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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      <text xml:lang="it" type="free">
        <div xml:id="echoid-div1639" type="section" level="1" n="418">
          <p>
            <s xml:id="echoid-s31962" xml:space="preserve">
              <pb o="496" file="0512" n="512" rhead="GNOMONICES"/>
            Quia vero hi duo circuli occurrunt plano horologij in M, vbi axis mundi eidẽ occurrit, faciuntq́;
              <lb/>
            </s>
            <s xml:id="echoid-s31963" xml:space="preserve">cum @o ſectiones communes, lineas rectas, quæ illis in Horizonte æquidiſtant, comprehendent
              <lb/>
              <note position="left" xlink:label="note-0512-01" xlink:href="note-0512-01a" xml:space="preserve">16. vndec.</note>
            huiuſmodi lineæ in plano horologij angulum æqualem illi angulo, quẽ in Horizonte priores il-
              <lb/>
              <note position="left" xlink:label="note-0512-02" xlink:href="note-0512-02a" xml:space="preserve">10. vndec.</note>
            læ lineæ efficiunt. </s>
            <s xml:id="echoid-s31964" xml:space="preserve">Quare cum angulus M m l, ſit illi æqualis, quòd arcus m l, ſimilis ſit arcui Ho-
              <lb/>
            rizontis inter circulum horæ 6. </s>
            <s xml:id="echoid-s31965" xml:space="preserve">à mer. </s>
            <s xml:id="echoid-s31966" xml:space="preserve">vel med. </s>
            <s xml:id="echoid-s31967" xml:space="preserve">noc. </s>
            <s xml:id="echoid-s31968" xml:space="preserve">& </s>
            <s xml:id="echoid-s31969" xml:space="preserve">alium illum circulum maximum interie-
              <lb/>
            cto, quia totidẽ gradus ac Minuta complectitur; </s>
            <s xml:id="echoid-s31970" xml:space="preserve">ſit autem M m, communis ſectio plani horolo-
              <lb/>
            gij, & </s>
            <s xml:id="echoid-s31971" xml:space="preserve">circuli horæ 6. </s>
            <s xml:id="echoid-s31972" xml:space="preserve">à mer. </s>
            <s xml:id="echoid-s31973" xml:space="preserve">vel med. </s>
            <s xml:id="echoid-s31974" xml:space="preserve">noc. </s>
            <s xml:id="echoid-s31975" xml:space="preserve">erit recta M l, communis ſectio plani horologij, & </s>
            <s xml:id="echoid-s31976" xml:space="preserve">
              <lb/>
            alterius circuli maximi per polos mundi, & </s>
            <s xml:id="echoid-s31977" xml:space="preserve">horam 23. </s>
            <s xml:id="echoid-s31978" xml:space="preserve">ab occ. </s>
            <s xml:id="echoid-s31979" xml:space="preserve">in tropico ♋, tranſeuntis; </s>
            <s xml:id="echoid-s31980" xml:space="preserve">ac proin
              <lb/>
            de, Sole exiſtente in hoc circulo, puta in eo puncto, vbi tropicum ♋, interſecat, proijcietur, per
              <lb/>
            propoſ. </s>
            <s xml:id="echoid-s31981" xml:space="preserve">11. </s>
            <s xml:id="echoid-s31982" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s31983" xml:space="preserve">1. </s>
            <s xml:id="echoid-s31984" xml:space="preserve">vmbra ſtyli in rectam l M f. </s>
            <s xml:id="echoid-s31985" xml:space="preserve">Cum ergo interuallum E f, ſumptum ſit æquale
              <lb/>
              <note position="left" xlink:label="note-0512-03" xlink:href="note-0512-03a" xml:space="preserve">10</note>
            longitudini vmbræ, cadet vmbra ſtyli hora 23. </s>
            <s xml:id="echoid-s31986" xml:space="preserve">ab occ. </s>
            <s xml:id="echoid-s31987" xml:space="preserve">in tropico ♋, in punctum f. </s>
            <s xml:id="echoid-s31988" xml:space="preserve">Commo-
              <lb/>
              <note position="left" xlink:label="note-0512-04" xlink:href="note-0512-04a" xml:space="preserve">Quomodo l@co
                <lb/>
              arcuũ horario-
                <lb/>
              rum, & latitu-
                <lb/>
              dinum vmbra-
                <lb/>
              rum accipi poſ-
                <lb/>
              ſint arcus oppo-
                <lb/>
