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
221 201
222 202
223 203
224 204
225 205
226 206
227 207
228 208
229 209
230 210
231 211
232 212
233 213
234 214
235 215
236 216
237 217
238 218
239 219
240 220
241 221
242 222
243 223
244 224
245 225
246 226
247 227
248 228
249 229
250 230
< >
page |< < (291) of 677 > >|
    <echo version="1.0RC">
      <text xml:lang="it" type="free">
        <div xml:id="echoid-div1010" type="section" level="1" n="248">
          <p style="it">
            <s xml:id="echoid-s19693" xml:space="preserve">
              <pb o="291" file="0307" n="307" rhead="LIBER SECVNDVS."/>
            quoque recta ducta per ſecunda puncta diuiſionum, quorum vnum ſit primæ diuiſionis, & </s>
            <s xml:id="echoid-s19694" xml:space="preserve">infra rectam
              <lb/>
            C D, & </s>
            <s xml:id="echoid-s19695" xml:space="preserve">alterum ſecundæ diuiſionis, & </s>
            <s xml:id="echoid-s19696" xml:space="preserve">ſupra rectam C D, perpendicularis erit ad lineam ipſi B A, proxi-
              <lb/>
            mam, tanget{q́ue} circulum B G F, in puncto proximo ipſi B. </s>
            <s xml:id="echoid-s19697" xml:space="preserve">Ita quoque cum tertijs punctis diuiſionum,
              <lb/>
            quartis, & </s>
            <s xml:id="echoid-s19698" xml:space="preserve">cæteris agatur. </s>
            <s xml:id="echoid-s19699" xml:space="preserve">Ratio huius rei hæc eſt: </s>
            <s xml:id="echoid-s19700" xml:space="preserve">quia dictæ lineæ horarum ab or. </s>
            <s xml:id="echoid-s19701" xml:space="preserve">& </s>
            <s xml:id="echoid-s19702" xml:space="preserve">occ. </s>
            <s xml:id="echoid-s19703" xml:space="preserve">diuidunt ſin-
              <lb/>
            gulos circulos ex A, deſcriptos in 24. </s>
            <s xml:id="echoid-s19704" xml:space="preserve">partes æquales, vt ex demonstratis in propoſ. </s>
            <s xml:id="echoid-s19705" xml:space="preserve">præcedenti liquet,
              <lb/>
            initio facto tam à puncto C, quàm à puncto D; </s>
            <s xml:id="echoid-s19706" xml:space="preserve">ita vt ſi proximum punctum infra C, fuerit hora 23. </s>
            <s xml:id="echoid-s19707" xml:space="preserve">ab
              <lb/>
            occ. </s>
            <s xml:id="echoid-s19708" xml:space="preserve">proximum punctum ſupra punctum D, ſit hora 23. </s>
            <s xml:id="echoid-s19709" xml:space="preserve">ab or. </s>
            <s xml:id="echoid-s19710" xml:space="preserve">& </s>
            <s xml:id="echoid-s19711" xml:space="preserve">c.</s>
            <s xml:id="echoid-s19712" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s19713" xml:space="preserve">LONGITVDINEM ſtyli, qui in centro collocatus horas indicet in horologio hac arte deli-
              <lb/>
              <note position="right" xlink:label="note-0307-01" xlink:href="note-0307-01a" xml:space="preserve">Longitudo ſty-
                <lb/>
              li quomodo in
                <lb/>
              ueſtigetur in po
                <lb/>
              ſteriori hac d
                <unsure/>
              e-
                <lb/>
              ſcriptione horo
                <lb/>
              logii Italici &
                <lb/>
              Babylonici.</note>
            neato, ita inueniemus. </s>
            <s xml:id="echoid-s19714" xml:space="preserve">Fiat angulus A B E, complemento altitudinis poli æqualis, quod quidem facile
              <lb/>
            efficietur, ſi ex B, arcus circuli deſcribatur, in eo{q́ue} complementum altitudinis poli à recta B A, verſus
              <lb/>
              <note position="left" xlink:label="note-0307-02" xlink:href="note-0307-02a" xml:space="preserve">10</note>
            C, ſupputetur. </s>
            <s xml:id="echoid-s19715" xml:space="preserve">Nam recta B E, ducta ex B, per finem ſupputationis conſtituet angulum A B F, com-
              <lb/>
            plemento altitudinis poli æqualem, abſcindet{q́ue} ex recta A E, longitudinem ſtyli A E, in centro A, affi-
              <lb/>
            gendi ad angulos rectos. </s>
            <s xml:id="echoid-s19716" xml:space="preserve">Si enim horologio in propria poſitione conſtituto, ita vt æquinoctiali circulo
              <lb/>
            æquidiſtet, & </s>
            <s xml:id="echoid-s19717" xml:space="preserve">recta C D, Horizonti ſit parallela, triangulum A B E, circa rectam A E, quæ commu-
              <lb/>
            nis ſectio eſt plani horologii, & </s>
            <s xml:id="echoid-s19718" xml:space="preserve">Meridiani circuli, moueri intelligatur, donec in plano Meridiani ſtatua-
              <lb/>
            tur rectum ad horologij planum, erit A E, axis mundi, & </s>
            <s xml:id="echoid-s19719" xml:space="preserve">B E, communis@ ſectio Horizontis per C D,
              <lb/>
            ducti, & </s>
            <s xml:id="echoid-s19720" xml:space="preserve">Meridiani, cum eſficiat cum meridiana linea A B, angulum complemento altitudinis poli æqua-
              <lb/>
            lem, vt res poſtulat, vt ex demonſtratis in propoſ. </s>
            <s xml:id="echoid-s19721" xml:space="preserve">50. </s>
            <s xml:id="echoid-s19722" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s19723" xml:space="preserve">colligitur. </s>
            <s xml:id="echoid-s19724" xml:space="preserve">Quare A E, longitudo ſtyli
              <lb/>
            erit, cum Sole in Horizonte, qui per C D, & </s>
            <s xml:id="echoid-s19725" xml:space="preserve">E B, ducitur, exiſtente extremitas vmbræ ipſius in lineam
              <lb/>
            horizontalem C D, proijciatur, vt conſtat. </s>
            <s xml:id="echoid-s19726" xml:space="preserve">Quòd ſi non placeat deſcribere arcum circuli ex B, ad conſti-
              <lb/>
              <note position="left" xlink:label="note-0307-03" xlink:href="note-0307-03a" xml:space="preserve">20</note>
            tuendum angulum complemento altitudinis poli æqualem, ſupputetur in circulo B G F, duplum comple-
              <lb/>
            menti altitudinis poli ab F, vſque ad G. </s>
            <s xml:id="echoid-s19727" xml:space="preserve">Recta enim ducta B G, conſtituet angulum A B G, comple-
              <lb/>
            mento altitudinis poli æqualem. </s>
            <s xml:id="echoid-s19728" xml:space="preserve">Cum enim (ſi ducta eſſet recta G A) angulus G A F, in centro duplus
              <lb/>
              <note position="right" xlink:label="note-0307-04" xlink:href="note-0307-04a" xml:space="preserve">33. ſext@.</note>
            ſit anguli complementi altitudinis poli in eodem centro conſtituti, quòd & </s>
            <s xml:id="echoid-s19729" xml:space="preserve">arcus F G, eiuſdem comple-
              <lb/>
            menti ſii duplus: </s>
            <s xml:id="echoid-s19730" xml:space="preserve">Duplus autem ſit angulus G A F, in centro anguli G B F, in circumferentia; </s>
            <s xml:id="echoid-s19731" xml:space="preserve">erit an-
              <lb/>
              <note position="right" xlink:label="note-0307-05" xlink:href="note-0307-05a" xml:space="preserve">20. tertij</note>
            gulus G B F, complemento altitudinis poli æqualis.</s>
            <s xml:id="echoid-s19732" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s19733" xml:space="preserve">INVENTO autem ſtylo A E, poterunt pro eius magnitudine deſcribi arcus, ſeu paralleli ſigno-
              <lb/>
              <note position="right" xlink:label="note-0307-06" xlink:href="note-0307-06a" xml:space="preserve">Quomodo in
                <lb/>
              poſteriori hoc
                <lb/>
              horologio arcus
                <lb/>
              ſignornm de-
                <lb/>
              ſeribantur.</note>
            rum, veluti propoſ. </s>
            <s xml:id="echoid-s19734" xml:space="preserve">50. </s>
            <s xml:id="echoid-s19735" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s19736" xml:space="preserve">docuimus; </s>
            <s xml:id="echoid-s19737" xml:space="preserve">vt videlicet in remotiſſimo eorum, & </s>
            <s xml:id="echoid-s19738" xml:space="preserve">in arcu ♋, vel ♑, ho-
              <lb/>
            rariæ lineæ terminentur, vt in præcedentis propoſ. </s>
            <s xml:id="echoid-s19739" xml:space="preserve">horologio factum eſt.</s>
            <s xml:id="echoid-s19740" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">30</note>
        </div>
        <div xml:id="echoid-div1015" type="section" level="1" n="249">
          <head xml:id="echoid-head257" xml:space="preserve">PROBLEMA 60. PROPOSITIO 60.</head>
          <head xml:id="echoid-head258" xml:space="preserve">HOROLOGIVM Antiquum æquinoctiale conſtituere.</head>
