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: 103
[Note]
Page: 103
[Note]
Page: 103
[Note]
Page: 103
[Note]
Page: 103
[Note]
Page: 104
[Note]
Page: 104
[Note]
Page: 104
[Note]
Page: 104
[Note]
Page: 104
[Note]
Page: 104
[Note]
Page: 104
[Note]
Page: 105
[Note]
Page: 105
[Note]
Page: 105
[Note]
Page: 105
[Note]
Page: 105
[Note]
Page: 105
[Note]
Page: 105
[Note]
Page: 105
[Note]
Page: 105
[Note]
Page: 105
[Note]
Page: 106
[Note]
Page: 106
[Note]
Page: 106
[Note]
Page: 106
[Note]
Page: 106
[Note]
Page: 106
[Note]
Page: 106
[Note]
Page: 106
< >
page |< < (651) of 677 > >|
    <echo version="1.0RC">
      <text xml:lang="it" type="free">
        <div xml:id="echoid-div2101" type="section" level="1" n="532">
          <p>
            <s xml:id="echoid-s42853" xml:space="preserve">
              <pb o="651" file="0667" n="667" rhead="LIBER OCTAVVS."/>
            K T L, reliquo π K, ex ſemicirculo K P N, ſimilis erit: </s>
            <s xml:id="echoid-s42854" xml:space="preserve">proptereaq́ue π K ρ, erit inſtar arcus diur
              <lb/>
            ni, & </s>
            <s xml:id="echoid-s42855" xml:space="preserve">π N ρ, inſtar nocturni in parallelo, cuius declinatio H K; </s>
            <s xml:id="echoid-s42856" xml:space="preserve">atque tot horæ compre-
              <lb/>
            hendentur in arcubus K π, π N, quot in arcubus K b, b L. </s>
            <s xml:id="echoid-s42857" xml:space="preserve">Non aliter oſtendemus, arcus
              <lb/>
            K h, K d, ſimiles eſſe, propterea quòd ſinus toti K R, K O, eandem proportionem habent,
              <lb/>
              <note position="right" xlink:label="note-0667-01" xlink:href="note-0667-01a" xml:space="preserve">4. ſexti.</note>
              <figure xlink:label="fig-0667-01" xlink:href="fig-0667-01a" number="428">
                <image file="0667-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0667-01"/>
              </figure>
            quam ſinus verſi K g, K e. </s>
            <s xml:id="echoid-s42858" xml:space="preserve">Eadem
              <lb/>
            ratio eſt de aliis horis. </s>
            <s xml:id="echoid-s42859" xml:space="preserve">Nam ſi k P,
              <lb/>
            diſtantia à meridie complectatur
              <lb/>
            6. </s>
            <s xml:id="echoid-s42860" xml:space="preserve">horas, tranſibit P L, æquidiſtans
              <lb/>
            ipſi B D, per centra O, R, cũ pro-
              <lb/>
              <note position="left" xlink:label="note-0667-02" xlink:href="note-0667-02a" xml:space="preserve">10</note>
            portionaliter ſecet rectas K N, KL.
              <lb/>
            </s>
            <s xml:id="echoid-s42861" xml:space="preserve">Vnde manifeſtum eſt, quadrantes
              <lb/>
              <note position="right" xlink:label="note-0667-03" xlink:href="note-0667-03a" xml:space="preserve">2. ſe@@@.</note>
            k T, K P, ſimiles eſſe. </s>
            <s xml:id="echoid-s42862" xml:space="preserve">Si vero KZ,
              <lb/>
            diſtantia à meridie quadrantem
              <lb/>
            ſuperet, oſtendemus, arcum K L,
              <lb/>
            arcui k Z, ſimilem eſſe, quemad-
              <lb/>
            modum demonſtratum eſt, arcũ
              <lb/>
            K b, arcui K π, eſſe ſimilem. </s>
            <s xml:id="echoid-s42863" xml:space="preserve">Im-
              <lb/>
            mo eadem ratione, ſi k p, diſtan-
              <lb/>
            tia à meridie cadat infra Horizon
              <lb/>
            tem, arcus K ſ, arcui k p, ſimilis
              <lb/>
              <note position="left" xlink:label="note-0667-04" xlink:href="note-0667-04a" xml:space="preserve">20</note>
            erit. </s>
            <s xml:id="echoid-s42864" xml:space="preserve">Idem prorſus demonſtrabi-
              <lb/>
            tur in Aequatore, & </s>
            <s xml:id="echoid-s42865" xml:space="preserve">parallelo au-
              <lb/>
            ſtrali. </s>
            <s xml:id="echoid-s42866" xml:space="preserve">Pro Aequatore enim ducta
              <lb/>
            eſt I i, ipſi B D, parallela, ad quã
              <lb/>
            demiſſa eſt perpendicularis Hi,
              <lb/>
            quæ in μ, à recta B D, ſecatur bifa
              <lb/>
            riam, propterea quòd arcus D I,
              <lb/>
            atque adeo & </s>
            <s xml:id="echoid-s42867" xml:space="preserve">B i, arcui B H, æqualis eſt. </s>
            <s xml:id="echoid-s42868" xml:space="preserve">Hinc enim fit, vt recta H i, bifariam, & </s>
            <s xml:id="echoid-s42869" xml:space="preserve">ad rectos angulos
              <lb/>
            ſecetur à recta B D. </s>
            <s xml:id="echoid-s42870" xml:space="preserve">Poſtea deſcriptus eſt ex μ, circa H i, circulus H u i, à cuius puncto u, ducta eſt
              <lb/>
            θ ß, ipſi B D, parallela, & </s>
            <s xml:id="echoid-s42871" xml:space="preserve">ex δ, ad HI, perpendicularis δ ε, vſque ad Meridianum, qui inſtar eſt
              <lb/>
              <note position="left" xlink:label="note-0667-05" xlink:href="note-0667-05a" xml:space="preserve">30</note>
            Aequatoris circa HI, deſcripti. </s>
            <s xml:id="echoid-s42872" xml:space="preserve">Vbi perſpicuum eſt, arcum H ε, ſimilem eſſe arcui H u, quòd pro-
              <lb/>
            portionales ſint ſinus toti H E, H μ, ſinubus verſis H δ, H θ. </s>
            <s xml:id="echoid-s42873" xml:space="preserve">Pro parallelo autem auſtrali, cuius
              <lb/>
            diameter r t, ducta eſt t γ, ipſi B D, parallela, ad quam demiſſa eſt perpendicularis r γ, qua diuiſa
              <lb/>
            bifariam in λ, deſcriptus eſt circa r γ; </s>
            <s xml:id="echoid-s42874" xml:space="preserve">circulus r 8 γ, à cuius puncto 8, quod infra Horizontem
              <lb/>
            eſt, diſtatq́ue à meridie 8. </s>
            <s xml:id="echoid-s42875" xml:space="preserve">horis, ducta eſt φ χ, ipſi B D, parallela, atque ex ψad r t, excitata perpen
              <lb/>
            dicularis ψ ω, vſq; </s>
            <s xml:id="echoid-s42876" xml:space="preserve">ad parallelum diametri r t. </s>
            <s xml:id="echoid-s42877" xml:space="preserve">Vbi etiã manifeſtum eſt, arcum paralleli r 3 4 γ ω,
              <lb/>
            ſimilem eſſe arcui r 8, propterea quod eandem proportionem habent ſinus toti r ξ, r λ, quam ſi-
              <lb/>
              <note position="right" xlink:label="note-0667-06" xlink:href="note-0667-06a" xml:space="preserve">4.ſexti.</note>
            nus verſi r ψ, r φ. </s>
            <s xml:id="echoid-s42878" xml:space="preserve">Ex quibus omnibus colligitur, D S, altitudinem eſſe Solis in boreali parallelo
              <lb/>
            diametri K L, quando Sol ſex horis à meridie abeſt; </s>