              ſiti in deſcriptio
                <lb/>
              nibus horologio
                <lb/>
              @um.</note>
            dius fortaſſe res peragetur, ſi arcus horarius in oppoſita parte numeretur in circulo i p l m n, nẽ-
              <lb/>
            pe arcus m l, qui occidentalis eſt, & </s>
            <s xml:id="echoid-s31989" xml:space="preserve">borealis, in parte orientali atque auſtrali, qualis eſt i n. </s>
            <s xml:id="echoid-s31990" xml:space="preserve">Ita e-
              <lb/>
            nim ſatis erit, ſi ducatur recta M n, in quam ex E, transferenda eſt longitudo vmbræ E f. </s>
            <s xml:id="echoid-s31991" xml:space="preserve">Idem
              <lb/>
            intelligendum eſt de arcubus latitudinum vmbrarum. </s>
            <s xml:id="echoid-s31992" xml:space="preserve">Nam ſi v.</s>
            <s xml:id="echoid-s31993" xml:space="preserve">g. </s>
            <s xml:id="echoid-s31994" xml:space="preserve">loco arcus D N, latitudinis
              <lb/>
            vmbræ horæ 6. </s>
            <s xml:id="echoid-s31995" xml:space="preserve">à mer. </s>
            <s xml:id="echoid-s31996" xml:space="preserve">in tropico ♋, qui occidentalis eſt, & </s>
            <s xml:id="echoid-s31997" xml:space="preserve">borealis, accipiatur oppoſit@s B t,
              <lb/>
            orientalis, & </s>
            <s xml:id="echoid-s31998" xml:space="preserve">auſtralis, ducenda tantu@ erit recta E t, ex qua longitudo vmbræ E O, abſcindi de
              <lb/>
            bet, &</s>
            <s xml:id="echoid-s31999" xml:space="preserve">c. </s>
            <s xml:id="echoid-s32000" xml:space="preserve">Rurſus inquiratur arcus horarius horæ eiuſdem 23. </s>
            <s xml:id="echoid-s32001" xml:space="preserve">ab occ. </s>
            <s xml:id="echoid-s32002" xml:space="preserve">in tropico ♑, nempe gr. </s>
            <s xml:id="echoid-s32003" xml:space="preserve">49.
              <lb/>
            </s>
            <s xml:id="echoid-s32004" xml:space="preserve">M. </s>
            <s xml:id="echoid-s32005" xml:space="preserve">26. </s>
            <s xml:id="echoid-s32006" xml:space="preserve">qui, quoniam occidentalis eſt, & </s>
            <s xml:id="echoid-s32007" xml:space="preserve">auſtralis, numeretur in parte oppoſita ex i, verſus borea
              <lb/>
            les partes, vſque ad p, & </s>
            <s xml:id="echoid-s32008" xml:space="preserve">occulta recta ducatur M p. </s>
            <s xml:id="echoid-s32009" xml:space="preserve">In hanc enim ſi ex E, transferatur longitudo
              <lb/>
              <note position="left" xlink:label="note-0512-05" xlink:href="note-0512-05a" xml:space="preserve">20</note>
            vmbræ reſpondens horæ 23. </s>
            <s xml:id="echoid-s32010" xml:space="preserve">ab occ. </s>
            <s xml:id="echoid-s32011" xml:space="preserve">in tropico ♑, vſque ad punctum h, erit h, punctum horæ
              <lb/>
            23. </s>
            <s xml:id="echoid-s32012" xml:space="preserve">in tropico ♑. </s>
            <s xml:id="echoid-s32013" xml:space="preserve">Poſtremo inueniemus arcum horarium eiuſdem horæ 23. </s>
            <s xml:id="echoid-s32014" xml:space="preserve">ab occ. </s>
            <s xml:id="echoid-s32015" xml:space="preserve">Sole exiſten-
              <lb/>
            te in Æquatore, gr. </s>
            <s xml:id="echoid-s32016" xml:space="preserve">21. </s>
            <s xml:id="echoid-s32017" xml:space="preserve">M. </s>
            <s xml:id="echoid-s32018" xml:space="preserve">49. </s>
            <s xml:id="echoid-s32019" xml:space="preserve">quem, quia occidentalis eſt, & </s>
            <s xml:id="echoid-s32020" xml:space="preserve">auſtralis, ſi numeremus in parte
              <lb/>
            oppoſita à puncto i, vſque ad u, ducamuſq́ue rectam M u, ſecabitur æquinoctialis linea in L, pũ-
              <lb/>
            cto horæ 23. </s>
            <s xml:id="echoid-s32021" xml:space="preserve">ab occ. </s>
            <s xml:id="echoid-s32022" xml:space="preserve">Ducta igitur recta f L h, dabit horam 23. </s>
