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 figures

< >
[Figure 231]
Page: 344
[Figure 232]
Page: 346
[Figure 233]
Page: 348
[Figure 234]
Page: 352
[Figure 235]
Page: 355
[Figure 236]
Page: 356
[Figure 237]
Page: 357
[Figure 238]
Page: 358
[Figure 239]
Page: 361
[Figure 240]
Page: 362
[Figure 241]
Page: 363
[Figure 242]
Page: 364
[Figure 243]
Page: 365
[Figure 244]
Page: 367
[Figure 245]
Page: 369
[Figure 246]
Page: 371
[Figure 247]
Page: 372
[Figure 248]
Page: 373
[Figure 249]
Page: 374
[Figure 250]
Page: 375
[Figure 251]
Page: 376
[Figure 252]
Page: 377
[Figure 253]
Page: 378
[Figure 254]
Page: 379
[Figure 255]
Page: 380
[Figure 256]
Page: 381
[Figure 257]
Page: 383
[Figure 258]
Page: 386
[Figure 259]
Page: 387
[Figure 260]
Page: 388
< >
page |< < (213) of 677 > >|
    <echo version="1.0RC">
      <text xml:lang="it" type="free">
        <div xml:id="echoid-div733" type="section" level="1" n="179">
          <p>
            <s xml:id="echoid-s14580" xml:space="preserve">
              <pb o="213" file="0233" n="233" rhead="LIBER SECVNDVS."/>
            mit, quarum vna borealis eſt, & </s>
            <s xml:id="echoid-s14581" xml:space="preserve">auſtralis altera) deſcribentur.</s>
            <s xml:id="echoid-s14582" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14583" xml:space="preserve">CÆTERVM in vtroque horologio ducenda eſt per G, locum gnomonis ad lineam meri-
              <lb/>
              <note position="right" xlink:label="note-0233-01" xlink:href="note-0233-01a" xml:space="preserve">Horizontalis
                <lb/>
              linea quid, &
                <lb/>
              quomodo in
                <lb/>
              horologio Ver-
                <lb/>
              ticali ducenda.</note>
            dianam perpendicularis A B, quæ quidem communis ſectio erit Horizontis, & </s>
            <s xml:id="echoid-s14584" xml:space="preserve">plani horologij,
              <lb/>
            diceturq́ue linea horizontalis.
              <lb/>
            </s>
            <s xml:id="echoid-s14585" xml:space="preserve">
              <figure xlink:label="fig-0233-01" xlink:href="fig-0233-01a" number="161">
                <image file="0233-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0233-01"/>
              </figure>
            Cum enim & </s>
            <s xml:id="echoid-s14586" xml:space="preserve">plan um horologij
              <lb/>
            Verticali propriè dicto æquidi-
              <lb/>
            ſtans, & </s>
            <s xml:id="echoid-s14587" xml:space="preserve">planũ Horizontis rectũ
              <lb/>
            ſit ad Meridiani planũ, erit quo-
              <lb/>
              <note position="right" xlink:label="note-0233-02" xlink:href="note-0233-02a" xml:space="preserve">19. vndec.</note>
            que communis illorum ſectio
              <lb/>
            ad idem planum Meridiani, ac
              <lb/>
              <note position="left" xlink:label="note-0233-03" xlink:href="note-0233-03a" xml:space="preserve">10</note>
            proinde, per defi. </s>
            <s xml:id="echoid-s14588" xml:space="preserve">3. </s>
            <s xml:id="echoid-s14589" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s14590" xml:space="preserve">11. </s>
            <s xml:id="echoid-s14591" xml:space="preserve">Eucl.
              <lb/>
            </s>
            <s xml:id="echoid-s14592" xml:space="preserve">& </s>
            <s xml:id="echoid-s14593" xml:space="preserve">ad meridianam lineam HI,
              <lb/>
            in Meridiani plano exiſtentem
              <lb/>
            perpendicularis in puncto G, cũ
              <lb/>
            in hoc puncto occurrat plano
              <lb/>
            Meridiani: </s>
            <s xml:id="echoid-s14594" xml:space="preserve">quod ita oſtendi po-
              <lb/>
            teſt. </s>
            <s xml:id="echoid-s14595" xml:space="preserve">Quoniam Horizon per gno
              <lb/>
            monem, qui in puncto G, per-
              <lb/>
            pendicularis eſt ad planum ho-
              <lb/>
            rologij, ductus horologio occur
              <lb/>
              <note position="left" xlink:label="note-0233-04" xlink:href="note-0233-04a" xml:space="preserve">20</note>
            rit in G, tranſibit quoque com-
              <lb/>
            munis ſectio Horizontis, & </s>
            <s xml:id="echoid-s14596" xml:space="preserve">ho-
              <lb/>
            rologij per idem punctum G.
