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

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        <div xml:id="echoid-div869" type="section" level="1" n="209">
          <p>
            <s xml:id="echoid-s17103" xml:space="preserve">
              <pb o="254" file="0270" n="270" rhead="GNOMONICES"/>
            las in punctis illis, in quibus eaſdem ſecant lineæ horarum à meridie, vel media nocte, ex propoſ.
              <lb/>
            </s>
            <s xml:id="echoid-s17104" xml:space="preserve">14. </s>
            <s xml:id="echoid-s17105" xml:space="preserve">ſuperioris lib. </s>
            <s xml:id="echoid-s17106" xml:space="preserve">exceptis lineis hor. </s>
            <s xml:id="echoid-s17107" xml:space="preserve">12. </s>
            <s xml:id="echoid-s17108" xml:space="preserve">& </s>
            <s xml:id="echoid-s17109" xml:space="preserve">24. </s>
            <s xml:id="echoid-s17110" xml:space="preserve">hæ enim non conueniunt cum dictis hyperbolis,
              <lb/>
            vt conſtat ex coroll. </s>
            <s xml:id="echoid-s17111" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s17112" xml:space="preserve">15. </s>
            <s xml:id="echoid-s17113" xml:space="preserve">eiuſdem lib. </s>
            <s xml:id="echoid-s17114" xml:space="preserve">ſuperioris.</s>
            <s xml:id="echoid-s17115" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s17116" xml:space="preserve">PORRO pro horologio Iralico orientali accipiendæ ſunt ex arcubus diurnis, nocturnisq́ue
              <lb/>
            illæ horæ ab occaſu duntaxat, quæ habent reſpondentes horas à media nocte, quoniam horæ à me
              <lb/>
            ridie in illo non continentur. </s>
            <s xml:id="echoid-s17117" xml:space="preserve">Pro occidentali verò ſumendę ſunt horæ illæ, quibus reſpondent
              <lb/>
            horæ à meridie, quòd hæ ſolæ in eo reperiantur deſcriptæ. </s>
            <s xml:id="echoid-s17118" xml:space="preserve">Idemq́ue obſeruetur in arcu diurno,
              <lb/>
            & </s>
            <s xml:id="echoid-s17119" xml:space="preserve">nocturno horarum 24. </s>
            <s xml:id="echoid-s17120" xml:space="preserve">Itaque has horas 9. </s>
            <s xml:id="echoid-s17121" xml:space="preserve">10. </s>
            <s xml:id="echoid-s17122" xml:space="preserve">11. </s>
            <s xml:id="echoid-s17123" xml:space="preserve">12. </s>
            <s xml:id="echoid-s17124" xml:space="preserve">13. </s>
            <s xml:id="echoid-s17125" xml:space="preserve">14. </s>
            <s xml:id="echoid-s17126" xml:space="preserve">ab occaſu deſcribemus in horo-
              <lb/>
            logio orientali per horas 2. </s>
            <s xml:id="echoid-s17127" xml:space="preserve">3. </s>
            <s xml:id="echoid-s17128" xml:space="preserve">4. </s>
            <s xml:id="echoid-s17129" xml:space="preserve">5. </s>
            <s xml:id="echoid-s17130" xml:space="preserve">6. </s>
            <s xml:id="echoid-s17131" xml:space="preserve">7. </s>
            <s xml:id="echoid-s17132" xml:space="preserve">à media nocte in arcu nocturno horarum 14. </s>
            <s xml:id="echoid-s17133" xml:space="preserve">Item ho-
              <lb/>
            ras has 9. </s>
            <s xml:id="echoid-s17134" xml:space="preserve">10. </s>
            <s xml:id="echoid-s17135" xml:space="preserve">11. </s>
            <s xml:id="echoid-s17136" xml:space="preserve">12. </s>
            <s xml:id="echoid-s17137" xml:space="preserve">ab occaſu per horas 3. </s>
            <s xml:id="echoid-s17138" xml:space="preserve">4. </s>
