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-div674" type="section" level="1" n="171">
          <p>
            <s xml:id="echoid-s13157" xml:space="preserve">
              <pb o="197" file="0217" n="217" rhead="LIBER SECVNDVS."/>
            Analemmatis propoſ. </s>
            <s xml:id="echoid-s13158" xml:space="preserve">1. </s>
            <s xml:id="echoid-s13159" xml:space="preserve">huius libri, ſumatur arcus E K, æqualis arcui C E, altitudinis poli, ita vt
              <lb/>
              <note position="right" xlink:label="note-0217-01" xlink:href="note-0217-01a" xml:space="preserve">Quomodo li-
                <lb/>
              nea horæ 12. ab
                <lb/>
              or. vel occ. du-
                <lb/>
              cenda ſi@ in h@-
                <lb/>
              rologio ho@@zõ-
                <lb/>
              tali.</note>
            recta ducta C K, diameter ſit paralleli omnium ſemper apparentium maximi, nempe communis
              <lb/>
            eius, & </s>
            <s xml:id="echoid-s13160" xml:space="preserve">Meridiani ſectio. </s>
            <s xml:id="echoid-s13161" xml:space="preserve">Et quoniam circulus horæ duodecimæ ab occaſu tangit dictum paral-
              <lb/>
            lelum in puncto K, quod in diametro eiuſdem paralleli opponitur puncto C, in quo eundem pa-
              <lb/>
            rallelum tangit Horizon, ſeu circulus horæ 24. </s>
            <s xml:id="echoid-s13162" xml:space="preserve">ab or. </s>
            <s xml:id="echoid-s13163" xml:space="preserve">vel occ. </s>
            <s xml:id="echoid-s13164" xml:space="preserve">vt cõſtat ex figura propoſ. </s>
            <s xml:id="echoid-s13165" xml:space="preserve">9. </s>
            <s xml:id="echoid-s13166" xml:space="preserve">ſuperio-
              <lb/>
            ris lib. </s>
            <s xml:id="echoid-s13167" xml:space="preserve">tranſibit Meridianus per K, cõtactum dictorum circulorum. </s>
            <s xml:id="echoid-s13168" xml:space="preserve">Cum ergo trãſeat quoque per
              <lb/>
            polos dicti paralleli, tranſibit quoque per polos circuli horæ 12. </s>
            <s xml:id="echoid-s13169" xml:space="preserve">ab or. </s>
            <s xml:id="echoid-s13170" xml:space="preserve">vel occ. </s>
            <s xml:id="echoid-s13171" xml:space="preserve">ex propoſ. </s>
            <s xml:id="echoid-s13172" xml:space="preserve">5. </s>
            <s xml:id="echoid-s13173" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s13174" xml:space="preserve">2.
              <lb/>
            </s>
            <s xml:id="echoid-s13175" xml:space="preserve">Theod. </s>
            <s xml:id="echoid-s13176" xml:space="preserve">Igitur per propoſ. </s>
            <s xml:id="echoid-s13177" xml:space="preserve">15. </s>
            <s xml:id="echoid-s13178" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s13179" xml:space="preserve">1. </s>
            <s xml:id="echoid-s13180" xml:space="preserve">Theod. </s>
            <s xml:id="echoid-s13181" xml:space="preserve">Meridianus ad dictum circulum rectus erit, & </s>
            <s xml:id="echoid-s13182" xml:space="preserve">hic vi-
              <lb/>
            ciſſim ad Meridianum rectus. </s>
            <s xml:id="echoid-s13183" xml:space="preserve">Rurſus quia dictus circulus horæ 12. </s>
            <s xml:id="echoid-s13184" xml:space="preserve">ab or. </s>
            <s xml:id="echoid-s13185" xml:space="preserve">vel occ. </s>
            <s xml:id="echoid-s13186" xml:space="preserve">cum ſit maxi-
              <lb/>
            mus, tranſit per centrum mundi D, oſtenſumq́; </s>
            <s xml:id="echoid-s13187" xml:space="preserve">eſt, eundem tranſire per K, erit recta ex K, per D,
              <lb/>
              <note position="left" xlink:label="note-0217-02" xlink:href="note-0217-02a" xml:space="preserve">10</note>
            educta communis ſectio Meridiani, & </s>
            <s xml:id="echoid-s13188" xml:space="preserve">circuli horæ 12. </s>
            <s xml:id="echoid-s13189" xml:space="preserve">ab or. </s>
            <s xml:id="echoid-s13190" xml:space="preserve">vel occ. </s>
            <s xml:id="echoid-s13191" xml:space="preserve">occurrens in plano horologii
              <lb/>
            lineæ meridianæ H I, in puncto L. </s>
            <s xml:id="echoid-s13192" xml:space="preserve">Dico iam rectam, quæ per L, ad lineam meridianam horologii
              <lb/>
            ducitur perpendicularis, eſſe lineam horæ 12. </s>
            <s xml:id="echoid-s13193" xml:space="preserve">ab or. </s>
            <s xml:id="echoid-s13194" xml:space="preserve">vel occ. </s>
            <s xml:id="echoid-s13195" xml:space="preserve">Quoniam enim tam planum horolo-
              <lb/>
            gij horizontalis, quàm planum circuli horæ 12. </s>
            <s xml:id="echoid-s13196" xml:space="preserve">ab or. </s>
            <s xml:id="echoid-s13197" xml:space="preserve">vel occ. </s>
            <s xml:id="echoid-s13198" xml:space="preserve">rectum eſt, vt proxime demonſtra-
              <lb/>
            uimus, ad Meridianum, erit quoque communis eorum ſectio, nimirum linea horæ 12. </s>
            <s xml:id="echoid-s13199" xml:space="preserve">ab or. </s>
            <s xml:id="echoid-s13200" xml:space="preserve">vel
              <lb/>
            occ. </s>
            <s xml:id="echoid-s13201" xml:space="preserve">ad eundem Meridianum, atque adeo & </s>
            <s xml:id="echoid-s13202" xml:space="preserve">ad lineam meridianam H I, in Meridiano exiſtentem,
              <lb/>
              <note position="right" xlink:label="note-0217-03" xlink:href="note-0217-03a" xml:space="preserve">19. vndec.</note>
            per defin. </s>
            <s xml:id="echoid-s13203" xml:space="preserve">3. </s>
            <s xml:id="echoid-s13204" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s13205" xml:space="preserve">11. </s>
            <s xml:id="echoid-s13206" xml:space="preserve">Eucl. </s>
            <s xml:id="echoid-s13207" xml:space="preserve">perpendicularis in puncto L, in quo diximus communem ſectionem cir-
              <lb/>
            culi horæ 12. </s>
            <s xml:id="echoid-s13208" xml:space="preserve">ab or. </s>
            <s xml:id="echoid-s13209" xml:space="preserve">vel occ. </s>
            <s xml:id="echoid-s13210" xml:space="preserve">& </s>
            <s xml:id="echoid-s13211" xml:space="preserve">Meridiani, ac proinde & </s>
            <s xml:id="echoid-s13212" xml:space="preserve">ipſum circulum horæ 12 ab or. </s>
            <s xml:id="echoid-s13213" xml:space="preserve">vel occ. </s>
            <s xml:id="echoid-s13214" xml:space="preserve">pla
              <lb/>
            no horologii occurrere. </s>
            <s xml:id="echoid-s13215" xml:space="preserve">Recta igitur in plano horologii ducta per L, ad meridianam lineam per-
              <lb/>
            pendicularis, dabit lineam horæ 12. </s>
            <s xml:id="echoid-s13216" xml:space="preserve">ab or. </s>
            <s xml:id="echoid-s13217" xml:space="preserve">vel occ. </s>
            <s xml:id="echoid-s13218" xml:space="preserve">Igitur ſi in lineam meridianam horologii ex
              <lb/>
              <note position="left" xlink:label="note-0217-04" xlink:href="note-0217-04a" xml:space="preserve">20</note>
            centro H, transferatur punctum L, ſumptum beneficio circini ex puncto H, portionis Analemma
              <lb/>
            tis, ac per L, lin ea perpendicularis ad meridianam lineam, vel parallela lineę horę 6. </s>
            <s xml:id="echoid-s13219" xml:space="preserve">à meridie, vel
              <lb/>
            media nocte, ſeu linea æquinoctiali ducatur, erit hæc ipſa linea horæ 12. </s>
            <s xml:id="echoid-s13220" xml:space="preserve">ab ortu, vel occaſu.
              <lb/>
            </s>
            <s xml:id="echoid-s13221" xml:space="preserve">
              <note position="right" xlink:label="note-0217-05" xlink:href="note-0217-05a" xml:space="preserve">Alia deſcriptio
                <lb/>
              horolog@i Itali-
                <lb/>
              ci horizontalis,
                <lb/>
              beneficio lineæ
                <lb/>
              horæ 12. ab or.
                <lb/>
              vel occ@ abſol-
                <lb/>
              uenda.</note>
            </s>
          </p>
          <p>
            <s xml:id="echoid-s13222" xml:space="preserve">DESCRIPTA autem hoc modo linea horæ duodecimæ ab ortu, vel occaſu, facile reliquæ
              <lb/>
            horæ ab occaſu deſcribentur, ſi diligenter in linea æquinoctiali, & </s>
            <s xml:id="echoid-s13223" xml:space="preserve">linea horæ duodecimæ ab or.
              <lb/>
            </s>
            <s xml:id="echoid-s13224" xml:space="preserve">vel occ. </s>
            <s xml:id="echoid-s13225" xml:space="preserve">notentur puncta ex tabula propoſ. </s>
            <s xml:id="echoid-s13226" xml:space="preserve">19. </s>
            <s xml:id="echoid-s13227" xml:space="preserve">& </s>
            <s xml:id="echoid-s13228" xml:space="preserve">tabula ſecunda propoſ. </s>
            <s xml:id="echoid-s13229" xml:space="preserve">20. </s>
            <s xml:id="echoid-s13230" xml:space="preserve">præcedentis libri, per
              <lb/>
            quæ lineæ horarum ab occaſu tranſeunt. </s>
            <s xml:id="echoid-s13231" xml:space="preserve">Rectæ enim correſpondentia puncta connectentes da-
              <lb/>
            bunt horarias lineas ab occaſu. </s>
            <s xml:id="echoid-s13232" xml:space="preserve">Exemplum. </s>
            <s xml:id="echoid-s13233" xml:space="preserve">Hora 23. </s>
            <s xml:id="echoid-s13234" xml:space="preserve">ab occaſu tranſit in linea æquinoctiali per
              <lb/>
            punctum horæ quintæ à meridie, vel media nocte, & </s>
            <s xml:id="echoid-s13235" xml:space="preserve">in linea horæ duodecimæ ab ortu, vel occaſu
              <lb/>
            per punctum horæ 5 {1/2}. </s>
            <s xml:id="echoid-s13236" xml:space="preserve">à meridie, vt ex dictis tabulis conſtat. </s>
            <s xml:id="echoid-s13237" xml:space="preserve">Igitur recta per illa duo puncta
              <lb/>
              <note position="left" xlink:label="note-0217-06" xlink:href="note-0217-06a" xml:space="preserve">30</note>
            tranſiens dabit horariam lineam, quæ horam 23. </s>
            <s xml:id="echoid-s13238" xml:space="preserve">ab occaſu indicet. </s>
            <s xml:id="echoid-s13239" xml:space="preserve">Eodem modo tranſibit linea
              <lb/>
            horæ 22. </s>
            <s xml:id="echoid-s13240" xml:space="preserve">ab occaſu per punctum horæ quartæ à meridie in linea æquinoctiali, & </s>
            <s xml:id="echoid-s13241" xml:space="preserve">per punctum ho
              <lb/>
            ræ quintæ à meridie in linea horæ duodecimæ ab ortu, vel occaſu; </s>
            <s xml:id="echoid-s13242" xml:space="preserve">& </s>
            <s xml:id="echoid-s13243" xml:space="preserve">ſic de cæteris.
              <lb/>
            </s>
            <s xml:id="echoid-s13244" xml:space="preserve">
              <note position="right" xlink:label="note-0217-07" xlink:href="note-0217-07a" xml:space="preserve">Alia deſcriptio
                <lb/>
              horolog@i Itali-
                <lb/>
              ci horizontalis,
                <lb/>
              ex tabula pri-
                <lb/>
              ma propoſ. 20.
                <lb/>
              ſuperioris lib.
                <lb/>
              vbi quęlibet ho
                <lb/>
              ra ab occ. paral-
                <lb/>
              lela eſt alicui
                <lb/>
              horæ à mer. vel
                <lb/>
              med. noc.</note>
            </s>
          </p>
          <p>
            <s xml:id="echoid-s13245" xml:space="preserve">POSSVNT etiam lineæ horarum ab occaſu facile ex tabula prima propoſ. </s>
            <s xml:id="echoid-s13246" xml:space="preserve">20. </s>
            <s xml:id="echoid-s13247" xml:space="preserve">ſuperioris li-
              <lb/>
            bri deſcribi hoc modo. </s>
            <s xml:id="echoid-s13248" xml:space="preserve">Per punctum horæ quintæ à meridie, vel media nocte in linea æquino-
              <lb/>
            ctiali, per quod nimirum tranſit hora 23. </s>
            <s xml:id="echoid-s13249" xml:space="preserve">ab occaſu, vt ex tabula propoſ. </s>
            <s xml:id="echoid-s13250" xml:space="preserve">19@ eiuſdem libri conſtat,
              <lb/>
            agatur recta parallela lineæ horæ 11 {1/2}. </s>
            <s xml:id="echoid-s13251" xml:space="preserve">à meridie, vel media nocte. </s>
            <s xml:id="echoid-s13252" xml:space="preserve">Hæc enim erit linea horæ 23.
              <lb/>
            </s>
            <s xml:id="echoid-s13253" xml:space="preserve">ab occaſu. </s>
            <s xml:id="echoid-s13254" xml:space="preserve">Sic quoque linea horæ 22. </s>
            <s xml:id="echoid-s13255" xml:space="preserve">ab occaſu per punctum horæ quartæ à meridie tranſiens,
              <lb/>
            parallela erit lineæ horæ vndecimæ à meridie, vel media nocte, &</s>
            <s xml:id="echoid-s13256" xml:space="preserve">c. </s>
            <s xml:id="echoid-s13257" xml:space="preserve">vt perſpicuum eſt ex tabula pri
              <lb/>
            ma propoſ. </s>
            <s xml:id="echoid-s13258" xml:space="preserve">20. </s>
            <s xml:id="echoid-s13259" xml:space="preserve">præcedentis libri, in qua quælibet binæ horæ parallelæ ſunt in horologio horizon
              <lb/>
              <note position="left" xlink:label="note-0217-08" xlink:href="note-0217-08a" xml:space="preserve">40</note>
            tali, vt in ſcholio propoſ. </s>
            <s xml:id="echoid-s13260" xml:space="preserve">22. </s>
            <s xml:id="echoid-s13261" xml:space="preserve">eiuſdem lib demonſtrauimus. </s>
            <s xml:id="echoid-s13262" xml:space="preserve">Deſcribentur autem expeditè huiuſ-
              <lb/>
            modi parallelæ, ſi ſumantur rectæ in æquinoctiali linea interceptę inter puncta, per quæ horæ ab
              <lb/>
            occ. </s>
            <s xml:id="echoid-s13263" xml:space="preserve">duci debent, iuxta tabulam propoſ. </s>
            <s xml:id="echoid-s13264" xml:space="preserve">19. </s>
            <s xml:id="echoid-s13265" xml:space="preserve">libri antecedentis, & </s>
            <s xml:id="echoid-s13266" xml:space="preserve">puncta horarum à meridie, vel
              <lb/>
            med noc. </s>
            <s xml:id="echoid-s13267" xml:space="preserve">quibus illæ, iuxta tabulam primam propoſ. </s>
            <s xml:id="echoid-s13268" xml:space="preserve">20. </s>
            <s xml:id="echoid-s13269" xml:space="preserve">eiuſdem lib. </s>
            <s xml:id="echoid-s13270" xml:space="preserve">æquidiſtantes ſunt, transfe
              <lb/>
            ranturq́ue ex H, centro horologii in lineam horæ ſextæ à meridie, vel media nocte. </s>
            <s xml:id="echoid-s13271" xml:space="preserve">Vt ſi lineæ in
              <lb/>
            æquinoctiali linea interiectæ inter punctum horæ vndecimæ à meridie@ cui æquidiſtat hora 22. </s>
            <s xml:id="echoid-s13272" xml:space="preserve">ab
              <lb/>
            occaſu, & </s>
            <s xml:id="echoid-s13273" xml:space="preserve">punctum horæ quartæ à meridie, per quod tranſit eadem hora 22. </s>
            <s xml:id="echoid-s13274" xml:space="preserve">ſumatur in linea ho-
              <lb/>
            ræ ſextæ à meridie æqualis H X, erit recta per X, & </s>
            <s xml:id="echoid-s13275" xml:space="preserve">punctum horæ quartæ à meridie ducta, lineę
              <lb/>
            horæ vndecimæ à meridie, vel media nocte paralle
              <unsure/>
            la, ac propterea horam 22. </s>
            <s xml:id="echoid-s13276" xml:space="preserve">ab occaſu indica-
              <lb/>
              <note position="right" xlink:label="note-0217-09" xlink:href="note-0217-09a" xml:space="preserve">33. primi.</note>
            bit, &</s>
            <s xml:id="echoid-s13277" xml:space="preserve">c. </s>
            <s xml:id="echoid-s13278" xml:space="preserve">Quòd ſi lineæ æquinoctiali agatur parallela longius ab ea diſtans, in quam transferantur
              <lb/>
              <note position="left" xlink:label="note-0217-10" xlink:href="note-0217-10a" xml:space="preserve">50</note>
            eędem rectę interceptę in linea æquinoctiali inter puncta, per quę duci debent horę ab occ. </s>
            <s xml:id="echoid-s13279" xml:space="preserve">& </s>
            <s xml:id="echoid-s13280" xml:space="preserve">pun
              <lb/>
            cta horarum à mer. </s>
            <s xml:id="echoid-s13281" xml:space="preserve">vel med. </s>
            <s xml:id="echoid-s13282" xml:space="preserve">noc. </s>
            <s xml:id="echoid-s13283" xml:space="preserve">quibus illę ęquidiſtant, initio ſemper facto ab horis à mer. </s>
            <s xml:id="echoid-s13284" xml:space="preserve">vel
              <lb/>
            med. </s>
            <s xml:id="echoid-s13285" xml:space="preserve">noc. </s>
            <s xml:id="echoid-s13286" xml:space="preserve">quibus ęquidiſtare debent horę ab occ. </s>
            <s xml:id="echoid-s13287" xml:space="preserve">multo accuratius ducentur horę ab occ. </s>
            <s xml:id="echoid-s13288" xml:space="preserve">cum
              <lb/>
            quęlibet per tria puncta ducatur, quorum vnum eſt in linea horæ ſextæ à mer. </s>
            <s xml:id="echoid-s13289" xml:space="preserve">vel med. </s>
            <s xml:id="echoid-s13290" xml:space="preserve">noc. </s>
            <s xml:id="echoid-s13291" xml:space="preserve">alterũ
              <lb/>
            in æquinoctiali linea, & </s>
            <s xml:id="echoid-s13292" xml:space="preserve">in parallela vltimò ducta tertium.
              <lb/>
            </s>
            <s xml:id="echoid-s13293" xml:space="preserve">
              <note position="right" xlink:label="note-0217-11" xlink:href="note-0217-11a" xml:space="preserve">Quæ horæ a@
                <lb/>
              occ. ſe mutuo
                <lb/>
              ſecent in linea
                <lb/>
              horæ 6 à mer.
                <lb/>
              vel med. noc.</note>
            </s>
          </p>
          <p>
            <s xml:id="echoid-s13294" xml:space="preserve">PRAETEREA hora 23. </s>
            <s xml:id="echoid-s13295" xml:space="preserve">& </s>
            <s xml:id="echoid-s13296" xml:space="preserve">13. </s>
            <s xml:id="echoid-s13297" xml:space="preserve">ab occaſu ſecant ſe mutuo, ſi rectę deſcriptę ſint, in linea
              <lb/>
            horę ſextę à meridie, vel med. </s>
            <s xml:id="echoid-s13298" xml:space="preserve">noc. </s>
            <s xml:id="echoid-s13299" xml:space="preserve">Item hora 22. </s>
            <s xml:id="echoid-s13300" xml:space="preserve">& </s>
            <s xml:id="echoid-s13301" xml:space="preserve">14. </s>
            <s xml:id="echoid-s13302" xml:space="preserve">necnon 21. </s>
            <s xml:id="echoid-s13303" xml:space="preserve">& </s>
            <s xml:id="echoid-s13304" xml:space="preserve">15. </s>
            <s xml:id="echoid-s13305" xml:space="preserve">&</s>
            <s xml:id="echoid-s13306" xml:space="preserve">c. </s>
            <s xml:id="echoid-s13307" xml:space="preserve">vt patet ex tabula
              <lb/>
            tertia propoſ. </s>
            <s xml:id="echoid-s13308" xml:space="preserve">20. </s>
            <s xml:id="echoid-s13309" xml:space="preserve">pręcedentis libri.
              <lb/>
            </s>
            <s xml:id="echoid-s13310" xml:space="preserve">
              <note position="right" xlink:label="note-0217-12" xlink:href="note-0217-12a" xml:space="preserve">Quæ lineæ ho-
                <lb/>
              ra@um ab occ. ſe
                <lb/>
              @@utu@ ſecẽt in
                <lb/>
              l@nea meridia-
                <lb/>
              na.</note>
            </s>
          </p>
          <p>
            <s xml:id="echoid-s13311" xml:space="preserve">RVRSVS ex tabula quarta propoſ. </s>
            <s xml:id="echoid-s13312" xml:space="preserve">eiuſdem, hora decima, & </s>
            <s xml:id="echoid-s13313" xml:space="preserve">decimaquarta ab occaſu ſe in-
              <lb/>
            terſecant in linea meridiana, ſeu horę duodecimę à meridie, vel med. </s>
            <s xml:id="echoid-s13314" xml:space="preserve">noc. </s>
            <s xml:id="echoid-s13315" xml:space="preserve">Item hora vndecima,
              <lb/>
            & </s>
            <s xml:id="echoid-s13316" xml:space="preserve">decimatertia, &</s>
            <s xml:id="echoid-s13317" xml:space="preserve">c. </s>
            <s xml:id="echoid-s13318" xml:space="preserve">Denique ex propoſ. </s>
            <s xml:id="echoid-s13319" xml:space="preserve">20. </s>
            <s xml:id="echoid-s13320" xml:space="preserve">ſuperioris libri, & </s>
            <s xml:id="echoid-s13321" xml:space="preserve">figura propoſ. </s>
            <s xml:id="echoid-s13322" xml:space="preserve">9. </s>
            <s xml:id="echoid-s13323" xml:space="preserve">libri eiuſdem, </s>
          </p>
        </div>
      </text>
    </echo>
Impressum