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 |< < (217) 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-s14825" xml:space="preserve">
              <pb o="217" file="0237" n="237" rhead="LIBER SECVNDVS."/>
            cet & </s>
            <s xml:id="echoid-s14826" xml:space="preserve">arcus auſtrales horologii auſtralis mutantur in boreali horologio in arcus boreales, & </s>
            <s xml:id="echoid-s14827" xml:space="preserve">con-
              <lb/>
            tra, vt ſupra dictum eſt.</s>
            <s xml:id="echoid-s14828" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14829" xml:space="preserve">DEMONSTRATIO autem huius rei non differt ab ea, quam in horologio horizontali
              <lb/>
            adduximus propoſ. </s>
            <s xml:id="echoid-s14830" xml:space="preserve">2. </s>
            <s xml:id="echoid-s14831" xml:space="preserve">huius libri. </s>
            <s xml:id="echoid-s14832" xml:space="preserve">Eſtenim & </s>
            <s xml:id="echoid-s14833" xml:space="preserve">Verticalis circulus Horizon quidam, & </s>
            <s xml:id="echoid-s14834" xml:space="preserve">angulus
              <lb/>
            D H I, æqualis altitudini poli ſupra ipſum, vt conſtat. </s>
            <s xml:id="echoid-s14835" xml:space="preserve">Quare eadem erit demonſtratio in vtro-
              <lb/>
            que horologio.</s>
            <s xml:id="echoid-s14836" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14837" xml:space="preserve">CÆTERVM in horologio Auſtrali arcus ſignorum auſtralium continentur inter centrũ
              <lb/>
              <note position="right" xlink:label="note-0237-01" xlink:href="note-0237-01a" xml:space="preserve">Qni arcus ad
                <lb/>
              ſigna auſtralia,
                <lb/>
              & qui ad borea
                <lb/>
              lia pertineant.</note>
            horologii, & </s>
            <s xml:id="echoid-s14838" xml:space="preserve">lineam æquinoctialem, borealium vero vltra lineam æquinoctialem: </s>
            <s xml:id="echoid-s14839" xml:space="preserve">In boreali au-
              <lb/>
            tem horologio contrario modo ſe res habet; </s>
            <s xml:id="echoid-s14840" xml:space="preserve">vt ex Analemmate huius propoſ. </s>
            <s xml:id="echoid-s14841" xml:space="preserve">colligitur. </s>
            <s xml:id="echoid-s14842" xml:space="preserve">Idem
              <lb/>
            etiam hinc apparere poteſt, quòd Sol in auſtralibus ſignis exiſtens breuiores vmbras facit in horo-
              <lb/>
              <note position="left" xlink:label="note-0237-02" xlink:href="note-0237-02a" xml:space="preserve">10</note>
            gio auſtrali circa meridiem, quàm cum in borealibus ſignis moratur: </s>
            <s xml:id="echoid-s14843" xml:space="preserve">quia in his maiores meridia
              <lb/>
            nas altitudines habet, quàm in illis. </s>
            <s xml:id="echoid-s14844" xml:space="preserve">Vnde cum breuiores vmbræ meridianæ fiant inter centrum
              <lb/>
            horologii auſtralis, & </s>
            <s xml:id="echoid-s14845" xml:space="preserve">lineam æquinoctialem, longiores autem vltra eandem lineam æquinoctia-
              <lb/>
            lem; </s>
            <s xml:id="echoid-s14846" xml:space="preserve">perſpicuum eſt, ſigna auſtralia eſſe inter centrum & </s>
            <s xml:id="echoid-s14847" xml:space="preserve">æquinoctialem lineam, borealia vero
              <lb/>
            vltra lineam æquinoctialem, &</s>
            <s xml:id="echoid-s14848" xml:space="preserve">c.</s>
            <s xml:id="echoid-s14849" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14850" xml:space="preserve">QVORVM autem ſignorum arcus ſint hyperbolæ, vel parabolæ, aut Ellipſes, percipiemus
              <lb/>
            exiis, quæ propoſ. </s>
            <s xml:id="echoid-s14851" xml:space="preserve">2. </s>
            <s xml:id="echoid-s14852" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s14853" xml:space="preserve">ſcripſimus.</s>