            <s xml:id="echoid-s17139" xml:space="preserve">5. </s>
            <s xml:id="echoid-s17140" xml:space="preserve">6. </s>
            <s xml:id="echoid-s17141" xml:space="preserve">à media nocte in arcu nocturno horarum
              <lb/>
              <note position="left" xlink:label="note-0270-01" xlink:href="note-0270-01a" xml:space="preserve">10</note>
            12. </s>
            <s xml:id="echoid-s17142" xml:space="preserve">Has autem 13. </s>
            <s xml:id="echoid-s17143" xml:space="preserve">14. </s>
            <s xml:id="echoid-s17144" xml:space="preserve">15. </s>
            <s xml:id="echoid-s17145" xml:space="preserve">16. </s>
            <s xml:id="echoid-s17146" xml:space="preserve">17. </s>
            <s xml:id="echoid-s17147" xml:space="preserve">ab occaſu per 7. </s>
            <s xml:id="echoid-s17148" xml:space="preserve">8. </s>
            <s xml:id="echoid-s17149" xml:space="preserve">9. </s>
            <s xml:id="echoid-s17150" xml:space="preserve">10. </s>
            <s xml:id="echoid-s17151" xml:space="preserve">11. </s>
            <s xml:id="echoid-s17152" xml:space="preserve">à media nocte in arcu diurno ho-
              <lb/>
            rarum 12. </s>
            <s xml:id="echoid-s17153" xml:space="preserve">Præterea hor. </s>
            <s xml:id="echoid-s17154" xml:space="preserve">9. </s>
            <s xml:id="echoid-s17155" xml:space="preserve">10. </s>
            <s xml:id="echoid-s17156" xml:space="preserve">ab occaſu per horas 4. </s>
            <s xml:id="echoid-s17157" xml:space="preserve">5. </s>
            <s xml:id="echoid-s17158" xml:space="preserve">à media nocte in arcu nocturno hora-
              <lb/>
            rum 10. </s>
            <s xml:id="echoid-s17159" xml:space="preserve">Has verò 10. </s>
            <s xml:id="echoid-s17160" xml:space="preserve">11. </s>
            <s xml:id="echoid-s17161" xml:space="preserve">12. </s>
            <s xml:id="echoid-s17162" xml:space="preserve">13. </s>
            <s xml:id="echoid-s17163" xml:space="preserve">14. </s>
            <s xml:id="echoid-s17164" xml:space="preserve">15. </s>
            <s xml:id="echoid-s17165" xml:space="preserve">16. </s>
            <s xml:id="echoid-s17166" xml:space="preserve">ab occaſu per 5. </s>
            <s xml:id="echoid-s17167" xml:space="preserve">6. </s>
            <s xml:id="echoid-s17168" xml:space="preserve">7. </s>
            <s xml:id="echoid-s17169" xml:space="preserve">8. </s>
            <s xml:id="echoid-s17170" xml:space="preserve">9. </s>
            <s xml:id="echoid-s17171" xml:space="preserve">10. </s>
            <s xml:id="echoid-s17172" xml:space="preserve">11. </s>
            <s xml:id="echoid-s17173" xml:space="preserve">à media no-
              <lb/>
            cte in arcu diurno horarum 14. </s>
            <s xml:id="echoid-s17174" xml:space="preserve">Et has 14. </s>
            <s xml:id="echoid-s17175" xml:space="preserve">15. </s>
            <s xml:id="echoid-s17176" xml:space="preserve">16. </s>
            <s xml:id="echoid-s17177" xml:space="preserve">17. </s>
            <s xml:id="echoid-s17178" xml:space="preserve">18. </s>
            <s xml:id="echoid-s17179" xml:space="preserve">ab occ. </s>
            <s xml:id="echoid-s17180" xml:space="preserve">per horas 7. </s>
            <s xml:id="echoid-s17181" xml:space="preserve">8. </s>
            <s xml:id="echoid-s17182" xml:space="preserve">9. </s>
            <s xml:id="echoid-s17183" xml:space="preserve">10. </s>
            <s xml:id="echoid-s17184" xml:space="preserve">11. </s>
            <s xml:id="echoid-s17185" xml:space="preserve">à med.
