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
191 171
192 172
193 173
194 174
195 175
196 176
197 177
198 178
199 179
200 180
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
< >
page |< < (279) of 677 > >|
    <echo version="1.0RC">
      <text xml:lang="it" type="free">
        <div xml:id="echoid-div970" type="section" level="1" n="237">
          <pb o="279" file="0295" n="295" rhead="LIBER SECVNDVS."/>
        </div>
        <div xml:id="echoid-div972" type="section" level="1" n="238">
          <head xml:id="echoid-head245" xml:space="preserve">PROBLEMA 53. PROPOSITIO 53.</head>
          <p>
            <s xml:id="echoid-s18899" xml:space="preserve">PARALLELOS Horizontis in eodem æquinoctiali horolo-
              <lb/>
            gio ducere.</s>
            <s xml:id="echoid-s18900" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s18901" xml:space="preserve">SIT Analemma A B C, in quo Horizon B C; </s>
            <s xml:id="echoid-s18902" xml:space="preserve">Verticalis A D; </s>
            <s xml:id="echoid-s18903" xml:space="preserve">axis mundi E F; </s>
            <s xml:id="echoid-s18904" xml:space="preserve">& </s>
            <s xml:id="echoid-s18905" xml:space="preserve">Aequator
              <lb/>
              <note position="right" xlink:label="note-0295-01" xlink:href="note-0295-01a" xml:space="preserve">Paralleli Hori-
                <lb/>
              zontis qua ra-
                <lb/>
              tione in eodem
                <lb/>
              horologio æqui
                <lb/>
              noctiali deſcri-
                <lb/>
              bantur.</note>
            G H. </s>
            <s xml:id="echoid-s18906" xml:space="preserve">Diuiſo autem ſemicirculo B A C, in grad. </s>
            <s xml:id="echoid-s18907" xml:space="preserve">180. </s>
            <s xml:id="echoid-s18908" xml:space="preserve">vel in pauciores partes æquales, prout ho-
              <lb/>
            rologium capax fuerit, (Nos illum diuiſimus in 12. </s>
            <s xml:id="echoid-s18909" xml:space="preserve">vt quælibet complectatur grad. </s>
            <s xml:id="echoid-s18910" xml:space="preserve">15.) </s>
            <s xml:id="echoid-s18911" xml:space="preserve">iungan-
              <lb/>
            tur bina puncta à recta B C, vel à puncto A, æqualiter remota, lineis rectis, quæ communes ſe-
              <lb/>
            ctiones erunt Meridiani, & </s>
            <s xml:id="echoid-s18912" xml:space="preserve">pa-
              <lb/>
              <note position="left" xlink:label="note-0295-02" xlink:href="note-0295-02a" xml:space="preserve">10</note>
              <figure xlink:label="fig-0295-01" xlink:href="fig-0295-01a" number="204">
                <image file="0295-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0295-01"/>
              </figure>
            rallelorum Horizontis, quos Al-
              <lb/>
            mucantarath dicunt. </s>
            <s xml:id="echoid-s18913" xml:space="preserve">Deinde ex
              <lb/>
            diuiſionum punctis per cẽtrum
              <lb/>
            D, ducantur rectæ lineæ, vt con-
              <lb/>
            ſtituantur triangula per axem in
              <lb/>
            conis, quorum baſes ſunt paral-
              <lb/>
            leli Horizontis tam infra Hori-
              <lb/>
            zontem, quàm ſupra, vertex au-
              <lb/>
            tem communis centrum mundi
              <lb/>
            D. </s>
            <s xml:id="echoid-s18914" xml:space="preserve">Meridianus enim A B C,
              <lb/>
              <note position="left" xlink:label="note-0295-03" xlink:href="note-0295-03a" xml:space="preserve">20</note>
            per axem A D, dictorũ conorũ
              <lb/>
            incedens facit triangula per axẽ,
              <lb/>
            ex propoſ. </s>
            <s xml:id="echoid-s18915" xml:space="preserve">3. </s>
            <s xml:id="echoid-s18916" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s18917" xml:space="preserve">1. </s>
            <s xml:id="echoid-s18918" xml:space="preserve">Apollonij. </s>
            <s xml:id="echoid-s18919" xml:space="preserve">In
              <lb/>
            axe quoque E F, accipiatur vtrin
              <lb/>
            que recta D I, gnomoni æqualis,
              <lb/>
            & </s>
            <s xml:id="echoid-s18920" xml:space="preserve">per I, Aequatori G H, vtrinq;
              <lb/>
            </s>
            <s xml:id="echoid-s18921" xml:space="preserve">parallela agatur K L. </s>
            <s xml:id="echoid-s18922" xml:space="preserve">Erit hæc
              <lb/>
            infra quidem G H, communis
              <lb/>
            ſectio Meridiani, & </s>
            <s xml:id="echoid-s18923" xml:space="preserve">plani ho-
              <lb/>
            rologij ſuperioris, illa verò ſupra
              <lb/>
              <note position="left" xlink:label="note-0295-04" xlink:href="note-0295-04a" xml:space="preserve">30</note>
            G H, communis ſectio Meridia-
              <lb/>
            ni & </s>
            <s xml:id="echoid-s18924" xml:space="preserve">plani horologii inferioris.