          <p>
            <s xml:id="echoid-s19741" xml:space="preserve">DIVIDANTVR ſingulæ portiones arcuum ſignorum, quas horizontalis linea amputat, in
              <lb/>
              <note position="right" xlink:label="note-0307-08" xlink:href="note-0307-08a" xml:space="preserve">Conſtructio ho
                <lb/>
              rologii Antiqui
                <lb/>
              æquinoctialis.</note>
            vtroque horologio tam ſuperiori, quàm inferiori, in 12. </s>
            <s xml:id="echoid-s19742" xml:space="preserve">partes æquales. </s>
            <s xml:id="echoid-s19743" xml:space="preserve">Deinde per proxima pun
              <lb/>
            cta infra, & </s>
            <s xml:id="echoid-s19744" xml:space="preserve">ſupra lineam horizontalem ad vtraſque partes quatuor lineæ rectæ ducantur, idemq́;
              <lb/>
            </s>
            <s xml:id="echoid-s19745" xml:space="preserve">fiat in ſequentibus punctis ſibi reſpondentibus, deſcriptumq́ue erit horologium Antiquum. </s>
            <s xml:id="echoid-s19746" xml:space="preserve">Nã
              <lb/>
            proxima linea infra lineam horizontalem ad dextram dabit in ſuperiori horologio horam 1. </s>
            <s xml:id="echoid-s19747" xml:space="preserve">in-
              <lb/>
              <note position="left" xlink:label="note-0307-09" xlink:href="note-0307-09a" xml:space="preserve">40</note>
            æqualem, ſubſequens ſecundam, & </s>
            <s xml:id="echoid-s19748" xml:space="preserve">c. </s>
            <s xml:id="echoid-s19749" xml:space="preserve">In inferiori idem cernitur ad ſiniſtrã horizontalis lineæ, hoc
              <lb/>
            eſt, in portione abſciſſa à linea horizontali, ſi tamen omnes eius partes inuertantur. </s>
            <s xml:id="echoid-s19750" xml:space="preserve">Demonſtrabi-
              <lb/>
            mus autem, rectè hac ratione deſcriptas eſſe horas inæquales, non aliter, ac oſtendimus propoſ.
              <lb/>
            </s>
            <s xml:id="echoid-s19751" xml:space="preserve">58. </s>
            <s xml:id="echoid-s19752" xml:space="preserve">huius libri, rectè ductas eſſe lineas horarum ab occaſu ſecundum primum modum; </s>
            <s xml:id="echoid-s19753" xml:space="preserve">ſi intelli-
              <lb/>
            gantur circuli maximi per polos mundi, & </s>
            <s xml:id="echoid-s19754" xml:space="preserve">per horas inæquales parallelorum Solis tranſire. </s>
            <s xml:id="echoid-s19755" xml:space="preserve">Hi
              <lb/>
            enim ſecabunt quoque arcus ſignorum in horologio æquinoctiali in partes æquales, per ea, quæ
              <lb/>
            propoſ. </s>
            <s xml:id="echoid-s19756" xml:space="preserve">49. </s>
            <s xml:id="echoid-s19757" xml:space="preserve">huius libri demonſtrauimus: </s>
            <s xml:id="echoid-s19758" xml:space="preserve">ac proinde per puncta diuiſionum arcuum ſignorum
              <lb/>
            circuli horarum inæqualium ducentur, vt de circulis horarum ab occaſu dictum eſt propoſ. </s>
            <s xml:id="echoid-s19759" xml:space="preserve">58. </s>
            <s xml:id="echoid-s19760" xml:space="preserve">
              <lb/>
            huius libri.</s>
            <s xml:id="echoid-s19761" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s19762" xml:space="preserve">IDEM horologium Antiquum, horarumve inæqualium delineabimus beneficio arcus diur
              <lb/>
              <note position="left" xlink:label="note-0307-10" xlink:href="note-0307-10a" xml:space="preserve">50</note>
              <note position="right" xlink:label="note-0307-11" xlink:href="note-0307-11a" xml:space="preserve">Eiuſdẽ
                <unsure/>
              horolo-
                <lb/>
              gii Antiqui æ-
                <lb/>
              quinoctialis de
                <lb/>
              ſcriptio per ar-
                <lb/>
              cum diurnum
                <lb/>
              horarum 18. &
                <lb/>
              nocturnum ho
                <lb/>
              rarum 6.</note>
            ni horarum 18. </s>
            <s xml:id="echoid-s19763" xml:space="preserve">& </s>
            <s xml:id="echoid-s19764" xml:space="preserve">nocturni horarum 6. </s>
            <s xml:id="echoid-s19765" xml:space="preserve">Nam hora 1. </s>
            <s xml:id="echoid-s19766" xml:space="preserve">inæqualis ducenda eſt in arcu diurno hora-
              <lb/>
            rum 18. </s>
            <s xml:id="echoid-s19767" xml:space="preserve">per horam 4 {1/2}. </s>
            <s xml:id="echoid-s19768" xml:space="preserve">à media nocte, & </s>
            <s xml:id="echoid-s19769" xml:space="preserve">in nocturno horarum 6. </s>
            <s xml:id="echoid-s19770" xml:space="preserve">per hor. </s>
            <s xml:id="echoid-s19771" xml:space="preserve">9 {1/2}. </s>
            <s xml:id="echoid-s19772" xml:space="preserve">à meridie. </s>
            <s xml:id="echoid-s19773" xml:space="preserve">Ho-
              <lb/>
            ra autem ſecunda per hor. </s>
            <s xml:id="echoid-s19774" xml:space="preserve">6. </s>
            <s xml:id="echoid-s19775" xml:space="preserve">à media nocte in priori arcu, & </s>
            <s xml:id="echoid-s19776" xml:space="preserve">per horam 10. </s>
            <s xml:id="echoid-s19777" xml:space="preserve">à meridie in poſte-
              <lb/>
            riori. </s>
            <s xml:id="echoid-s19778" xml:space="preserve">Hora deinde tertia inæqualis ducenda eſt in arcu diurno horarum 18. </s>
            <s xml:id="echoid-s19779" xml:space="preserve">per hor. </s>
            <s xml:id="echoid-s19780" xml:space="preserve">7 {1/2}. </s>
            <s xml:id="echoid-s19781" xml:space="preserve">à media
              <lb/>
            nocte, & </s>
            <s xml:id="echoid-s19782" xml:space="preserve">in arcu nocturno horarum 6. </s>
            <s xml:id="echoid-s19783" xml:space="preserve">per hor. </s>
            <s xml:id="echoid-s19784" xml:space="preserve">10 {1/2} à meridie. </s>
            <s xml:id="echoid-s19785" xml:space="preserve">Hora vero quarta inæqualis tranſi-
              <lb/>
            re debet in priori arcu per hor. </s>
            <s xml:id="echoid-s19786" xml:space="preserve">9. </s>
            <s xml:id="echoid-s19787" xml:space="preserve">à media nocte, & </s>
            <s xml:id="echoid-s19788" xml:space="preserve">in arcu poſteriori per hor. </s>
            <s xml:id="echoid-s19789" xml:space="preserve">11. </s>
            <s xml:id="echoid-s19790" xml:space="preserve">à meridie. </s>
            <s xml:id="echoid-s19791" xml:space="preserve">Quin
              <lb/>
            ta autem hora inæqualis ducenda eſt per hor. </s>
            <s xml:id="echoid-s19792" xml:space="preserve">10 {1/2}. </s>
            <s xml:id="echoid-s19793" xml:space="preserve">à media nocte in arcu diurno horarum 18. </s>
            <s xml:id="echoid-s19794" xml:space="preserve">& </s>
            <s xml:id="echoid-s19795" xml:space="preserve">
              <lb/>
            in arcu nocturno horarum 6.</s>
            <s xml:id="echoid-s19796" xml:space="preserve">
              <unsure/>
            per hor. </s>
            <s xml:id="echoid-s19797" xml:space="preserve">11 {1/2}. </s>
            <s xml:id="echoid-s19798" xml:space="preserve">à meridie. </s>
            <s xml:id="echoid-s19799" xml:space="preserve">Hora vero ſexta inæqualis à linea meridia-
              <lb/>
            na, ſine horæ 12. </s>
            <s xml:id="echoid-s19800" xml:space="preserve">aſtronomicæ non differt. </s>
            <s xml:id="echoid-s19801" xml:space="preserve">Poſt hæc hora ſeptima inæqualis ducenda eſt in arcu
              <lb/>
            diurno horarum 18. </s>
            <s xml:id="echoid-s19802" xml:space="preserve">per hor 1 {1/2}. </s>
            <s xml:id="echoid-s19803" xml:space="preserve">à meridie, & </s>
            <s xml:id="echoid-s19804" xml:space="preserve">in arcu nocturno horarum 6. </s>
            <s xml:id="echoid-s19805" xml:space="preserve">per hor. </s>
            <s xml:id="echoid-s19806" xml:space="preserve">{1/2}. </s>
            <s xml:id="echoid-s19807" xml:space="preserve">à media
              <lb/>
            nocte. </s>
            <s xml:id="echoid-s19808" xml:space="preserve">Octaua autem hora inæqualis ducenda eſt in priori arcu per hor. </s>
            <s xml:id="echoid-s19809" xml:space="preserve">3. </s>
            <s xml:id="echoid-s19810" xml:space="preserve">à meridie, & </s>
            <s xml:id="echoid-s19811" xml:space="preserve">in </s>
          </p>
        </div>
      </text>
    </echo>
Impressum