              <lb/>
            </s>
            <s xml:id="echoid-s17186" xml:space="preserve">noc. </s>
            <s xml:id="echoid-s17187" xml:space="preserve">in arcu diurno horarum 10. </s>
            <s xml:id="echoid-s17188" xml:space="preserve">Eadem ratione in occidentali horologio ex tabulis dictis repe-
              <lb/>
            riemus horas à mer. </s>
            <s xml:id="echoid-s17189" xml:space="preserve">per quas horæ ab occ. </s>
            <s xml:id="echoid-s17190" xml:space="preserve">ducendæ ſunt. </s>
            <s xml:id="echoid-s17191" xml:space="preserve">Quoniam verò hora 18. </s>
            <s xml:id="echoid-s17192" xml:space="preserve">ab occaſu
              <lb/>
            vnicum punctum habet in vtroque horologio, nempe in orientali horam 11. </s>
            <s xml:id="echoid-s17193" xml:space="preserve">a media nocte in ar-
              <lb/>
            cu diurno horarum 10. </s>
            <s xml:id="echoid-s17194" xml:space="preserve">in occidentali autem horam primam à meridie in arcu diurno horarum
              <lb/>
            14. </s>
            <s xml:id="echoid-s17195" xml:space="preserve">ducemus eam in horologio orientali per horam 11. </s>
            <s xml:id="echoid-s17196" xml:space="preserve">à med. </s>
            <s xml:id="echoid-s17197" xml:space="preserve">noc. </s>
            <s xml:id="echoid-s17198" xml:space="preserve">in arcu diurno horarum 10. </s>
            <s xml:id="echoid-s17199" xml:space="preserve">
              <lb/>
            & </s>
            <s xml:id="echoid-s17200" xml:space="preserve">per horam 6. </s>
            <s xml:id="echoid-s17201" xml:space="preserve">à media nocte in arcu nocturno horarum 24. </s>
            <s xml:id="echoid-s17202" xml:space="preserve">In occidentali vero horologio per
              <lb/>
              <note position="left" xlink:label="note-0270-02" xlink:href="note-0270-02a" xml:space="preserve">20</note>
            horam 1. </s>
            <s xml:id="echoid-s17203" xml:space="preserve">à mer in arcu diurno horarum 14. </s>
            <s xml:id="echoid-s17204" xml:space="preserve">& </s>
            <s xml:id="echoid-s17205" xml:space="preserve">per horam 6. </s>
            <s xml:id="echoid-s17206" xml:space="preserve">à meridie in arcu diurno horarum
              <lb/>
            24. </s>
            <s xml:id="echoid-s17207" xml:space="preserve">In vtroq; </s>
            <s xml:id="echoid-s17208" xml:space="preserve">autem horologio linea horæ 18. </s>
            <s xml:id="echoid-s17209" xml:space="preserve">ab occaſu parallela eſt æquinoctiali lineæ, vt ex ſcho-
              <lb/>
            lio propoſ. </s>
            <s xml:id="echoid-s17210" xml:space="preserve">22. </s>
            <s xml:id="echoid-s17211" xml:space="preserve">ſuperioris lib. </s>
            <s xml:id="echoid-s17212" xml:space="preserve">perſpicuum eſt.</s>
            <s xml:id="echoid-s17213" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s17214" xml:space="preserve">POSTREMO idem horologium Italicum abſoluetur beneficio lineæ horæ 12. </s>
            <s xml:id="echoid-s17215" xml:space="preserve">ab ortu, & </s>
            <s xml:id="echoid-s17216" xml:space="preserve">
              <lb/>
              <note position="left" xlink:label="note-0270-03" xlink:href="note-0270-03a" xml:space="preserve">Alia deſcriptio
                <lb/>
              horologii Itali-
                <lb/>
              ci Meridiani p
                <unsure/>
                <lb/>
              lincam horæ
                <lb/>
              12. ab or. & occ.