            <s xml:id="echoid-s14854" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">Quomodo ex
            <lb/>
          uno arcu oppo-
            <lb/>
          ſicus arcus de-
            <lb/>
          ſcribatur, &c.</note>
          <p>
            <s xml:id="echoid-s14855" xml:space="preserve">HIC etiam commodius, & </s>
            <s xml:id="echoid-s14856" xml:space="preserve">accuratius deſcribemus hyperbolas ſignorum borealium infra li-
              <lb/>
            neam æquinoctialem, beneficio hyperbolarum ſignorum auſtralium ſupra lineam æquinoctialem
              <lb/>
            deſcriptarum; </s>
            <s xml:id="echoid-s14857" xml:space="preserve">ſi per doctrinam, quam propoſ. </s>
            <s xml:id="echoid-s14858" xml:space="preserve">2. </s>
            <s xml:id="echoid-s14859" xml:space="preserve">huius libri tradidimus, prius inueniantur dia-
              <lb/>
              <note position="left" xlink:label="note-0237-04" xlink:href="note-0237-04a" xml:space="preserve">20</note>
            metri tranſuerſæ ſectionum oppoſitarum, earumq́; </s>
            <s xml:id="echoid-s14860" xml:space="preserve">centra, &</s>
            <s xml:id="echoid-s14861" xml:space="preserve">c.</s>
            <s xml:id="echoid-s14862" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14863" xml:space="preserve">POSSVMVS quoque vti duobus illis modis, quos ad finem eiuſdem propoſ. </s>
            <s xml:id="echoid-s14864" xml:space="preserve">2. </s>
            <s xml:id="echoid-s14865" xml:space="preserve">huius libri
              <lb/>
            ſcripſimus. </s>
            <s xml:id="echoid-s14866" xml:space="preserve">Qua de re conſule ea, quæ ibi tradidimus. </s>
            <s xml:id="echoid-s14867" xml:space="preserve">Parallelos igitur, ſiue arcus ſignorum Zo-
              <lb/>
            diaci in Verticali horologio prædicto deſcripſimus. </s>
            <s xml:id="echoid-s14868" xml:space="preserve">Quod faciendum erat.</s>
            <s xml:id="echoid-s14869" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div749" type="section" level="1" n="180">
          <head xml:id="echoid-head183" style="it" xml:space="preserve">SCHOLIVM.</head>
          <p style="it">
            <s xml:id="echoid-s14870" xml:space="preserve">HOC modo eaſdem lineas horarias præcedentis figuræ ex H, egredientes deſcribit Andreas Schone
              <lb/>
              <note position="right" xlink:label="note-0237-05" xlink:href="note-0237-05a" xml:space="preserve">Praxis pulcher-
                <lb/>
              rima pro lineis
                <lb/>
              horariis in figu
                <lb/>
              ra radioiũ Zo-
                <lb/>
              diaei ducendis,
                <lb/>
              ſine interuallis
                <lb/>
              horariis horo-
                <lb/>
              logii.</note>
            rus. </s>
            <s xml:id="echoid-s14871" xml:space="preserve">Ducta recta H I B, quæ conſtituat angulum A H B, æqualem complemẽto altitudinis poli ſupra Ho
              <lb/>
            rizontem, vel ipſi altitudini poli ſupra Verticalem circulũ, vt & </s>
            <s xml:id="echoid-s14872" xml:space="preserve">nos fecimus, ſumit in ea punctũ quod-
              <lb/>
              <note position="left" xlink:label="note-0237-06" xlink:href="note-0237-06a" xml:space="preserve">30</note>
            cunque φ, per quod ipſi D H, parallelam agit φ V, quæ rectã ductam ex H, ipſi D C, parallelã ſecet in
              <lb/>
            V, puncto, è quo, vt centro, interuallo {q́ue} V φ, circulum deſcribit. </s>
            <s xml:id="echoid-s14873" xml:space="preserve">Hoc diuiſo in partes 24. </s>
            <s xml:id="echoid-s14874" xml:space="preserve">æquales, eadẽ
              <lb/>
            facit, quæ in ſcholio propoſ. </s>
            <s xml:id="echoid-s14875" xml:space="preserve">2. </s>
            <s xml:id="echoid-s14876" xml:space="preserve">huius libri de borizontali horologio docuimus.</s>
            <s xml:id="echoid-s14877" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s14878" xml:space="preserve">EX figura autem radiorum conſtructa, vt docet Andreas Schonerus, deſcribi poterit horologiũ Ver
              <lb/>
              <note position="right" xlink:label="note-0237-07" xlink:href="note-0237-07a" xml:space="preserve">Deſcriptio ho-
                <lb/>
              rologii
                <unsure/>
              Vertica
                <lb/>
              lis ex figura ra-
                <lb/>
              diorũ Andreæ
                <lb/>
              Schoneri.</note>
            ticale ad datam ſtyli magnitudinem, vt de horizontali diximus in ſcholio propoſ. </s>
            <s xml:id="echoid-s14879" xml:space="preserve">2. </s>
            <s xml:id="echoid-s14880" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s14881" xml:space="preserve">dummodo
              <lb/>
            angulus ρ D H, æqualis fiat altitudini poli, non autem eius complemento, vt in horizont ali horologio.</s>
            <s xml:id="echoid-s14882" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s14883" xml:space="preserve">STYLVS iuxta poſteriorem modum deſcribendi parallelos ſignorum, qui per figur am radiorum Zo
              <lb/>
              <note position="right" xlink:label="note-0237-08" xlink:href="note-0237-08a" xml:space="preserve">Qua ratione ex
                <lb/>
              figura radiorũ
                <lb/>
              longitudo ſtyli,
                <lb/>
              eiusq́; locus in
                <lb/>
              horologio inue
                <lb/>
              niatur.</note>
            diaci abſoluitur, habetur, ſi ex D, ad H I, perpendicularis ducatur D ρ, vel certe recta D ρ, faciens angu
              <lb/>
            lum ρ D I, æqualem angulo complemento altitudinis poli ſupra Horizontem. </s>
            <s xml:id="echoid-s14884" xml:space="preserve">Longitudo enim ſtyli eſt ip-
              <lb/>
            ſa recta D ρ: </s>
            <s xml:id="echoid-s14885" xml:space="preserve">Locus vero eius eſt punctum ρ, diſtans ab H, centro horologij interuallo H ρ, in linea me
              <lb/>
              <note position="left" xlink:label="note-0237-09" xlink:href="note-0237-09a" xml:space="preserve">40</note>
            ridiana, vel ab æquinoctiali linea F K, ſpatio I ρ, in eadem linea meridiana, verſus centrum H.</s>
            <s xml:id="echoid-s14886" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s14887" xml:space="preserve">DESCRIPTIS autem lineis horarijs in proxime antecedenti figura ex puncto H, ſi ſecundum
              <lb/>
              <note position="right" xlink:label="note-0237-10" xlink:href="note-0237-10a" xml:space="preserve">Quomodo per
                <lb/>
              figuram radio-
                <lb/>
              rum Zodiaci
                <lb/>
              maius aut mi-
                <lb/>
              nus horologiũ
                <lb/>
              deſcubendum
                <lb/>
              ſit.</note>
            poſteriorem hunc modum ex dicta figura radiorum zodiaci deſumptum, maius, aut minus horologium cõ
              <lb/>
            ſtruendum ſit, deſcribenda erit figura radiorum Zodiaci magis, vel minus diſtans à puncto H, &</s>
            <s xml:id="echoid-s14888" xml:space="preserve">c. </s>
            <s xml:id="echoid-s14889" xml:space="preserve">vt de
              <lb/>
            horologio Horizontali dictum eſt in ſcholio propoſ. </s>
            <s xml:id="echoid-s14890" xml:space="preserve">2. </s>
            <s xml:id="echoid-s14891" xml:space="preserve">huius lib.</s>
            <s xml:id="echoid-s14892" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s14893" xml:space="preserve">QVOD ſimagnitudo ſiyli data ſit, inueniemus hac ratione diſtantiam figuræ radiorum Zodiaci à
              <lb/>
              <note position="right" xlink:label="note-0237-11" xlink:href="note-0237-11a" xml:space="preserve">Quomodo ex
                <lb/>
              data ſtyli longi
                <lb/>