              <lb/>
            </s>
            <s xml:id="echoid-s18925" xml:space="preserve">Secabit autem vtraque recta KL,
              <lb/>
            latera triangulorum per axem in
              <lb/>
            punctis M, N, O, P, Q, R, eruntq́ue diametri ſectionum conicarum M L, N L, O L, P L, Q R. </s>
            <s xml:id="echoid-s18926" xml:space="preserve">
              <lb/>
            Si igitur puncta M, N, O, P, (omittimus hic punctum Q, quoniam conica ſectio per ipſum du-
              <lb/>
            cta extra tropicos cadit) transferantur in lineam meridianam infra horizontalem lineam in horo
              <lb/>
            logio ſuperiori, incipiendo in hac figura ab S, puncto Horizontis, in horologio verò ab m, puncto
              <lb/>
            horizontalis lineæ & </s>
            <s xml:id="echoid-s18927" xml:space="preserve">per propoſitionem 8. </s>
            <s xml:id="echoid-s18928" xml:space="preserve">ſupetioris lib. </s>
            <s xml:id="echoid-s18929" xml:space="preserve">circa lineam meridianam dictæ coni-
              <lb/>
            cæ ſectiones deſcribantur tranſeuntes per puncta M, N, O, P, (quæ ſectiones conicę partim erunt
              <lb/>
              <note position="left" xlink:label="note-0295-05" xlink:href="note-0295-05a" xml:space="preserve">40</note>
            hyperbolæ, partim ellipſes, vt ex propoſ. </s>
            <s xml:id="echoid-s18930" xml:space="preserve">6. </s>
            <s xml:id="echoid-s18931" xml:space="preserve">& </s>
            <s xml:id="echoid-s18932" xml:space="preserve">7. </s>
            <s xml:id="echoid-s18933" xml:space="preserve">ſuperioris lib. </s>
            <s xml:id="echoid-s18934" xml:space="preserve">conſtat: </s>
            <s xml:id="echoid-s18935" xml:space="preserve">Parallelus autem Horizon
              <lb/>
            tis grad. </s>
            <s xml:id="echoid-s18936" xml:space="preserve">48. </s>
            <s xml:id="echoid-s18937" xml:space="preserve">erit parabola, ex propoſ. </s>
            <s xml:id="echoid-s18938" xml:space="preserve">5. </s>
            <s xml:id="echoid-s18939" xml:space="preserve">eiuſdem lib. </s>
            <s xml:id="echoid-s18940" xml:space="preserve">ſuperioris, quòd illum Aequator in puncto
              <lb/>
            G, contingat) & </s>
            <s xml:id="echoid-s18941" xml:space="preserve">à linea horizontali eò magis ſemper recedentes, quò longius ex vtraque parte li-
              <lb/>
            neæ meridianę fuerint productæ, deſcripti erunt paralleli Horizontis. </s>
            <s xml:id="echoid-s18942" xml:space="preserve">In horologio inferiori
              <lb/>
            transferendæ ſunt rectæ S T, S V, in lineam meridianam à puncto m, infra lineam horizon-
              <lb/>
            talem, &</s>
            <s xml:id="echoid-s18943" xml:space="preserve">c. </s>
            <s xml:id="echoid-s18944" xml:space="preserve">Nam T L, eſt diameter conicæ ſectionis paralleli Horizontis grad. </s>
            <s xml:id="echoid-s18945" xml:space="preserve">15. </s>
            <s xml:id="echoid-s18946" xml:space="preserve">ſupra Hori-
              <lb/>
            zontem, & </s>
            <s xml:id="echoid-s18947" xml:space="preserve">V L, diameter conicæ ſectionis paralleli Horizontis grad. </s>
            <s xml:id="echoid-s18948" xml:space="preserve">30. </s>
            <s xml:id="echoid-s18949" xml:space="preserve">&</s>
            <s xml:id="echoid-s18950" xml:space="preserve">c. </s>
            <s xml:id="echoid-s18951" xml:space="preserve">Eſt igitur G H,
              <lb/>
            tanquam Horizon, & </s>
