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 |< < (167) of 677 > >|
    <echo version="1.0RC">
      <text xml:lang="it" type="free">
        <div xml:id="echoid-div576" type="section" level="1" n="146">
          <p style="it">
            <s xml:id="echoid-s10797" xml:space="preserve">
              <pb o="167" file="0187" n="187" rhead="LIBER SECVNDVS."/>
            aut minus diſtantem à puncto H, intercepta.</s>
            <s xml:id="echoid-s10798" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s10799" xml:space="preserve">STYLVS ſiue gnomon ex poſteriori modo deſcribendi parallelos ſignorum, hoc eſt, ex figuraradio-
              <lb/>
              <note position="right" xlink:label="note-0187-01" xlink:href="note-0187-01a" xml:space="preserve">Quã ratione ex
                <lb/>
              figura radiorũ
                <lb/>
              longitudo ſtyli,
                <lb/>
              eiusq́; locus in
                <lb/>
              horologio explo
                <lb/>
              retur.</note>
            rum, habetur, ſi e x puncto D, vbi radius Aequatoris axem A λ, ſecat, ad H I, perpendicularis ducatur,
              <lb/>
            D ρ, vel certè recta D ρ, faciens angulum ρ D I, æqualem angulo altitudinis poli. </s>
            <s xml:id="echoid-s10800" xml:space="preserve">Longitudo enim ſtyli
              <lb/>
            est ipſarecta D ρ: </s>
            <s xml:id="echoid-s10801" xml:space="preserve">Locus verò eius eſt punctum ρ, diſtans ab H, centro horologij interuallo H ρ, in linea
              <lb/>
            meridiana, vel ab æquinoctiali linea F K, ſpatio I ρ, in eadem linea meridiana verſus centrum H.</s>
            <s xml:id="echoid-s10802" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s10803" xml:space="preserve">QVOD ſi magnitudo gnomonis data ſit, inueniemus hac ratione diſtantiam figuræ radiorum Zodia-
              <lb/>
              <note position="right" xlink:label="note-0187-02" xlink:href="note-0187-02a" xml:space="preserve">Quomodo cx
                <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>
            ci à puncto H, in axe H D. </s>
            <s xml:id="echoid-s10804" xml:space="preserve">Nam horariæ lineæ ex H, procedentes eædem omnino manent, vt diximus, in
              <lb/>
            eadem altitudine poli. </s>
            <s xml:id="echoid-s10805" xml:space="preserve">In portione Analemmatis, quam propoſ. </s>
            <s xml:id="echoid-s10806" xml:space="preserve">1. </s>
            <s xml:id="echoid-s10807" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s10808" xml:space="preserve">deſcripſimus, abſcindatur ex
              <lb/>
            A D, diametro Verticalis circuli protracta, recta D M, æqualis gnomoni dato, & </s>
            <s xml:id="echoid-s10809" xml:space="preserve">per M, ipſi B C, diame
              <lb/>
              <note position="left" xlink:label="note-0187-03" xlink:href="note-0187-03a" xml:space="preserve">10</note>
            tro Horizontis parallela agatur N O, ſecans axem E D, in N, & </s>
            <s xml:id="echoid-s10810" xml:space="preserve">Aequatoris diametrũ F D, in O; </s>
            <s xml:id="echoid-s10811" xml:space="preserve">Pun
              <lb/>
            ctum ergo D, in figura radiorum Zodiaci huius propoſ. </s>
            <s xml:id="echoid-s10812" xml:space="preserve">in quo conueniunt omnes radij Zodiaci, diſtare de-
              <lb/>
            bet ab H, interuallo D N, cuiuſmodi eſt punctum D, prope A, in dicta figura radiorum Zodiaci huius pro-
              <lb/>
            poſ. </s>
            <s xml:id="echoid-s10813" xml:space="preserve">Si enim ex illo puncto D, demittatur perpendicularis ad H D, pro radio Aequatoris, & </s>
            <s xml:id="echoid-s10814" xml:space="preserve">ſimul ex D,
              <lb/>
            aliorum ſignorum radij emittantur, vt in Analemmate propoſ. </s>
            <s xml:id="echoid-s10815" xml:space="preserve">1. </s>
            <s xml:id="echoid-s10816" xml:space="preserve">ſuperioris lib. </s>
            <s xml:id="echoid-s10817" xml:space="preserve">deſcribemus beneficio li-