                <lb/>
              & per lineam
                <lb/>
              horæ 24. ab or.
                <lb/>
              uel occ.</note>
            occaſu, vt conſtat ex tabula ſecunda propoſ. </s>
            <s xml:id="echoid-s17217" xml:space="preserve">20. </s>
            <s xml:id="echoid-s17218" xml:space="preserve">ſuperioris lib. </s>
            <s xml:id="echoid-s17219" xml:space="preserve">cui titulus eſt, LINEA HOR Æ,
              <lb/>
            XII. </s>
            <s xml:id="echoid-s17220" xml:space="preserve">AB ORTV, VEL OCCASV. </s>
            <s xml:id="echoid-s17221" xml:space="preserve">Item beneficio lineæ horæ 24. </s>
            <s xml:id="echoid-s17222" xml:space="preserve">ab ortu, vel occaſu,
              <lb/>
            (quæ eadem eſt, quæ linea horizontalis) vt colligitur ex prima tabula eiuſdem propoſitionis, cui
              <lb/>
            titulus eſt, LINEA HOR Æ XXIIII. </s>
            <s xml:id="echoid-s17223" xml:space="preserve">AB ORTV, VEL OCCASV. </s>
            <s xml:id="echoid-s17224" xml:space="preserve">Immo accu-
              <lb/>
            ratius deſcribetur beneficio lineæ horæ 12. </s>
            <s xml:id="echoid-s17225" xml:space="preserve">ab or. </s>
            <s xml:id="echoid-s17226" xml:space="preserve">vel occ. </s>
            <s xml:id="echoid-s17227" xml:space="preserve">ac lineæ horæ 24. </s>
            <s xml:id="echoid-s17228" xml:space="preserve">ab or. </s>
            <s xml:id="echoid-s17229" xml:space="preserve">vel occ. </s>
            <s xml:id="echoid-s17230" xml:space="preserve">vnà cum
              <lb/>
            linea æquinoctiali, propterea quòd in orientali horologio lineæ horarum ab occaſu, quæ parum
              <lb/>
              <note position="left" xlink:label="note-0270-04" xlink:href="note-0270-04a" xml:space="preserve">30</note>
            diſtant à linea horæ 12. </s>
            <s xml:id="echoid-s17231" xml:space="preserve">ab ortu, vel occaſu, vix ipſam lineam horæ 12. </s>
            <s xml:id="echoid-s17232" xml:space="preserve">interſecant, quod idem
              <lb/>
            cernitur in linels horarum ab occaſu, quæ parum à linea horizontali diſtant in horologio occi-
              <lb/>
            dentali, ſi cum linea horizontali conferantur, Hæc enim vix ab illis ſecatur. </s>
            <s xml:id="echoid-s17233" xml:space="preserve">Vnde in prioribus
              <lb/>
            deſcribendis vtemur linea horizontali, & </s>
            <s xml:id="echoid-s17234" xml:space="preserve">linea æquinoctiali: </s>
            <s xml:id="echoid-s17235" xml:space="preserve">In p@ſterioribus vero linea horæ 12.