            <s xml:id="echoid-s32023" xml:space="preserve">ab occ. </s>
            <s xml:id="echoid-s32024" xml:space="preserve">& </s>
            <s xml:id="echoid-s32025" xml:space="preserve">ſic de cæteris. </s>
            <s xml:id="echoid-s32026" xml:space="preserve">Eſt tamẽ
              <lb/>
            hic conſideratione dignum, quamlibet rectam occultam ex M, per extremum punctum cuiuſuis
              <lb/>
            lineæ horariæ in tropico ♋, ductam, ſi vltra centrum M, producatur, tranſire per extremum pun
              <lb/>
            ctum lineæ alterius horę in eodem tropico, quę a priore duodecim horis diſtar. </s>
            <s xml:id="echoid-s32027" xml:space="preserve">Ita vides rectam
              <lb/>
            f M, quæ per f, punctum extremũ horæ 23. </s>
            <s xml:id="echoid-s32028" xml:space="preserve">ab occ. </s>
            <s xml:id="echoid-s32029" xml:space="preserve">in tropico ♋, ducitur, productam vltra M,
              <lb/>
            trãſire per q, punctum extremum horæ 11. </s>
            <s xml:id="echoid-s32030" xml:space="preserve">ab occ. </s>
            <s xml:id="echoid-s32031" xml:space="preserve">in eodem tropico: </s>
            <s xml:id="echoid-s32032" xml:space="preserve">Item rectam r M ſ, duci
              <lb/>
              <note position="left" xlink:label="note-0512-06" xlink:href="note-0512-06a" xml:space="preserve">30</note>
            per extrema puncta horarum 22. </s>
            <s xml:id="echoid-s32033" xml:space="preserve">& </s>
            <s xml:id="echoid-s32034" xml:space="preserve">10. </s>
            <s xml:id="echoid-s32035" xml:space="preserve">ab occ. </s>
            <s xml:id="echoid-s32036" xml:space="preserve">&</s>
            <s xml:id="echoid-s32037" xml:space="preserve">c. </s>
            <s xml:id="echoid-s32038" xml:space="preserve">Quocirca ſi duæ horæ ab or. </s>
            <s xml:id="echoid-s32039" xml:space="preserve">vel occ. </s>
            <s xml:id="echoid-s32040" xml:space="preserve">duode-
              <lb/>
              <note position="left" xlink:label="note-0512-07" xlink:href="note-0512-07a" xml:space="preserve">Satis e@@, ſi pro
                <lb/>
              duabus horis
                <lb/>
              ab or. vel occ.
                <lb/>
              quarũ vna ab al
                <lb/>
              tera duodecim
                <lb/>
              horis abeſt, vnus
                <lb/>
              arcus horarius
                <lb/>
              inueſtigetur.</note>
            cim horis inter ſe diſtantes, in vnum tropicum cadant, ſatis erit, ſi vnius duntaxat arcus hora-
              <lb/>
            rius inueſtigetur. </s>
            <s xml:id="echoid-s32041" xml:space="preserve">Ratio huius rei eſt, quod circulus maximus per polos mundi, & </s>
            <s xml:id="echoid-s32042" xml:space="preserve">per quamlibet
              <lb/>
            horam ab occ. </s>
            <s xml:id="echoid-s32043" xml:space="preserve">in tropico ductus tranſeat quoque in eodem tropico per horam oppoſitam, quæ
              <lb/>
            nimirum ab ea duodecim horis abeſt, cum tropicum bifariã ſecet, ex propoſ. </s>
            <s xml:id="echoid-s32044" xml:space="preserve">15. </s>
            <s xml:id="echoid-s32045" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s32046" xml:space="preserve">1. </s>
            <s xml:id="echoid-s32047" xml:space="preserve">Theod.
              <lb/>
            </s>
            <s xml:id="echoid-s32048" xml:space="preserve">Hinc enim fit, vt & </s>
            <s xml:id="echoid-s32049" xml:space="preserve">communis eius, & </s>
            <s xml:id="echoid-s32050" xml:space="preserve">plani horologij ſectio per M, ducta tranſeat in plano ho-
              <lb/>
            rologij per duas illas horas oppoſitas.</s>
            <s xml:id="echoid-s32051" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s32052" xml:space="preserve">HÆC autem deſcriptio horologij per arcus horarios expeditiſſime fit in horis à mer. </s>
            <s xml:id="echoid-s32053" xml:space="preserve">& </s>
            <s xml:id="echoid-s32054" xml:space="preserve">med.