            <s xml:id="echoid-s18952" xml:space="preserve">E F, veluti Verticalis; </s>
            <s xml:id="echoid-s18953" xml:space="preserve">B C, quaſi Aequator quidam, & </s>
            <s xml:id="echoid-s18954" xml:space="preserve">paralleli Horizontis
              <lb/>
            inſtar parallelorum noui Aequatoris B C. </s>
            <s xml:id="echoid-s18955" xml:space="preserve">Quibus poſitis, erunt Verticales circuli inſtar horario-
              <lb/>
            rum circulorum, qui omnes meridianam lineam horologij ſecant in puncto X, vbi eandem ſecat
              <lb/>
              <note position="left" xlink:label="note-0295-06" xlink:href="note-0295-06a" xml:space="preserve">50</note>
            A D, axis Horizontis, quem nunc munere Æquatoris cuiuſdam noui fungi diximus: </s>
            <s xml:id="echoid-s18956" xml:space="preserve">Ita vt ſi per-
              <lb/>
            mutatio hæc circulorum benè conſideretur, deſcriptio hæc parallelorum Horizontis à deſcriptio-
              <lb/>
            ne parallelorum Aequatoris in horizontali horologio non differat.</s>
            <s xml:id="echoid-s18957" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s18958" xml:space="preserve">ALITER. </s>
            <s xml:id="echoid-s18959" xml:space="preserve">Deſcripto quadrante A B C, cuiuslibet magnitudinis, eoq́ue diuiſo in grad. </s>
            <s xml:id="echoid-s18960" xml:space="preserve">90.
              <lb/>
            </s>
            <s xml:id="echoid-s18961" xml:space="preserve">
              <note position="right" xlink:label="note-0295-07" xlink:href="note-0295-07a" xml:space="preserve">Alia deſcriptio
                <lb/>
              parallelorũ Ho
                <lb/>
              rizontis in eo-
                <lb/>
              dem æquino-
                <lb/>
              ctiali horolo
                <unsure/>
              -
                <lb/>
              gio.</note>
            vel in partes pauciores, pro capacitate horologii, ducantur ex A, centro per puncta diuiſionum li-
              <lb/>
            neæ rectæ, quæ reſpondebunt radijs parallelorum Horizontis in quadrante D C 90. </s>
            <s xml:id="echoid-s18962" xml:space="preserve">figuræ ante-
              <lb/>
            cedentis comprehenſis, initio facto à recta A B, vt figura indicat. </s>
            <s xml:id="echoid-s18963" xml:space="preserve">Deinde ex figura præcedentis
              <lb/>
            propoſ. </s>
            <s xml:id="echoid-s18964" xml:space="preserve">rectæ F p, in linea A C, huius figuræ ſumatur æqualis A D; </s>
            <s xml:id="echoid-s18965" xml:space="preserve">Et rectæ m F, vel m e, acci-
              <lb/>
            piatur in linea A B, æqualis AE, ducaturq́; </s>
            <s xml:id="echoid-s18966" xml:space="preserve">recta D E. </s>
            <s xml:id="echoid-s18967" xml:space="preserve">Erit triangulũ hoc A D E, omnino æquale triã
              <lb/>
              <note position="right" xlink:label="note-0295-08" xlink:href="note-0295-08a" xml:space="preserve">4. primi.</note>
            gulo F p m, figuræ præcedentis propoſ. </s>
            <s xml:id="echoid-s18968" xml:space="preserve">cum anguli ad puncta A, & </s>
            <s xml:id="echoid-s18969" xml:space="preserve">F, recti ſint, contineanturq́ue
              <lb/>
            æqualibus lateribus, ex conſtructione. </s>
            <s xml:id="echoid-s18970" xml:space="preserve">Itaque linea D E, meridianæ lineæ p m, æqualis erit. </s>
            <s xml:id="echoid-s18971" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum