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

Table of Notes

< >
[Note]
Page: 51
[Note]
Page: 51
[Note]
Page: 51
[Note]
Page: 51
[Note]
Page: 51
[Note]
Page: 51
[Note]
Page: 51
[Note]
Page: 51
[Note]
Page: 52
[Note]
Page: 52
[Note]
Page: 52
[Note]
Page: 52
[Note]
Page: 52
[Note]
Page: 52
[Note]
Page: 52
[Note]
Page: 52
[Note]
Page: 52
[Note]
Page: 52
[Note]
Page: 52
[Note]
Page: 53
[Note]
Page: 53
[Note]
Page: 53
[Note]
Page: 53
[Note]
Page: 53
[Note]
Page: 53
[Note]
Page: 53
[Note]
Page: 53
[Note]
Page: 53
[Note]
Page: 53
[Note]
Page: 53
< >
page |< < (379) of 677 > >|
    <echo version="1.0RC">
      <text xml:lang="it" type="free">
        <div xml:id="echoid-div1263" type="section" level="1" n="316">
          <pb o="379" file="0395" n="395" rhead="LIBER TERTIVS."/>
          <p>
            <s xml:id="echoid-s24852" xml:space="preserve">INTELLIGANTVR quoque rectæ χ e, d f, moueri circa rectam χ d, donec perpendi-
              <lb/>
            culares ſint ad planum inclinatum, ambæ quidem ſurſum verſus in illis horologiis, quæ auſtrum
              <lb/>
            reſpiciunt, at verò in ijs, quæ ſpectant ad boream, recta quidem χ e, deorſum, recta verò d f, ſur-
              <lb/>
            ſum verſus. </s>
            <s xml:id="echoid-s24853" xml:space="preserve">Fient enim hac ratione puncta e, f, cadem, quæ φ, & </s>
            <s xml:id="echoid-s24854" xml:space="preserve">ω, propter æqualitatem linea-
              <lb/>
            rum χ φ, χ e, & </s>
            <s xml:id="echoid-s24855" xml:space="preserve">d ω, d f. </s>
            <s xml:id="echoid-s24856" xml:space="preserve">Cum igitur axis mundi per puncta φ, ω, tranſeat, vt iam demonſtra-
              <lb/>
            uimus, tranſibit idem per puncta e, f, in illo ſitu. </s>
            <s xml:id="echoid-s24857" xml:space="preserve">Quia verò axis tranſit quoque per centrum ρ, vel
              <lb/>
            vbi centrum non eſt, æquidiſtat lineæ indicis χ d, (vt enim paulo ante demonſtrauimus, idcirco
              <lb/>
            linea meridiana, & </s>
            <s xml:id="echoid-s24858" xml:space="preserve">linea indicis in horologio, vbi centrum non eſt, parallelæ ſunt, quia vtraque
              <lb/>
            parallela eſt axi mundi, vt conſtat ex demonſtratione propoſ. </s>
            <s xml:id="echoid-s24859" xml:space="preserve">18. </s>
            <s xml:id="echoid-s24860" xml:space="preserve">primi libri) fit vt recta e f, tran-
              <lb/>
              <note position="left" xlink:label="note-0395-01" xlink:href="note-0395-01a" xml:space="preserve">10</note>
            ſeat quoque per centrum ρ, vel ipſi χ d, æquidiſtet. </s>
            <s xml:id="echoid-s24861" xml:space="preserve">Nam ſi circumducatur vnà cum rectis χ e,
              <lb/>
            d f, circa χ d, coniungetur cum axe, ita vt idem ſit axis, quæ recta e f. </s>
            <s xml:id="echoid-s24862" xml:space="preserve">Quamobrem axis eleuan-
              <lb/>
            dus eſt ex centro ρ, ſecundum angulum f ρ d, vel e ρ χ, qui quidem eſt angulus altitudinis poli
              <lb/>
            ſupra planum inclinatum: </s>
            <s xml:id="echoid-s24863" xml:space="preserve">(quia huiuſmodi angulus æqualis eſt ei, quem axis mundi, & </s>
            <s xml:id="echoid-s24864" xml:space="preserve">commu
              <lb/>
              <note position="right" xlink:label="note-0395-02" xlink:href="note-0395-02a" xml:space="preserve">29. primi.</note>
            nis ſectio noui Meridiani ipſius plani inclinati, & </s>
            <s xml:id="echoid-s24865" xml:space="preserve">circuli maximi, cui planum horologii inclina-
              <lb/>
            ti æquidiſtat, conſtituunt; </s>
            <s xml:id="echoid-s24866" xml:space="preserve">propterea quod hæc communis ſectio parallela eſt.</s>
            <s xml:id="echoid-s24867" xml:space="preserve">
              <unsure/>
            rectæ χ d, in plano
              <lb/>
              <note position="right" xlink:label="note-0395-03" xlink:href="note-0395-03a" xml:space="preserve">16. vndec.</note>
            horologii. </s>
            <s xml:id="echoid-s24868" xml:space="preserve">Manifeſtum autem eſt, hunc angulum in Meridiano proprio plani inclinati conſtiru-
              <lb/>
            tum in centro mundi inſiſtere arcui altitudinis poli ſupra illum circulum maximum, cui horolo-
              <lb/>
            gium æquidiſtat) vel certè, vbi centrum non habetur, vt in tertia figura, eleuandus eſt ſecundum
              <lb/>
            perpendiculares χ e, d f, quæ æquales ſunt inter ſe, propterea quòd axis e f, lineæ indicis χ d,
              <lb/>
            æquidiſtat, vt probatum eſt. </s>
            <s xml:id="echoid-s24869" xml:space="preserve">Facile autem erit intelligere, cur in planis auſtrum reſpicientibus
              <lb/>
              <note position="left" xlink:label="note-0395-04" xlink:href="note-0395-04a" xml:space="preserve">20</note>
            utraque linea χ e, d f, ducenda ſit eadem ex parte recte χ d, in planis autem, quæ boreales partes
              <lb/>
            reſpiciunt, una ex parte dextra, & </s>
            <s xml:id="echoid-s24870" xml:space="preserve">altera ex ſiniſtra. </s>
            <s xml:id="echoid-s24871" xml:space="preserve">Quoniam enim in illis, ut diximus, vtrumque
              <lb/>
            triangulum E φ χ, φ ω d, ſurſum uerſus uoluitur circa rectas E χ, φ d, donec rectum ſit ad pla-
              <lb/>
            num inclinatum, ducenda eſt utraque linea χ e, d f, ex eadem parte rectæ χ d, ut cum utraque
              <lb/>
            circumuertitur, donec perpẽdicularis ſit ad planum inclinatum ex parte ſuperiori, puncta e, f, ca-
              <lb/>
            dant in puncta φ, ω, per quæ axis ducitur, & </s>
            <s xml:id="echoid-s24872" xml:space="preserve">quorum utrumque ex parte ſuperiori exiſtit. </s>
            <s xml:id="echoid-s24873" xml:space="preserve">Quia
              <lb/>
            uerò in his triangulum E φ χ, deorſum, & </s>
            <s xml:id="echoid-s24874" xml:space="preserve">φ ω d, ſurſum uerſus moueri intelligitur circa rectas
              <lb/>
            E φ, φ d, vt diximus, donec rectum ſit ad planum inclinatum, neceſſe eſt, unam ex una parte,
              <lb/>
            & </s>
            <s xml:id="echoid-s24875" xml:space="preserve">ex altera alteram duci, ut cum utraque circumducitur, donec ad planum inclinatum ſit perpẽ-
              <lb/>
            dicularis, recta quidem d f, ex parte ſuperiori plani ſit erecta, punctumq́; </s>
            <s xml:id="echoid-s24876" xml:space="preserve">f, in punctum ω, (quod
              <lb/>
              <note position="left" xlink:label="note-0395-05" xlink:href="note-0395-05a" xml:space="preserve">30</note>
            et iam ſupra planum eſt) cadat, recta verò χ e, ex parte inferiori erigatur, punctumq́ue e, idem
              <lb/>
            fiat, quod φ, punctum infra planum quoque exiſtens. </s>
            <s xml:id="echoid-s24877" xml:space="preserve">Ita enim fiet, vt recta ef, axem mundi, quẽ
              <lb/>
            per puncta φ, ω, tranſire oſtendimus, referat; </s>
            <s xml:id="echoid-s24878" xml:space="preserve">immò ſequetur, vt eadem linea conſtituatur ex e f,
              <lb/>
            & </s>
            <s xml:id="echoid-s24879" xml:space="preserve">axe mundi. </s>
            <s xml:id="echoid-s24880" xml:space="preserve">Similiter patet ratio, cur in prioribus horologijs accipiatur totus axis ρ fe, in po-
              <lb/>
            ſterioribus autem portio duntaxat ρ f, & </s>
            <s xml:id="echoid-s24881" xml:space="preserve">non ρ e: </s>
            <s xml:id="echoid-s24882" xml:space="preserve">quia videlicet in illis totus axis ρ f e, extat ſupra
              <lb/>
            planum inclinatum, quòd & </s>
            <s xml:id="echoid-s24883" xml:space="preserve">puncta f, e, ſupra idem planum exiſtant; </s>
            <s xml:id="echoid-s24884" xml:space="preserve">In his verò portio axis ρ f,
              <lb/>
            exiſtit quidem ſupra planum, at ρ e, infra, propterea quòd & </s>
            <s xml:id="echoid-s24885" xml:space="preserve">punctum f, ſupra idem, at punctum
              <lb/>
            e, infra exiſtit, vt ex dictis perſpicuum eſt.</s>
            <s xml:id="echoid-s24886" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s24887" xml:space="preserve">QVIA verò axis mundi ρ f, rectus eſt, per propoſ. </s>
            <s xml:id="echoid-s24888" xml:space="preserve">10. </s>
            <s xml:id="echoid-s24889" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s24890" xml:space="preserve">1. </s>
            <s xml:id="echoid-s24891" xml:space="preserve">Theod. </s>
            <s xml:id="echoid-s24892" xml:space="preserve">ad Æquatorem, tranſitq́;
              <lb/>
            </s>
            <s xml:id="echoid-s24893" xml:space="preserve">per eius centrum, atque adeò rectos angulos facit, per defin. </s>
            <s xml:id="echoid-s24894" xml:space="preserve">3. </s>
            <s xml:id="echoid-s24895" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s24896" xml:space="preserve">11. </s>
            <s xml:id="echoid-s24897" xml:space="preserve">Eucl. </s>
            <s xml:id="echoid-s24898" xml:space="preserve">cum quacunque recta
              <lb/>
              <note position="left" xlink:label="note-0395-06" xlink:href="note-0395-06a" xml:space="preserve">40</note>
            ex centro Aequatoris in eius plano ducta, efficitur, vt ſi punctum I, in axe pro centro mundi, ſiue
              <lb/>
            Æquatoris accipiatur, (poteſt enim quodcunque punctum axis ρ f, pro centro mundi ſumi, cum
              <lb/>
            inſenſibilis ſit, ac imperceptibilis eius diſtantia à centro mundi, ſi cum diſtantia ipſius à Sole cõ-
              <lb/>
            feratur, vt in ſphæra oſtendimus) recta G I, quæ perpendicularis eſt ad axem e f, ſecatq́ue lineam
              <lb/>
            indicis in G, ſit communis ſectio Aequatoris, & </s>
            <s xml:id="echoid-s24899" xml:space="preserve">plani per rectas χ e, d f, quæ ad planum incli-
              <lb/>
            natum perpendiculares ſunt, & </s>
            <s xml:id="echoid-s24900" xml:space="preserve">per lineam indicis χ d, atquc axem e f, ducti, quod quidem pla-
              <lb/>
              <note position="right" xlink:label="note-0395-07" xlink:href="note-0395-07a" xml:space="preserve">18. vndec.</note>
            num rectum eſt ad planum inclinatum, inſtar noui cuiuſdam, ac proprii Meridiani ipſius plani
              <lb/>
            inclinati: </s>