            <s xml:id="echoid-s42879" xml:space="preserve">Item D Y, eſſe Solis altitudinem, cum diſtan
              <lb/>
            tia Solis à meridie eſt arcus K Z; </s>
            <s xml:id="echoid-s42880" xml:space="preserve">ac denique D q, altitudinem Solis eſſe ſupra inferiorem faciem
              <lb/>
              <note position="left" xlink:label="note-0667-07" xlink:href="note-0667-07a" xml:space="preserve">40</note>
            Horizontis, cum Solis diſtantia à meridie eſt arcus K p, quadrantem ſuperans: </s>
            <s xml:id="echoid-s42881" xml:space="preserve">Deinde D ß, eſſe
              <lb/>
            altitudinem Solis in Aequatore diſtantiam habentis arcum H u: </s>
            <s xml:id="echoid-s42882" xml:space="preserve">Poſtremo D χ, altitudinem So-
              <lb/>
            lis eſſe ſupra faciem inferiorem Horizontis in parallelo auſtrali diametri r t, quando diſtantia à@
              <lb/>
            meridie eſt arcus r 8, infra Horizontem cadens.</s>
            <s xml:id="echoid-s42883" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s42884" xml:space="preserve">HIS oſtenſis, liquido conſtat, in parallelis præcedentis quadrantis recte inuentas eſſe altitudi-
              <lb/>
            nes Solis. </s>
            <s xml:id="echoid-s42885" xml:space="preserve">Nam v.</s>
            <s xml:id="echoid-s42886" xml:space="preserve">g. </s>
            <s xml:id="echoid-s42887" xml:space="preserve">in quadrante parallelus ♏, & </s>
            <s xml:id="echoid-s42888" xml:space="preserve">♓, QlO a, reſpondet Meridiano proximi Ana
              <lb/>
            lemmatis A B C D, recta autem A B, Horizontis diametro A B, & </s>
            <s xml:id="echoid-s42889" xml:space="preserve">arcus O l, arcui meridianæ al-
              <lb/>
            titudinis B r, & </s>
            <s xml:id="echoid-s42890" xml:space="preserve">arcus O Q, hoc eſt, illi ęqualis O a, arcui B 6, cum hic æqualis ſit arcui depreſſio-
              <lb/>
            nis meridianæ D t, hoc e@t, arcui meridianæ altitudinis paralleli oppoſiti, quemadmodum & </s>
            <s xml:id="echoid-s42891" xml:space="preserve">in
              <lb/>
            quadrante arcus O Q, vel O a, æqualis acceptus eſt altitudini meridianæ paralleli oppoſiti. </s>
            <s xml:id="echoid-s42892" xml:space="preserve">Dein-
              <lb/>
              <note position="left" xlink:label="note-0667-08" xlink:href="note-0667-08a" xml:space="preserve">50</note>
            de recta R a, in quadrante reſpondet rectæ t γ, in Analemmate, cum tam R a, per finem depreſ-
              <lb/>
            ſionis meridianæ in quadrante parallela Horizonti A B, quàm t γ, per finem depreſſionis meri-
              <lb/>
            dianæ in Analemmate Horizonti B D, parallela ducatur: </s>
            <s xml:id="echoid-s42893" xml:space="preserve">Recta vero l R, in quadrante rectæ r γ,
              <lb/>
            in Analemmate reſpondet, cum vtraque ex fine altitudinis meridianæ perpendicularis ducatur
              <lb/>
            ad Horizontem. </s>
            <s xml:id="echoid-s42894" xml:space="preserve">Circulus denique α l n R, in quadrante reſpondet circulo r 8 γ, in Analemmate.
              <lb/>
            </s>
            <s xml:id="echoid-s42895" xml:space="preserve">Vnde quemadmodum in Analemmate rectę per horas circuli r 8 γ, ductæ parallelæ Horizontis
              <lb/>
            di
              <unsure/>
            ametro B D, dant in Meridiano A B C D, altitudines Solis, ita quoque in quadrante rectæ per
              <lb/>
            horas circuli α l n R, ductæ æquidiſtantes Horizonti A C, eaſdem altitudines indicabunt in pa-
              <lb/>
            ral
              <unsure/>
            lelo Q l O a, qui inſtar eſt Meridiani in Analemmate. </s>
            <s xml:id="echoid-s42896" xml:space="preserve">Eademq́ue ratio eſt in cæteris parallelis
              <lb/>
            quadrantis. </s>
            <s xml:id="echoid-s42897" xml:space="preserve">Omnia enim, quæ in proximo Analemmate conſtruenda præcepimus pro Solis alti-
              <lb/>
            tudinibus inueſtigandis, eadem in ſingulis parallelis quadrantis facta ſunt, vt altitudines Solis </s>
          </p>
        </div>
      </text>
    </echo>
Impressum