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

Page concordance

< >
Scan Original
201 181
202 182
203 183
204 184
205 185
206 186
207 187
208 188
209 189
210 190
211 191
212 192
213 193
214 194
215 195
216 196
217 197
218 198
219 199
220 200
221 201
222 202
223 203
224 204
225 205
226 206
227 207
228 208
229 209
230 210
< >
page |< < (209) of 677 > >|
    <echo version="1.0RC">
      <text xml:lang="it" type="free">
        <div xml:id="echoid-div717" type="section" level="1" n="178">
          <p style="it">
            <s xml:id="echoid-s14328" xml:space="preserve">
              <pb o="209" file="0229" n="229" rhead="LIBER SECVNDVS."/>
            ductus cadit in oppoſitam partem; </s>
            <s xml:id="echoid-s14329" xml:space="preserve">hoc eſt, ea lege & </s>
            <s xml:id="echoid-s14330" xml:space="preserve">conditione, vt conuerſo ad nos horologio auſtrali,
              <lb/>
            exiſtenteq́, puncto F, ad ſiniſtram, & </s>
            <s xml:id="echoid-s14331" xml:space="preserve">K, ad dexteram, lineę horar ie in facie oppoſita, & </s>
            <s xml:id="echoid-s14332" xml:space="preserve">boreali ducan-
              <lb/>
            tur omnino reſpondentes horarijs lineis auſtralis horologij per centrum H, eductis; </s>
            <s xml:id="echoid-s14333" xml:space="preserve">adeò vt nobis faciem
              <lb/>
            plani borealem aſpicientibus punctum F, poſitum ſit ad dexterarn, & </s>
            <s xml:id="echoid-s14334" xml:space="preserve">K, ad ſiniſtram; </s>
            <s xml:id="echoid-s14335" xml:space="preserve">contra ſcilicet,
              <lb/>
            quàm in auſtr ali contingit; </s>
            <s xml:id="echoid-s14336" xml:space="preserve">vel quod idem eſt, F, vergat in occaſum, & </s>
            <s xml:id="echoid-s14337" xml:space="preserve">K, in ortum, vt in auſtrali.</s>
            <s xml:id="echoid-s14338" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s14339" xml:space="preserve">ERIT autem horologium boreale arte proxime tradita delineatum omnino ęquale, & </s>
            <s xml:id="echoid-s14340" xml:space="preserve">ſimile au-
              <lb/>
            ſtrali ob ęqualitatem axium H A, H D; </s>
            <s xml:id="echoid-s14341" xml:space="preserve">gnomonum C A, G D; </s>
            <s xml:id="echoid-s14342" xml:space="preserve">communium ſectionum Aequatoris, & </s>
            <s xml:id="echoid-s14343" xml:space="preserve">
              <lb/>
            Meridiani A B, D I; </s>
            <s xml:id="echoid-s14344" xml:space="preserve">& </s>
            <s xml:id="echoid-s14345" xml:space="preserve">portionum meridianę lineę H B, H I, inter centrum horologii, & </s>
            <s xml:id="echoid-s14346" xml:space="preserve">lineas ęquino
              <lb/>
            ctiales poſitarum. </s>
            <s xml:id="echoid-s14347" xml:space="preserve">Hinc enim efficitur, triangulum H B L, in boreali horologio, cuius later a ſunt linea me
              <lb/>
            ridiana H B, ęquinoctialis B L, & </s>
            <s xml:id="echoid-s14348" xml:space="preserve">linea horę quintę H L, ęquale eſſe, & </s>
            <s xml:id="echoid-s14349" xml:space="preserve">ſimile prorſus triangulo H I K,
              <lb/>
              <note position="left" xlink:label="note-0229-01" xlink:href="note-0229-01a" xml:space="preserve">10</note>
              <note position="right" xlink:label="note-0229-02" xlink:href="note-0229-02a" xml:space="preserve">26. primi.</note>
            in horologio auſtrali, cuius etiam latera ſunt meridiana linea H I, ęquinoctialis I K, & </s>
            <s xml:id="echoid-s14350" xml:space="preserve">linea horę 5.
              <lb/>
            </s>
            <s xml:id="echoid-s14351" xml:space="preserve">H K; </s>
            <s xml:id="echoid-s14352" xml:space="preserve">propterea quod duo anguli illius B H L, H B L, duobus angulis huius I H K, H I K, ęquales ſunt,
              <lb/>
            (Nam anguli ad H, æquales ſunt, cum ſint ad verticem, & </s>
            <s xml:id="echoid-s14353" xml:space="preserve">anguli ad B, I, recti.) </s>
            <s xml:id="echoid-s14354" xml:space="preserve">& </s>
            <s xml:id="echoid-s14355" xml:space="preserve">latus H B, lateri
              <lb/>
              <note position="right" xlink:label="note-0229-03" xlink:href="note-0229-03a" xml:space="preserve">15. primi.</note>
            H I, ęquale, vt oſtenſum eſt, & </s>
            <s xml:id="echoid-s14356" xml:space="preserve">c. </s>
            <s xml:id="echoid-s14357" xml:space="preserve">Eadem ratio eſt de cęteris triangulis, quorum baſes ſunt lineę horarię
              <lb/>
            inter centrum H, & </s>
            <s xml:id="echoid-s14358" xml:space="preserve">lineas ęquinoctales poſitę, ſubtenſęque angulis rectis ad B, I, comprehenſis ſub me-
              <lb/>
            ridiana linea, & </s>
            <s xml:id="echoid-s14359" xml:space="preserve">lineis ęquinoctialibus. </s>
            <s xml:id="echoid-s14360" xml:space="preserve">Totum ergo horologium boreale toti auſtrali ęquale erit, & </s>
            <s xml:id="echoid-s14361" xml:space="preserve">ſimi
              <lb/>
            le, cum ſingulę partes ſingulis partibus ęquales ſint & </s>
            <s xml:id="echoid-s14362" xml:space="preserve">ſimiles.</s>
            <s xml:id="echoid-s14363" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">Si lineamenta
            <lb/>
          auſtialis horo-
            <lb/>
          logu deicriban
            <lb/>
          tur in facie pla
            <lb/>
          ni oppoſita, ita
            <lb/>
          vt ad vnguem-
            <lb/>
          reſpondeant li-
            <lb/>
          neamentis ho-
            <lb/>
          rologii auſtra-
            <lb/>
          lis, & poſt hanc
            <lb/>
          deſcriptionem
            <lb/>
          pars ſuperior
            <lb/>
          mutetur in in-
            <lb/>
          feriorem, deſcri
            <lb/>
          ptum crit horo
            <lb/>
          gium boreale.</note>
          <p style="it">
            <s xml:id="echoid-s14364" xml:space="preserve">VNDE ſi in parte oppoſita plani horologii deſcribantur lineę reſpondentes ad vnguem lineis in ho-
              <lb/>
            rologio auſtrali, & </s>
            <s xml:id="echoid-s14365" xml:space="preserve">deinde pars ſuperior mutetur in inferiorem, ac proinde & </s>
            <s xml:id="echoid-s14366" xml:space="preserve">illa, quę poſt deſcriptionẽ
              <lb/>
            illam dextra eſt, fiat ſiniſtra, et contra, deſcriptum erit horologium boreale in facie plani horologii borea-
              <lb/>
              <note position="left" xlink:label="note-0229-05" xlink:href="note-0229-05a" xml:space="preserve">20</note>
            li. </s>
            <s xml:id="echoid-s14367" xml:space="preserve">Quia hac ratione punctum K, quod in auſtrali horologio nobis eſt ad dexteram, & </s>
            <s xml:id="echoid-s14368" xml:space="preserve">in boreali poſt illam
              <lb/>
            deſcriptionem ad ſiniſtram, fit nobis iterum ad dexteram, ſi ſuperior pars in inſeriorem mutetur, vt con-
              <lb/>
            ſtat. </s>
            <s xml:id="echoid-s14369" xml:space="preserve">Sed hac de re plura in propoſ. </s>
            <s xml:id="echoid-s14370" xml:space="preserve">ſequenti ſcribemus.</s>
            <s xml:id="echoid-s14371" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s14372" xml:space="preserve">EX his omnibus (vt ad id, quod propoſitum eſt, veniamus) perſpicuum eſſe arbitror, horologium au
              <lb/>
            ſtrale indicare horas in facie plani V erticalis boreali, ſi omnia immut entur, vt dictum eſt, hoc eſt, ſi ſu-
              <lb/>
            perior pars mutetur in inferiorem, & </s>
            <s xml:id="echoid-s14373" xml:space="preserve">quæ poſt hanc mutationem nobis ad horologium conuerſis dextra
              <lb/>
            eſt, fiat ſiniſtra, & </s>
            <s xml:id="echoid-s14374" xml:space="preserve">contra. </s>
            <s xml:id="echoid-s14375" xml:space="preserve">Nam auſtrale horologium H R K, ſi inuertatur, vt punctum I, ſurſum ver-
              <lb/>
            ſus, & </s>
            <s xml:id="echoid-s14376" xml:space="preserve">H, deorſum verſus ponatur, punctum{q́ue} R, quod in eo ſitu nobis ad horologium conuerſis eſt ad
              <lb/>
            dextram, in ſiniſtram partem, & </s>
            <s xml:id="echoid-s14377" xml:space="preserve">K, in dextram cadat, acquiret omnino eundem ſitum, quem habet bo-
              <lb/>
            reale horologium L H B, in facie oppoſita delineatum, vbi punctum L, nobis ad horologium conuerſis
              <lb/>
              <note position="left" xlink:label="note-0229-06" xlink:href="note-0229-06a" xml:space="preserve">30</note>
            poſitum eſt ad dextram, & </s>
            <s xml:id="echoid-s14378" xml:space="preserve">B, ad ſinistram, vt manifestum eſt. </s>
            <s xml:id="echoid-s14379" xml:space="preserve">Similiter ex ijs, quæ in ſcbolio propoſ. </s>
            <s xml:id="echoid-s14380" xml:space="preserve">1.