            <s xml:id="echoid-s24901" xml:space="preserve">adeò vt recta G I, non ſolum ſit in plano G I f d, ſed etiam in plano Aequatoris, quan-
              <lb/>
            doquidem axis cum ea in plano G I f d, exiſtente angulum rectum facit in I: </s>
            <s xml:id="echoid-s24902" xml:space="preserve">alias ſi Aequator nõ
              <lb/>
            tranſiret per rectam I G, ſed per aliam quampiam ex puncto I, quod pro centro Aequatoris acce-
              <lb/>
            ptum eſt, ductam, eſſet axis, per defin. </s>
            <s xml:id="echoid-s24903" xml:space="preserve">3. </s>
            <s xml:id="echoid-s24904" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s24905" xml:space="preserve">11. </s>
            <s xml:id="echoid-s24906" xml:space="preserve">Eucl. </s>
            <s xml:id="echoid-s24907" xml:space="preserve">ad hanc quoque perpendicularis, propte-
              <lb/>
              <note position="left" xlink:label="note-0395-08" xlink:href="note-0395-08a" xml:space="preserve">50</note>
            rea quòd rectus eſt ad planum Aequatoris. </s>
            <s xml:id="echoid-s24908" xml:space="preserve">Quare in plano G I f d, duæ perpendiculares ad axẽ
              <lb/>
            in puncto I, ducerentur, quod eſt abſurdum. </s>
            <s xml:id="echoid-s24909" xml:space="preserve">Occurret igitur Aequatoris planum per rectam I G,
              <lb/>
            ductum plano horologii inclinati in puncto G, lineæ indicis, ibiq́ue ipſum ſecabit; </s>
            <s xml:id="echoid-s24910" xml:space="preserve">ac proinde
              <lb/>
            per punctum G, ducenda erit linea æquinoctialis, hoc eſt, ſectio communis Aequatoris, & </s>
            <s xml:id="echoid-s24911" xml:space="preserve">plani
              <lb/>
              <note position="right" xlink:label="note-0395-09" xlink:href="note-0395-09a" xml:space="preserve">18. vndec.</note>
            horologii inclinati. </s>
            <s xml:id="echoid-s24912" xml:space="preserve">Quoniam verò planum G I f d, rectum eſt ad Aequatorem, propterea quòd
              <lb/>
            axis e f, per quem ducitur, ad eundem rectus eſt, vt diximus, (quod idem ex propoſ. </s>
            <s xml:id="echoid-s24913" xml:space="preserve">15. </s>
            <s xml:id="echoid-s24914" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s24915" xml:space="preserve">1.
              <lb/>
            </s>
            <s xml:id="echoid-s24916" xml:space="preserve">Theod. </s>
            <s xml:id="echoid-s24917" xml:space="preserve">conſtare poteſt, propterea quòd planum G I f d, per axem Aequatoris e f, atque adeo per
              <lb/>
            eius polos ductum ſit) erit viciſſim & </s>
            <s xml:id="echoid-s24918" xml:space="preserve">Aequator ad planum G I f d, rectus: </s>
            <s xml:id="echoid-s24919" xml:space="preserve">Eſt autem & </s>
            <s xml:id="echoid-s24920" xml:space="preserve">planum
              <lb/>
            horologij inclinati rectũ ad idem planũ G I f d, eò quòd hoc ad illud proximè oſtenſum ſit rectũ. </s>
            <s xml:id="echoid-s24921" xml:space="preserve">
              <lb/>
            Igitur & </s>
            <s xml:id="echoid-s24922" xml:space="preserve">communis ſectio Aequatoris, & </s>
            <s xml:id="echoid-s24923" xml:space="preserve">plani horologij inclinati ad idem planum G I f d,
              <lb/>
              <note position="right" xlink:label="note-0395-10" xlink:href="note-0395-10a" xml:space="preserve">19. vndec.</note>
            </s>
          </p>
        </div>
      </text>
    </echo>
Impressum