              <lb/>
            </s>
            <s xml:id="echoid-s17236" xml:space="preserve">ab or. </s>
            <s xml:id="echoid-s17237" xml:space="preserve">vel occ. </s>
            <s xml:id="echoid-s17238" xml:space="preserve">& </s>
            <s xml:id="echoid-s17239" xml:space="preserve">linea æquinoctiali.</s>
            <s xml:id="echoid-s17240" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s17241" xml:space="preserve">PORRO lineam horæ 12. </s>
            <s xml:id="echoid-s17242" xml:space="preserve">ab ortu, vel occaſu hac ratione delineabimus. </s>
            <s xml:id="echoid-s17243" xml:space="preserve">Ex puncto A, deſcri
              <lb/>
              <note position="left" xlink:label="note-0270-05" xlink:href="note-0270-05a" xml:space="preserve">Deſcriptio li-
                <lb/>
              neæ horę 12. ab
                <lb/>
              or. uel occ. in
                <lb/>
              horologio Me-
                <lb/>
              ridiano.</note>
            bemus circulum cuiuſcunque magnitudinis @ L, qui ſecet lineam horæ 6. </s>
            <s xml:id="echoid-s17244" xml:space="preserve">à meridie, vel media
              <lb/>
            nocte, productam in M; </s>
            <s xml:id="echoid-s17245" xml:space="preserve">eritq́ue arcus K M, (ſi in deſcriptione lineæ horæ 6. </s>
            <s xml:id="echoid-s17246" xml:space="preserve">erratum non eſt, alti-
              <lb/>
            tudo poli ſupra Horizontem, propter angulum K A M, propterea quòd angulus contentus linea
              <lb/>
            horæ 6. </s>
            <s xml:id="echoid-s17247" xml:space="preserve">& </s>
            <s xml:id="echoid-s17248" xml:space="preserve">linea æquinoctiali rectus eſt, ex conſtructione, & </s>
            <s xml:id="echoid-s17249" xml:space="preserve">reliquus angulus ex hoc recto, quem
              <lb/>
              <note position="left" xlink:label="note-0270-06" xlink:href="note-0270-06a" xml:space="preserve">40</note>
            linea æquinoctialis infra horizontalem cum linea horizontali facit in A, ſit angulus altitudinis
              <lb/>
            Æquatoris ſupra Horizontem, ex conſtructione, vt propoſ. </s>
            <s xml:id="echoid-s17250" xml:space="preserve">25 huius lib, dictum eſt. </s>
            <s xml:id="echoid-s17251" xml:space="preserve">Deinde arcui
              <lb/>
            K M, ſumemus æqualem arcum M L, & </s>
            <s xml:id="echoid-s17252" xml:space="preserve">per L, & </s>
            <s xml:id="echoid-s17253" xml:space="preserve">A, rectam producemus L A. </s>
            <s xml:id="echoid-s17254" xml:space="preserve">Quam dico eſſe li-
              <lb/>
            neam horæ 12 ab ortu, vel occaſu. </s>
            <s xml:id="echoid-s17255" xml:space="preserve">Quoniam enim communes ſectiones circuli horæ 12. </s>
            <s xml:id="echoid-s17256" xml:space="preserve">ab or-
              <lb/>
            tu, vel occaſu factæ in planis parallelis, puta in Meridiani plano, & </s>
            <s xml:id="echoid-s17257" xml:space="preserve">plano horologii, parallelæ ſunt;
              <lb/>
            </s>
            <s xml:id="echoid-s17258" xml:space="preserve">
              <note position="left" xlink:label="note-0270-07" xlink:href="note-0270-07a" xml:space="preserve">16. vndec.</note>
            Item & </s>
            <s xml:id="echoid-s17259" xml:space="preserve">communes ſectiones Horizontis factæ in eiſdem planis; </s>
            <s xml:id="echoid-s17260" xml:space="preserve">erit angulus ſub illis ſectionibus
              <lb/>
            in plano Meridiani comprehenſus æqualis angulo ſub eiſdem ſectionibus contento in plano ho-
              <lb/>
              <note position="left" xlink:label="note-0270-08" xlink:href="note-0270-08a" xml:space="preserve">10. vndec.</note>
            rologii. </s>
            <s xml:id="echoid-s17261" xml:space="preserve">Cum ergo A K, ſit communis ſectio Horizontis, & </s>
            <s xml:id="echoid-s17262" xml:space="preserve">plani horologii, & </s>
            <s xml:id="echoid-s17263" xml:space="preserve">angulus K A L,
              <lb/>
            æqualis ei, quem in plano Meridiani conſtituunt communes ſectiones factæ à circulo horæ 12. </s>
            <s xml:id="echoid-s17264" xml:space="preserve">ab
              <lb/>
            ortu, vel occaſu, & </s>
            <s xml:id="echoid-s17265" xml:space="preserve">Horizonte, propterea quòd arcus K L, ſimilis eſt arcui Meridiani inter Hori-
              <lb/>
              <note position="left" xlink:label="note-0270-09" xlink:href="note-0270-09a" xml:space="preserve">50</note>
            zontem, & </s>
            <s xml:id="echoid-s17266" xml:space="preserve">circulum horæ 12. </s>
            <s xml:id="echoid-s17267" xml:space="preserve">interiecto, vt conſtat ex figura propoſ. </s>
            <s xml:id="echoid-s17268" xml:space="preserve">9. </s>
            <s xml:id="echoid-s17269" xml:space="preserve">ſuperioris lib. </s>
            <s xml:id="echoid-s17270" xml:space="preserve">cùm diame-
              <lb/>
            ter paralleli omnium ſemper apparentium maximi punctis K, L, claudatur; </s>
            <s xml:id="echoid-s17271" xml:space="preserve">erit recta L A, com-
              <lb/>
            munis ſectio circuli horæ 12. </s>
            <s xml:id="echoid-s17272" xml:space="preserve">ab ortu, vel occaſu, & </s>
            <s xml:id="echoid-s17273" xml:space="preserve">plani horologii; </s>
            <s xml:id="echoid-s17274" xml:space="preserve">quod eſt propoſitum. </s>
            <s xml:id="echoid-s17275" xml:space="preserve">Diui-
              <lb/>
            det autem ſemper linea æquinoctialis angulum contentum ſub linea horæ 12. </s>
            <s xml:id="echoid-s17276" xml:space="preserve">ab ortu, vel occaſu,
              <lb/>
            & </s>
            <s xml:id="echoid-s17277" xml:space="preserve">horizontali linea in vtroque horologio bifariam. </s>
            <s xml:id="echoid-s17278" xml:space="preserve">Cum enim angulus M A L, ſit ęqualis alti-
              <lb/>
            tudini poli ſupra Horizontem, erit reliquus ex recto contentus ſub linea L A, & </s>
            <s xml:id="echoid-s17279" xml:space="preserve">linea æquinoctia-
              <lb/>
            li æqualis altitudini Æquatoris ſupra Horizontem. </s>
            <s xml:id="echoid-s17280" xml:space="preserve">Quare cum & </s>
            <s xml:id="echoid-s17281" xml:space="preserve">angulus acutus contentus ſub
              <lb/>
            linea horizontali, & </s>
            <s xml:id="echoid-s17282" xml:space="preserve">linea æquinoctiali æqualis ſit, per conſtructionem, eidem altitudini Æquato-
              <lb/>
            ris; </s>
            <s xml:id="echoid-s17283" xml:space="preserve">ęquales inter ſe erunt anguli, quos linea æquinoctialis cum linea horæ 12. </s>
            <s xml:id="echoid-s17284" xml:space="preserve">& </s>
            <s xml:id="echoid-s17285" xml:space="preserve">horizontali linea
              <lb/>
            facit. </s>
            <s xml:id="echoid-s17286" xml:space="preserve">Vnde facile quoque ducetur linea horæ 12. </s>
            <s xml:id="echoid-s17287" xml:space="preserve">ſi ad lineã æquinoctialẽ cõſtituatur angulus altitu
              <lb/>
              <note position="left" xlink:label="note-0270-10" xlink:href="note-0270-10a" xml:space="preserve">Alia deſcriptio
                <lb/>
              lineæ horæ 12.
                <lb/>
              ab or. uel occ.</note>
            dinis Æquatoris verſus angulum obtuſum, quem linea æquinoctialis cum horizontali conſtituit.</s>
            <s xml:id="echoid-s17288" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum