ mer. # Poſt \\ mer. # Poſt \\ mer. # Ante \\ mer. # Ante \\ mer. H. M. # H. M. # H. M. # H. M. # H. M. # H. M. # H. M. # H. M. # H. M. # H. M. # H. M. # H. M. 6. 0. # 3. 6. # 0. 51. # 1. 32. # 3. 26. # 4. 51. # 6. 0. # 7. 9. # 8. 34. # 10. 8. # 11. 9. # 8. 14.</note>
        </div>
        <div xml:id="echoid-div631" type="section" level="1" n="163">
          <head xml:id="echoid-head166" xml:space="preserve">III. Sole exiſtente in principio ♋.</head>
          <note position="right" xml:space="preserve">
            <lb/>
          ♋ # ♌ # ♍ # ♎ # ♉ # ♐ # ♑ # ♒ # ♓ # ♈ # ♉ # ♊ Ante \\ mer. # Ante \\ mer. # Ante \\ mer. # Añ vel \\ poſt m. # Poſt \\ mer. # Poſt \\ mer. # Poſt \\ mer. # Poſt \\ mer. # Poſt \\ mer. # Poſt vel \\ añ mer. # Ante \\ mer. # Ante \\ mer. H. M. # H. M. # H. M. # H. M. # H. M. # H. M. # H. M. # H. M. # H. M. # H. M. # H. M. # H. M. 7. 32. # 5. 9. # 2. 34. # 0. 0. # 2. 34. # 5. 9. # 7. 32. # 9. 26. # 10. 51. # 12. 0. # 10. 50. # 8. 26.</note>
        </div>
        <div xml:id="echoid-div632" type="section" level="1" n="164">
          <head xml:id="echoid-head167" xml:space="preserve">IIII. Sole exiſtente in principio ♑.</head>
          <note position="right" xml:space="preserve">
            <lb/>
          ♑ # ♒ # ♓ # ♈ # ♉ # ♊ # ♋ # ♌ # ♍ # ♎ # ♏ # ♐ Ante \\ mer. # Ante \\ mer. # Ante \\ mer. # Añ vel \\ poſt m. # Poſt \\ mer. # Poſt \\ mer. # Poſt \\ mer. # Poſt \\ mer. # Poſt \\ mer. # Poſt vel \\ añ mer. # Ante \\ mer. # Ante \\ mer. H. M. # H. M. # H. M. # H. M. # H. M # H. M. # H. M. # H. M. # H. M. # H. M. # H. M # H. M. 4. 28. # 2. 34. # 1. 10. # 0. 0. # 1. 10. # 2. 34. # 4. 28. # 6. 51. # 9. 26. # 12. 0. # 9. 26. # 6. 51.</note>
          <p>
            <s xml:id="echoid-s11650" xml:space="preserve">EX his tabulis ita aſcendentia ſigna deſcribemus, hoc eſt, communes ſectiones plani horolo-
              <lb/>
              <note position="left" xlink:label="note-0198-09" xlink:href="note-0198-09a" xml:space="preserve">Deſc
                <unsure/>
              riptio ſi-
                <lb/>
              gnorum aſcen-
                <lb/>
              dentium in eo-
                <lb/>
              dem horologio
                <lb/>
              horizontali.</note>
            gij, & </s>
            <s xml:id="echoid-s11651" xml:space="preserve">Eclipticæ eo tempore, quo initia ſignorum ſupra Horizontem aſcendunt. </s>
            <s xml:id="echoid-s11652" xml:space="preserve">In has enim
              <lb/>
            communes ſectiones, quas planum horologii facit cum Ecliptica, prout varias poſitiones ſortitur
              <lb/>
            ad motum diurnum, cadit vmbra gnomonis, per propoſ. </s>
            <s xml:id="echoid-s11653" xml:space="preserve">11. </s>
            <s xml:id="echoid-s11654" xml:space="preserve">præcedentis lib. </s>
            <s xml:id="echoid-s11655" xml:space="preserve">Sole exiſtẽte in quo-
              <lb/>
              <note position="left" xlink:label="note-0198-10" xlink:href="note-0198-10a" xml:space="preserve">50</note>
            cunque puncto Eclipticæ ſupra Horizontem, dum Ecliptica illos ſitus habet, quos communes ſe-
              <lb/>
            ctiones prædictæ referunt, hoc eſt, dum ſignorum initia ſupra Horizontem emergunt. </s>
            <s xml:id="echoid-s11656" xml:space="preserve">Suppute-
              <lb/>
            tur hora, qua initium ♉, Sole exiſtente in principio ♈, aſcendit, ſumpta ex prima tabella; </s>
            <s xml:id="echoid-s11657" xml:space="preserve">nem-
              <lb/>
            pe hor.</s>
            <s xml:id="echoid-s11658" xml:space="preserve">4 Min. </s>
            <s xml:id="echoid-s11659" xml:space="preserve">51. </s>
            <s xml:id="echoid-s11660" xml:space="preserve">ab A, in B, (quia principium ♉, ante meridiem tunc oritur, & </s>
            <s xml:id="echoid-s11661" xml:space="preserve">ſemicirculus Æ-
              <lb/>
            quatoris ab A, verſus B, eſt orientalis, vt conſtat, ſi intelligatur circulus ex E, deſcriptus, hoc eſt,
              <lb/>
            Æquator, in propria poſitione) & </s>
            <s xml:id="echoid-s11662" xml:space="preserve">ex B, per centrum E, ducatur recta occulta ſecans lineam æqui-
              <lb/>
            noctialem in C. </s>
            <s xml:id="echoid-s11663" xml:space="preserve">Nam punctum C, erit illud, in quod ſtyli vmbra cadit prædicta hora, qua princi-
              <lb/>
            pium ♉, aſcendit; </s>
            <s xml:id="echoid-s11664" xml:space="preserve">atque adeo per C, tranſibit communis ſectio plani horologii, & </s>
            <s xml:id="echoid-s11665" xml:space="preserve">Eclipticæ eo
              <lb/>
            tempore. </s>
            <s xml:id="echoid-s11666" xml:space="preserve">Deinde ex quarta tabella ſumatur hora, qua idem initium ♉, aſcendit, Sole in princi-
              <lb/>
            pio ♑, exiſtente, nimirum hor. </s>
            <s xml:id="echoid-s11667" xml:space="preserve">1. </s>
            <s xml:id="echoid-s11668" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s11669" xml:space="preserve">10. </s>
            <s xml:id="echoid-s11670" xml:space="preserve">quæ ab A, in D, partem Æquatoris occidentalem, quia
              <lb/>
            initium ♉, poſt meridiem tunc oritur, ſupputetur, & </s>
            <s xml:id="echoid-s11671" xml:space="preserve">ex D, per E, recta ducatur ſecans </s>
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