              <lb/>
            nearum horariarum inter hoſce radios, & </s>
            <s xml:id="echoid-s10818" xml:space="preserve">punctum H, comprehenſarum parallelos ſignorum, vt prius;
              <lb/>
            </s>
            <s xml:id="echoid-s10819" xml:space="preserve">quos percurret extremitas vmbræ à gnomone dato D M, proiectæ, vt ex demonſtratis conſtat. </s>
            <s xml:id="echoid-s10820" xml:space="preserve">Nam ſi ex
              <lb/>
            dicto puncto D, demittatur ad H I B, perpendicularis D K, erit hæc æqualis gnomoni dato D M. </s>
            <s xml:id="echoid-s10821" xml:space="preserve">Cum
              <lb/>
            enim angulus D H K, in triangulo D H K, figuræ radiorum Zodiaci huius propoſ. </s>
            <s xml:id="echoid-s10822" xml:space="preserve">æqualis ſit angulo
              <lb/>
            D N M, in triangulo D N M, portionis Analemmatis propoſ. </s>
            <s xml:id="echoid-s10823" xml:space="preserve">1. </s>
            <s xml:id="echoid-s10824" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s10825" xml:space="preserve">(Vterque enim eſt angulus
              <lb/>
              <note position="left" xlink:label="note-0187-04" xlink:href="note-0187-04a" xml:space="preserve">20</note>
            altitudinis poli) & </s>
            <s xml:id="echoid-s10826" xml:space="preserve">recti anguli ad K, & </s>
            <s xml:id="echoid-s10827" xml:space="preserve">M, æquales ſint; </s>
            <s xml:id="echoid-s10828" xml:space="preserve">ſit autem & </s>
            <s xml:id="echoid-s10829" xml:space="preserve">latus H D, lateri D N, æquale,
              <lb/>
            ex constructione; </s>
            <s xml:id="echoid-s10830" xml:space="preserve">erunt & </s>
            <s xml:id="echoid-s10831" xml:space="preserve">reliqua latera, nempe D K, D M, inter ſe, & </s>
            <s xml:id="echoid-s10832" xml:space="preserve">H K, N M, inter ſe æqualia.
              <lb/>
            </s>
            <s xml:id="echoid-s10833" xml:space="preserve">
              <note position="right" xlink:label="note-0187-05" xlink:href="note-0187-05a" xml:space="preserve">26. primi.</note>
            Quod est propoſitum. </s>
            <s xml:id="echoid-s10834" xml:space="preserve">Mutatis autem arcubus ſignorum, mutatur quoque ęquinoctialis linea, quæ tanto
              <lb/>
              <note position="right" xlink:label="note-0187-06" xlink:href="note-0187-06a" xml:space="preserve">Deſcriptio pa-
                <lb/>
              rallelorum, qui
                <lb/>
              non per ſigno -
                <lb/>
              rum initia, ſed
                <lb/>
              per alia puncta
                <lb/>
              Zodiaci tran-
                <lb/>
              ſeunt, in eodem
                <lb/>
              horologio.</note>
            ſpatio in linea meridiana abeſt ſemper à centro H, quanta est portio rectæ H B, in figura radiorum huius
              <lb/>
            propoſ. </s>
            <s xml:id="echoid-s10835" xml:space="preserve">inter H, & </s>
            <s xml:id="echoid-s10836" xml:space="preserve">radium Aequatoris inter cepta, vt & </s>
            <s xml:id="echoid-s10837" xml:space="preserve">paulo ante diximus.</s>
            <s xml:id="echoid-s10838" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s10839" xml:space="preserve">IAM verò ſi accipiamus declinationes aliorum punctorum Zodiaci, eorum{q́ue} parallelos in prima fi-
              <lb/>
            gura huius propoſ. </s>
            <s xml:id="echoid-s10840" xml:space="preserve">vel eorum radios ex D, in tertia figura ducamus, deſcribemus eodem modo eorum pa-
              <lb/>
            rallelos in prædicto horologio.</s>
            <s xml:id="echoid-s10841" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s10842" xml:space="preserve">IMMO propoſito die primo cuiuſque menſis, vel alio quouis, ſi quæratur locus Solis illo die in Zo-
              <lb/>
              <note position="right" xlink:label="note-0187-07" xlink:href="note-0187-07a" xml:space="preserve">Deſcriptio pa-
                <lb/>
              ralleli, in quo
                <lb/>
              Sol exiſtit quo-
                <lb/>
              libet die propo
                <lb/>
              ſito, in eodẽ ho
                <lb/>
              rologio.</note>
            diaco, & </s>
            <s xml:id="echoid-s10843" xml:space="preserve">declinatio, at que in prima figura huius propoſ. </s>
            <s xml:id="echoid-s10844" xml:space="preserve">eius parallelus, vel in figura radiorum eius ra-
              <lb/>
              <note position="left" xlink:label="note-0187-08" xlink:href="note-0187-08a" xml:space="preserve">30</note>
            dius ex D, ducatur, deſcribetur eadem ratione in horologio linea quædam flexa, quam vmbræ extremitas
              <lb/>
            percurret die illo propoſito.</s>
            <s xml:id="echoid-s10845" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s10846" xml:space="preserve">HAC ratione deſcribi poſſunt in horologio dies feſti ſanctorum, hoc eſt, lineæ quædam inflexę, quas
              <lb/>
              <note position="right" xlink:label="note-0187-09" xlink:href="note-0187-09a" xml:space="preserve">Deſcriptio die-
                <lb/>
              rum feſtorũ in
                <lb/>
              eodem horolo-
                <lb/>
              gio.</note>
            vmbra ſtyli percurrit illis diebus.</s>
            <s xml:id="echoid-s10847" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s10848" xml:space="preserve">HIS autem omnibus parallelis ſignorum aſcribi poſſunt characteres ſignorum, dies menſium, qui-
              <lb/>
              <note position="right" xlink:label="note-0187-10" xlink:href="note-0187-10a" xml:space="preserve">Quid aſcriben-
                <lb/>
              du ſit arcubus
                <lb/>
              ſignorum in ho
                <lb/>
              rologĩo delinea
                <lb/>
              tis.</note>
            bus vmbrę extremitas illos percurrit; </s>
            <s xml:id="echoid-s10849" xml:space="preserve">tempus ortus Solis & </s>
            <s xml:id="echoid-s10850" xml:space="preserve">occaſus, dierum & </s>
            <s xml:id="echoid-s10851" xml:space="preserve">crepuſculorum magni-
              <lb/>
            tudines, & </s>
            <s xml:id="echoid-s10852" xml:space="preserve">alia huiuſmodi, cuiuſmodi eſſet in horologio Italico, & </s>
            <s xml:id="echoid-s10853" xml:space="preserve">Babylonico, de quibus propoſ. </s>
            <s xml:id="echoid-s10854" xml:space="preserve">10. </s>
            <s xml:id="echoid-s10855" xml:space="preserve">& </s>
            <s xml:id="echoid-s10856" xml:space="preserve">
              <lb/>
            11. </s>
            <s xml:id="echoid-s10857" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s10858" xml:space="preserve">agetur, tempus meridiei, & </s>
            <s xml:id="echoid-s10859" xml:space="preserve">c.</s>
            <s xml:id="echoid-s10860" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s10861" xml:space="preserve">IN huius verò rei gratiam ducendæ ſunt quædam lineæ parallelæ ipſi lineę meridianæ tam ad ſini-
              <lb/>
            ſtram, quàm ad dexteram, vt in ſecunda figur a huius propoſ. </s>
            <s xml:id="echoid-s10862" xml:space="preserve">apparet. </s>
            <s xml:id="echoid-s10863" xml:space="preserve">Hę autem parallelę, quo remo-
              <lb/>
              <note position="left" xlink:label="note-0187-11" xlink:href="note-0187-11a" xml:space="preserve">40</note>
            tiores erunt à meridiana linea, eo maiori temporis ſpatio vmbra gnomonis in horologio excipietur.</s>
            <s xml:id="echoid-s10864" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s10865" xml:space="preserve">RVRSVS quoniam Sol à ♑, per ♈, aſcendit vſque ad ♋; </s>
            <s xml:id="echoid-s10866" xml:space="preserve">à ♋, verò per ♎, vſque ad ♑, deſcen-
              <lb/>
            dit, aſcribenda erunt ad priora ſigna, hæc verba. </s>
            <s xml:id="echoid-s10867" xml:space="preserve">A S C E N S V S S O L I S; </s>
            <s xml:id="echoid-s10868" xml:space="preserve">ad poſteriora verò hæc.
              <lb/>
            </s>
            <s xml:id="echoid-s10869" xml:space="preserve">D E S C E N S V S S O L I S. </s>
            <s xml:id="echoid-s10870" xml:space="preserve">Exemplum habes in horologio ſuperiori. </s>
            <s xml:id="echoid-s10871" xml:space="preserve">Quod etiam intelligendum
              <lb/>
            eſt in alijs horologijs, vt in Verticali, Meridiano Aequinoctiali, & </s>
            <s xml:id="echoid-s10872" xml:space="preserve">c.</s>
            <s xml:id="echoid-s10873" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s10874" xml:space="preserve">POSTREMO eoſdem parallelos, arcusve ſignorum in horologio, quod in ſcholio pręcedentis pro-
              <lb/>
              <note position="right" xlink:label="note-0187-12" xlink:href="note-0187-12a" xml:space="preserve">Qua atte arcus
                <lb/>
              ſignorum in ho
                <lb/>
              rologio, quod
                <lb/>
              centrum non
                <lb/>
              habear, deſcribẽ
                <lb/>
              di ſiut.</note>
            poſ. </s>
            <s xml:id="echoid-s10875" xml:space="preserve">etiamſi cent rum eius non haberemus, eiſdem ferè rationibus, quibus in hac propoſ. </s>
            <s xml:id="echoid-s10876" xml:space="preserve">vſi ſumus, deſcribe
              <lb/>
            mus. </s>
            <s xml:id="echoid-s10877" xml:space="preserve">Nam quòd ad priorem rationem attinet, ſi deſcribatur Analemma pro data altitudine poli, vt in
              <lb/>
            propoſito exemplo ad latitudinem grad. </s>
            <s xml:id="echoid-s10878" xml:space="preserve">20. </s>
            <s xml:id="echoid-s10879" xml:space="preserve">cum parallelis ſignorum, eorundem radijs, vt in conis ha-
              <lb/>
            beantur triangula per axem, at que adeò in recta R O, (quæ Horizonti B C, æquidiſtare debet ſecundum
              <lb/>
              <note position="left" xlink:label="note-0187-13" xlink:href="note-0187-13a" xml:space="preserve">50</note>
            diſtantiam rectæ D G, ſtylo F M, ęqualis) diametri ſectionum conicarum; </s>
            <s xml:id="echoid-s10880" xml:space="preserve">at que puncta K, L, M. </s>
            <s xml:id="echoid-s10881" xml:space="preserve">Q, P,
              <lb/>
            N, ex puncto I, (vbi Aequatoris diameter rectam. </s>
            <s xml:id="echoid-s10882" xml:space="preserve">R O, diuidit) accepta transferantur in lineam meri-
              <lb/>
            dianam A B, ex puncto E, vbi æquinoctialis linea, ac meridiana ſe interſecant; </s>
            <s xml:id="echoid-s10883" xml:space="preserve">postremo verò circa dia-
              <lb/>
            metros ſectionum conicarum deſcribantur ſectiones conicæ, ſecundum doctrinam propoſ. </s>
            <s xml:id="echoid-s10884" xml:space="preserve">8. </s>
            <s xml:id="echoid-s10885" xml:space="preserve">ſuperioris lib.
              <lb/>
            </s>
            <s xml:id="echoid-s10886" xml:space="preserve">it a vt per illa puncta K, L, M, & </s>
            <s xml:id="echoid-s10887" xml:space="preserve">c. </s>
            <s xml:id="echoid-s10888" xml:space="preserve">in horologio tranſeant, deſcripti erunt paralleli ſignorum.</s>
            <s xml:id="echoid-s10889" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s10890" xml:space="preserve">QVOD verò attinet ad posteriorem rationem ex figura radiorum Zodiaci depromptam, it a rem
              <lb/>
            perficiemus. </s>
            <s xml:id="echoid-s10891" xml:space="preserve">Inradium Aequatoris D C, transferantur omnia interualla inter centrum B, (ex quo cir-
              <lb/>
            culus deſcriptus fuit, at que in partes 24. </s>
            <s xml:id="echoid-s10892" xml:space="preserve">æquales diuiſus) & </s>
            <s xml:id="echoid-s10893" xml:space="preserve">horas in ęquinoctiali linea C D, interiecta, à
              <lb/>
            puncto D, imprimendo puncta in ipſo radio Aequatoris. </s>
            <s xml:id="echoid-s10894" xml:space="preserve">Deinde in axe D G, abſcindatur recta D G,
              <lb/>
            æqualis portioni axis F G, in horologio, ad finem ſcholij ant ecedentis propoſ. </s>
            <s xml:id="echoid-s10895" xml:space="preserve">deſcripto, & </s>
            <s xml:id="echoid-s10896" xml:space="preserve">per G, radio
              <lb/>
            Aequatoris D C, parallela agatur G H, in quam eodem modo à puncto G, transferantur ſpatia </s>
          </p>
        </div>
      </text>
    </echo>
Impressum