              <lb/>
            </s>
            <s xml:id="echoid-s14381" xml:space="preserve">huius libri tradidimus, manifeſtum eſt, portionem illam lineę meridianæ, quæ in horologio Auſtrali indi-
              <lb/>
            cabat horam 12. </s>
            <s xml:id="echoid-s14382" xml:space="preserve">meridiei, in boreali monstrare horam 12. </s>
            <s xml:id="echoid-s14383" xml:space="preserve">mediæ noctis; </s>
            <s xml:id="echoid-s14384" xml:space="preserve">& </s>
            <s xml:id="echoid-s14385" xml:space="preserve">horas, quæ ibi à meridie nu-
              <lb/>
            merabantur, hic à media nocte, et quæibi à media nocte, hic à meridie computandas eſſe: </s>
            <s xml:id="echoid-s14386" xml:space="preserve">quoniam vide-
              <lb/>
            licet, vt proxime demonstratum eſt, horæ Auſtralis horologij vltra centrum horologij dant in facie bo-
              <lb/>
            reali eaſdem numero horas; </s>
            <s xml:id="echoid-s14387" xml:space="preserve">& </s>
            <s xml:id="echoid-s14388" xml:space="preserve">vt ex dicto ſcholio conſtat, horę antemeridianæ vltra centrum horolo-
              <lb/>
            gij productæ faciunt pomeridianas, & </s>
            <s xml:id="echoid-s14389" xml:space="preserve">pomeridianæ antemeridianas. </s>
            <s xml:id="echoid-s14390" xml:space="preserve">Quod etiam facile intelligetur, ſi
              <lb/>
            in facie boreali concipiantur per axem H A, ducti circuli horarij. </s>
            <s xml:id="echoid-s14391" xml:space="preserve">Nam vmbra axis, vel ſtyli, dummodo
              <lb/>
            Sol faciem borealem illuſtret, proijcietur in meridianam lineam H B, Sole exiſtente in ſemicirculo Meri-
              <lb/>
            diani ſub terra, in lineas verò horarias verſus punctum L, quod nobis in boreali horologio eſt ad dexte-
              <lb/>
              <note position="left" xlink:label="note-0229-07" xlink:href="note-0229-07a" xml:space="preserve">40</note>
            ram, Sole exiſtente in ſemicirculis horarijs poſt mediã noctem, hoc eſt, in ſemicir culis, qui opponuntur il-
              <lb/>
            lis, in quibus Sol exiſtit, cum vmbra axis, vel ſtyli in Auſtrali horologio proijcitur in horarias lineas ver
              <lb/>
            ſus K, & </s>
            <s xml:id="echoid-s14392" xml:space="preserve">c. </s>
            <s xml:id="echoid-s14393" xml:space="preserve">vt perſpicuum eſt, ſi & </s>
            <s xml:id="echoid-s14394" xml:space="preserve">horologium boreale L H B, & </s>
            <s xml:id="echoid-s14395" xml:space="preserve">axis H A, & </s>
            <s xml:id="echoid-s14396" xml:space="preserve">circuli horarij in propria
              <lb/>
            poſitione concipiantur. </s>
            <s xml:id="echoid-s14397" xml:space="preserve">Hæc omnia planiora fient, ſi horologium boreale L H B, in facie oppoſita, vt di-
              <lb/>
            ctum eſt, delineatum confer atur cum boreali horologio, quod ante deſcripſimus. </s>
            <s xml:id="echoid-s14398" xml:space="preserve">Deprehendemus enim
              <lb/>
            hoc illi omnino ſimile eſſe, & </s>
            <s xml:id="echoid-s14399" xml:space="preserve">æquale.</s>
            <s xml:id="echoid-s14400" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s14401" xml:space="preserve">EADEM hæc demonſtratio in horologia tam à V erticali circulo, quàm ab Horizonte declinan-
              <lb/>
              <note position="right" xlink:label="note-0229-08" xlink:href="note-0229-08a" xml:space="preserve">Ea, quæ proxi-
                <lb/>
              me dicta ſunt
                <lb/>
              de inuerſione
                <lb/>
              omnium parti@
                <lb/>
              horologii, intel
                <lb/>
              ligenda quoque
                <lb/>
              ſunt in horolo-
                <lb/>
              giis declinanti-
                <lb/>
              bus, & inclina-
                <lb/>
              tis.</note>
            tia: </s>
            <s xml:id="echoid-s14402" xml:space="preserve">Item in inclinata ad Horizontem, & </s>
            <s xml:id="echoid-s14403" xml:space="preserve">in ea, quæ & </s>
            <s xml:id="echoid-s14404" xml:space="preserve">à Verticali circulo declinant, & </s>
            <s xml:id="echoid-s14405" xml:space="preserve">ad Horizontem
              <lb/>
            ſunt inclinata, de quibus libro inſequenti dicemus, quadrat omni ex parte; </s>
            <s xml:id="echoid-s14406" xml:space="preserve">ſi modo in illis rectam B I, nõ
              <lb/>
            intelligamus eſſe meridianam, ſed lineam ſtyli, ſiue indicis, & </s>
            <s xml:id="echoid-s14407" xml:space="preserve">pro Meridiano circulo per axem A D, & </s>
            <s xml:id="echoid-s14408" xml:space="preserve">
              <lb/>
              <note position="left" xlink:label="note-0229-09" xlink:href="note-0229-09a" xml:space="preserve">50</note>
            meridianam lineam B I, ducto ſumamus circulum alium maximum, qui per axem A D, & </s>
            <s xml:id="echoid-s14409" xml:space="preserve">lineam ſtyli
              <lb/>
            B I, ducitur, inſtar noui cuiuſdam Meridiani in illorum horologiorum planis, vt ſuis locis monebimus.
              <lb/>
            </s>
            <s xml:id="echoid-s14410" xml:space="preserve">Quodcunque enim horologium eiuſmodi in vna facie plani deſcriptum, vt v. </s>
            <s xml:id="echoid-s14411" xml:space="preserve">g. </s>
            <s xml:id="echoid-s14412" xml:space="preserve">in ea, quæ à meridie decli-
              <lb/>
            nat, ſi planum ad Horizontem fuerit rectum, vel in ſuperiori facie, ſi planum ad Horizontem fuerit incli-
              <lb/>
            natum, erit quoque horologium in facie plani eiuſdem oppoſita deſcribendum, vt in ea, quę à Septentrio-
              <lb/>
            ne declinat, vel in facie inferiori; </s>
            <s xml:id="echoid-s14413" xml:space="preserve">ſi tamen omnes partes inuertantur, vt diximus, hoc eſt, ſuperior primũ
              <lb/>
            mutetur in inferiorem, & </s>
            <s xml:id="echoid-s14414" xml:space="preserve">quæ poſt hanc mutationem primam dextra eſt, euadat ſiniſtra, & </s>
            <s xml:id="echoid-s14415" xml:space="preserve">contra. </s>
            <s xml:id="echoid-s14416" xml:space="preserve">Quæ
              <lb/>
            omnia ſuo loco perſpicua erunt.</s>
            <s xml:id="echoid-s14417" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s14418" xml:space="preserve">HACTENVS conſtruximus V erticale horologium in plana ſuperficie quacunque, vt illud po-
              <lb/>
            ſtea in murum, vel planum, quod ad Horizontem rectum eſt, & </s>
            <s xml:id="echoid-s14419" xml:space="preserve">directò ad meridiem, Septentrionemve
              <lb/>
            ſpectat, transferri poſſit, ita vt H E, meridiana linea ad Horizontem ſit perpendicularis, </s>
          </p>
        </div>
      </text>
    </echo>
Impressum