              <lb/>
            </s>
            <s xml:id="echoid-s32055" xml:space="preserve">
              <note position="left" xlink:label="note-0512-08" xlink:href="note-0512-08a" xml:space="preserve">Deſc@iptio hora
                <lb/>
              rum à mer. &
                <lb/>
              med. noc. per ar
                <lb/>
              cus horarios ex-
                <lb/>
              peditiſſima eſt.</note>
            noc. </s>
            <s xml:id="echoid-s32056" xml:space="preserve">propterea quod, cum omnes hiiuſmodi horæ per centrum M, tranſeant, neceſſe non ſit pro
              <lb/>
            ſingulis horis ternos arcus inquirere, vt in hora 23. </s>
            <s xml:id="echoid-s32057" xml:space="preserve">ab occ. </s>
            <s xml:id="echoid-s32058" xml:space="preserve">factum eſt, ſed ſatis fuerit, ſi ſinguli ar
              <lb/>
              <note position="left" xlink:label="note-0512-09" xlink:href="note-0512-09a" xml:space="preserve">40</note>
            cus quærantur; </s>
            <s xml:id="echoid-s32059" xml:space="preserve">cuiuſmodi ſunt ſequentes pro ſingulis horis à mer. </s>
            <s xml:id="echoid-s32060" xml:space="preserve">& </s>
            <s xml:id="echoid-s32061" xml:space="preserve">med. </s>
            <s xml:id="echoid-s32062" xml:space="preserve">noc. </s>
            <s xml:id="echoid-s32063" xml:space="preserve">horologij hori-
              <lb/>
            zontalis, ad latitudinem Grad. </s>
            <s xml:id="echoid-s32064" xml:space="preserve">42.</s>
            <s xml:id="echoid-s32065" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1645" type="section" level="1" n="419">
          <head xml:id="echoid-head434" xml:space="preserve">Arcus horarij in horologio horizontali pro horis à mer.
            <lb/>
          & med. noc. ad latitudinem Grad. 42.</head>
          <note position="right" xml:space="preserve">
            <lb/>
          Horę à media \\ nocte. # 6 # 7 # 8 # 9 # 10 # 11 # 12 # Oriẽtales.
            <lb/>
          Horæ à meridie. # 6 # 5 # 4 # 3 # 2 # 1 # 0 # Occidenta.
            <lb/>
          Arcus ho- \\ rarij. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # G. M. # 0. 0. # 21. 49. # 40. 48. # 56. 13. # 68. 53. # 79. 50. # 90. 0. # Auſtrales.</note>
          <p>
            <s xml:id="echoid-s32066" xml:space="preserve">Ex quibus arcubus, ſi numerentur à punctis i, m, verſus partes boreales, ſeu oppoſitas, cum ipſi
              <lb/>
            ſint auſtrales, & </s>
            <s xml:id="echoid-s32067" xml:space="preserve">ex M, centro horologij per fines numerationum lineę rectæ ducantur, quæ ſi ab-
              <lb/>
            ſcindantur ſecundum interualla longitudinum vmbrarum, quas Sol habet, cum @ tropicis exi-
              <lb/>
            ſtit, deſcriptum erit horologium aſtronomicum. </s>
            <s xml:id="echoid-s32068" xml:space="preserve">Exemplum habes in hora 7. </s>
            <s xml:id="echoid-s32069" xml:space="preserve">à med. </s>
            <s xml:id="echoid-s32070" xml:space="preserve">noc. </s>
            <s xml:id="echoid-s32071" xml:space="preserve">& </s>
            <s xml:id="echoid-s32072" xml:space="preserve">5.
              <lb/>
            </s>
            <s xml:id="echoid-s32073" xml:space="preserve">à mer. </s>
            <s xml:id="echoid-s32074" xml:space="preserve">quarum vtraque arcum horarium habet auſtralem gr. </s>
            <s xml:id="echoid-s32075" xml:space="preserve">21. </s>
            <s xml:id="echoid-s32076" xml:space="preserve">M. </s>
            <s xml:id="echoid-s32077" xml:space="preserve">49. </s>
            <s xml:id="echoid-s32078" xml:space="preserve">qui ſi numeretur à pun-
              <lb/>
            ctis i, & </s>
            <s xml:id="echoid-s32079" xml:space="preserve">m, verſus partes oppoſitas, id eſt, boreales, vſque ad α, & </s>
            <s xml:id="echoid-s32080" xml:space="preserve">u, ducanturq́ue rectæ M α,
              <lb/>
            M u, in quas interualla longitudinis vmbræ earundem horarum in tropico ♋, transferantur, de-
              <lb/>
            ſcriptæ erunt lineæ horarum 7. </s>
            <s xml:id="echoid-s32081" xml:space="preserve">à med. </s>
            <s xml:id="echoid-s32082" xml:space="preserve">noc. </s>
            <s xml:id="echoid-s32083" xml:space="preserve">& </s>
            <s xml:id="echoid-s32084" xml:space="preserve">5. </s>
            <s xml:id="echoid-s32085" xml:space="preserve">à mer. </s>
            <s xml:id="echoid-s32086" xml:space="preserve">Idemq́ue de cæteris horis faciendum eſt.</s>
            <s xml:id="echoid-s32087" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
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