              <lb/>
            </s>
            <s xml:id="echoid-s14597" xml:space="preserve">Quare recta A B, quæ in plano
              <lb/>
            horologij per G, ad meridianam
              <lb/>
            lineam H I, perpendicularis du-
              <lb/>
            cta eſt, communis ſectio eſt Hori
              <lb/>
            zontis, ac plani horologij, eſtq́; </s>
            <s xml:id="echoid-s14598" xml:space="preserve">
              <lb/>
            æquinoctiali lineæ parallela, vt
              <lb/>
            in ſcholio propoſ. </s>
            <s xml:id="echoid-s14599" xml:space="preserve">22. </s>
            <s xml:id="echoid-s14600" xml:space="preserve">ſuperioris
              <lb/>
              <note position="left" xlink:label="note-0233-05" xlink:href="note-0233-05a" xml:space="preserve">30</note>
            lib. </s>
            <s xml:id="echoid-s14601" xml:space="preserve">tradidimus.</s>
            <s xml:id="echoid-s14602" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14603" xml:space="preserve">QVONIAM vero Sole exi-
              <lb/>
              <note position="right" xlink:label="note-0233-06" xlink:href="note-0233-06a" xml:space="preserve">In omni horo-
                <lb/>
              logio portio il-
                <lb/>
              la, quæ ſupra li
                <lb/>
              neam horizon-
                <lb/>
              talem dcſcripta
                <lb/>
              eſt, ſuperuaca
                <lb/>
              nea eſt, ac pro-
                <lb/>
              inde reſecãda.</note>
            ſtente in Horizonte, cum videli-
              <lb/>
            cet oritur, vel occidit, vmbra ſty-
              <lb/>
            li proijcitur in communem ſectionem Horizontis ac plani horologij, hoc eſt, in rectam A B, vt cõ
              <lb/>
            ſtar ex propoſ. </s>
            <s xml:id="echoid-s14604" xml:space="preserve">11. </s>
            <s xml:id="echoid-s14605" xml:space="preserve">ſuperioris lib. </s>
            <s xml:id="echoid-s14606" xml:space="preserve">fit, vt toto reliquo tempore cuiuſque diei, cum Sol ſupta Horizon
              <lb/>
            tem eleuatus eſt, eadem vmbra cadat in planum horologij infra lineam horizontalem. </s>
            <s xml:id="echoid-s14607" xml:space="preserve">Quare
              <lb/>
            in omni horologio reſecanda eſt pars illa, quæ ſupra lineam horizontalem extat, tanquam ſuper-
              <lb/>
            uacanea, ita vt in horologio Verticali, quod ad boream ſpectat, ſolum ea particula relinquatur,
              <lb/>
            quæ inter horizontalem lineam, & </s>
            <s xml:id="echoid-s14608" xml:space="preserve">arcum, ſeu parallelum ♋, comprehenditur.</s>
            <s xml:id="echoid-s14609" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">40</note>
          <note position="right" xml:space="preserve">Portio hotolo-
            <lb/>
          gii borea lis in-
            <lb/>
          fra lineam hori
            <lb/>
          zontalem æqua
            <lb/>
          lis eſt portioni
            <lb/>
          horologii au-
            <lb/>
          ſtralis ſupra ho
            <lb/>
          rizontalem li-
            <lb/>
          neam.</note>
          <p>
            <s xml:id="echoid-s14610" xml:space="preserve">HÆC autem pars Verticalis horologij borealis inter lineam horizontalem, & </s>
            <s xml:id="echoid-s14611" xml:space="preserve">arcum ♋,
              <lb/>
            cõprehenſa, æqualis omnino eſt illi parti, quam linea horizõtalis ex Auſtrali horologio, tanquam
              <lb/>
            ſuperfluã, abſcindit. </s>
            <s xml:id="echoid-s14612" xml:space="preserve">Tantũ enim diſtat in horologio boreali parallelus ♋, ab H, centro horologii,
              <lb/>
            quantum ab eodem in Auſtrali parallelus ♑, abeſt, vt conſtat ex Analemmate huius propoſ. </s>
            <s xml:id="echoid-s14613" xml:space="preserve">Quod
              <lb/>
            ita probari poteſt. </s>
            <s xml:id="echoid-s14614" xml:space="preserve">Quoniam in triangulo D G K, ad ſiniſtram, duo anguli D, G, æquales ſunt duo
              <lb/>
            bus angulis D, G, in triangulo D G N, ad dexteram; </s>
            <s xml:id="echoid-s14615" xml:space="preserve">quòd anguli G, recti ſint, & </s>
            <s xml:id="echoid-s14616" xml:space="preserve">anguli D, ad Ver
              <lb/>
            ticem conſtituti, æquales: </s>
            <s xml:id="echoid-s14617" xml:space="preserve">Sunt autem & </s>
            <s xml:id="echoid-s14618" xml:space="preserve">latera D G, D G, æqualia, propterea quòd vtrumque gno
              <lb/>
              <note position="right" xlink:label="note-0233-09" xlink:href="note-0233-09a" xml:space="preserve">15. primi.</note>
            moni eſt æquale; </s>
            <s xml:id="echoid-s14619" xml:space="preserve">erunt & </s>
            <s xml:id="echoid-s14620" xml:space="preserve">latera D K, D N, æqualia, & </s>
            <s xml:id="echoid-s14621" xml:space="preserve">anguli reliqui K, N, æquales. </s>
            <s xml:id="echoid-s14622" xml:space="preserve">Quamobrẽ,
              <lb/>
              <note position="right" xlink:label="note-0233-10" xlink:href="note-0233-10a" xml:space="preserve">26. primi.</note>
            cum in triangulis D H K, D H N, & </s>
            <s xml:id="echoid-s14623" xml:space="preserve">anguli K D H, N D H, ad verticem D, æquales ſint, erun@
              <lb/>
              <note position="right" xlink:label="note-0233-11" xlink:href="note-0233-11a" xml:space="preserve">15. primi.</note>
            quoque latera H K, H N, æqualia; </s>
            <s xml:id="echoid-s14624" xml:space="preserve">ac proinde cum per K, tranſeat ſectio conica ♋, in boreali ho-
              <lb/>
              <note position="left" xlink:label="note-0233-12" xlink:href="note-0233-12a" xml:space="preserve">50</note>
              <note position="right" xlink:label="note-0233-13" xlink:href="note-0233-13a" xml:space="preserve">26. primi.</note>
            rologio, & </s>
            <s xml:id="echoid-s14625" xml:space="preserve">per N, ſectio conica ♑, in auſtrali, tantum diſtabit in horologio boreali arcus ♋, ab
              <lb/>
            H, quantum diſtat ab eodem puncto H, arcus ♑, in horologio Auſtrali. </s>
            <s xml:id="echoid-s14626" xml:space="preserve">Igitur cum in conis ♋,
              <lb/>
            & </s>
            <s xml:id="echoid-s14627" xml:space="preserve">♑, triangula per axem ſint æqualia, Item & </s>
            <s xml:id="echoid-s14628" xml:space="preserve">rectæ D K, D N, & </s>
            <s xml:id="echoid-s14629" xml:space="preserve">anguli D K H, D N H, æquales,
              <lb/>
            vt demonſtratum eſt; </s>
            <s xml:id="echoid-s14630" xml:space="preserve">erit ſectio conica ♋, cuins diameter K Q, in horologio boreali, æqualis ſe-
              <lb/>
            ctioni conicæ ♑, cuius diameter N Q, in horologio Auſtrali: </s>
            <s xml:id="echoid-s14631" xml:space="preserve">propterea quòd planum illius ho-
              <lb/>
            rologij ita ſecat triangulum per axem in cono vmbræ ♋, vt à plano huius horologij ſecatur trian
              <lb/>
            gulum per axem in cono vmbræ ♑, ob æqualitatem rectarum D K, D N, & </s>
            <s xml:id="echoid-s14632" xml:space="preserve">angulorum D K H,
              <lb/>
            D N H, vt oſtẽſum eſt. </s>
            <s xml:id="echoid-s14633" xml:space="preserve">Si igitur pars illa horologij Auſtralis abſciſſa à linea horizontali ſuperpona
              <lb/>
            tur horologio boreali, (ita vt pars illa, quæ nunc eſt ſuperior, fiat inferior, & </s>
            <s xml:id="echoid-s14634" xml:space="preserve">quæ inferior, euadat
              <lb/>
            ſuperior; </s>
            <s xml:id="echoid-s14635" xml:space="preserve">& </s>
            <s xml:id="echoid-s14636" xml:space="preserve">pars quæ dextra eſt, inuerſo hoc modo, vt dictum eſt, horologio, quæ nimirum eſt ver-
              <lb/>
            ſus A, fiat ſiniſtra, & </s>
            <s xml:id="echoid-s14637" xml:space="preserve">ſiniſtra ſiat dextra, quemadmodum ſupra demonſtrauimus fieri debere, ſi </s>
          </p>
        </div>
      </text>
    </echo>
Impressum