              tudine inuenia
                <lb/>
              tur diſtantia ra
                <lb/>
              diorum Zodia-
                <lb/>
              ci à puncto H,
                <lb/>
              in figura radio-
                <lb/>
              rum.</note>
            puncto H, in axe H D. </s>
            <s xml:id="echoid-s14894" xml:space="preserve">In portione Analemmatis propoſ. </s>
            <s xml:id="echoid-s14895" xml:space="preserve">præcedentis abſcindatur ex B D C, protracta
              <lb/>
            recta D M, æqualis gnomoni dato, & </s>
            <s xml:id="echoid-s14896" xml:space="preserve">per M, ipſi A D, diametro Verticalis parallela agatur N O, ſecans
              <lb/>
            axem D E, in N, & </s>
            <s xml:id="echoid-s14897" xml:space="preserve">Aequatoris diametrum F D, in O. </s>
            <s xml:id="echoid-s14898" xml:space="preserve">Punctum enim D, figurę radiorum huius pro-
              <lb/>
            poſ. </s>
            <s xml:id="echoid-s14899" xml:space="preserve">in quo conueniunt omnes radij zodiaci, diſtare debet ab H, interuallo D N, vt de horologio horizõ-
              <lb/>
              <note position="left" xlink:label="note-0237-12" xlink:href="note-0237-12a" xml:space="preserve">50</note>
            tali diximus in ſcholio propoſ. </s>
            <s xml:id="echoid-s14900" xml:space="preserve">2. </s>
            <s xml:id="echoid-s14901" xml:space="preserve">huius lib.</s>
            <s xml:id="echoid-s14902" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s14903" xml:space="preserve">HIC etiam in horologio illo, quod in ſcholio præcedentis propoſ. </s>
            <s xml:id="echoid-s14904" xml:space="preserve">docuimus conficere, etiam ſi centrũ
              <lb/>
              <note position="right" xlink:label="note-0237-13" xlink:href="note-0237-13a" xml:space="preserve">Qua ratione at
                <lb/>
              cus ſignorũ in
                <lb/>
              horologio Ver-
                <lb/>
              ticali, vbi cen-
                <lb/>
              trum non habe
                <lb/>
              tur, deſcriban-
                <lb/>
              tur.</note>
            eius non habeatur, deſcribemus arcus ſignorum, vt in ſcholio propoſ. </s>
            <s xml:id="echoid-s14905" xml:space="preserve">2. </s>
            <s xml:id="echoid-s14906" xml:space="preserve">huius libri tradidimus.</s>
            <s xml:id="echoid-s14907" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s14908" xml:space="preserve">QV AMVIS autem rectè demonſtratum ſit hac propoſ. </s>
            <s xml:id="echoid-s14909" xml:space="preserve">portionem ſuperiorẽ horologij auſtralis,
              <lb/>
            quam horizontalis linea abſcindit, exhibere nobis horologium boreale, ſi omnes eius partes ita permuten-
              <lb/>
            tur, vt ſuperior vertatur in inferiorem, hoc eſt, horizontalis linea occupet ſuperiorem locum, & </s>
            <s xml:id="echoid-s14910" xml:space="preserve">pars,
              <lb/>
            quæ in eo ſitu nobis ad horologiũ conuerſis dextra eſt, fiat ſiniſtra, & </s>
            <s xml:id="echoid-s14911" xml:space="preserve">contra: </s>
            <s xml:id="echoid-s14912" xml:space="preserve">operætamen pretium me fa
              <lb/>
            cturum exiſtimaui, idem vniuerſe hoc loco oſtendere, nimirum non ſolum in Verticali horologia auſtrali,
              <lb/>
            ſed in alijs etiam omnibus (vt in meridiano, polari, in eo quod à Verticali declinat, & </s>
            <s xml:id="echoid-s14913" xml:space="preserve">in eo quod ab Hori
              <lb/>
            zonte, in inclinato ad Horizontem, & </s>
            <s xml:id="echoid-s14914" xml:space="preserve">in eo quod à Verticali declinat, ſimulq́, ad Horizontem inclinatũ
              <lb/>
            eſt) lineam horizontalem ad partes ſuperiores portionem auferre, quæ in facie plani horologii </s>
          </p>
        </div>
      </text>
    </echo>
Impressum