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 contents

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[211.] SCHOLIVM.
Page: 271 (255)
[212.] PROBLEMA 36. PROPOSITIO 36. HOROLOGIVM Antiquum Meridianum conſtituere.
Page: 272 (256)
[213.] SCHOLIVM.
Page: 272 (256)
[214.] DE HOROLOGIIS POLARIBVS. PROBLEMA 37. PROPOSITIO 37.
Page: 272 (256)
[215.] SCHOLIVM.
Page: 274 (258)
[216.] PROBLEMA 38. PROPOSITIO 38.
Page: 274 (258)
[217.] PROBLEMA 39. PROPOSITIO 39.
Page: 276 (260)
[218.] PROBLEMA 40. PROPOSITIO 40.
Page: 276 (260)
[219.] PROBLEMA 41. PROPOSITIO 41.
Page: 278 (262)
[220.] PROBLEMA 42. PROPOSITIO 42.
Page: 280 (264)
[221.] PROBLEMA 43. PROPOSITIO 43.
Page: 281 (265)
[222.] PROBLEMA 44. PROPOSITIO 44.
Page: 281 (265)
[223.] SCHOLIVM.
Page: 282 (266)
[224.] PROBLEMA. 45. PROPOSITIO 45.
Page: 282 (266)
[225.] SCHOLIVM.
Page: 284 (268)
[226.] PROBLEMA 46. PROPOSITIO 46.
Page: 285 (269)
[227.] PROBLEMA 47. PROPOSITIO 47.
Page: 288 (272)
[228.] SCHOLIVM.
Page: 288 (272)
[229.] PROBLEMA 48. PROPOSITIO 48.
Page: 288 (272)
[230.] SCHOLIVM.
Page: 289 (273)
[231.] DE HOROLOGIIS ÆQVINOCTIALIBVS. PROBLEMA 49. PROPOSITIO 49.
Page: 289 (273)
[232.] SCHOLIVM.
Page: 290 (274)
[233.] PROBLEMA 50. PROPOSITIO 50.
Page: 290 (274)
[234.] SCHOLIVM.
Page: 292 (276)
[235.] PROBLEMA 51. PROPOSITIO 51.
Page: 293 (277)
[236.] PROBLEMA 52. PROPOSITIO 52.
Page: 293 (277)
[237.] SCHOLIVM.
Page: 294 (278)
[238.] PROBLEMA 53. PROPOSITIO 53.
Page: 295 (279)
[239.] SCHOLIVM.
Page: 297 (281)
[240.] PROBLEMA 54. PROPOSITIO 54.
Page: 297 (281)
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            <s xml:id="echoid-s18701" xml:space="preserve">
              <pb o="276" file="0292" n="292" rhead="GNOMONICES"/>
            deſcribendus erit circulus alicuius gradus Eclipticæ prope equinoctialẽ circulum, vt in horologio
              <lb/>
            ſuperiori v. </s>
            <s xml:id="echoid-s18702" xml:space="preserve">g. </s>
            <s xml:id="echoid-s18703" xml:space="preserve">gradus 25. </s>
            <s xml:id="echoid-s18704" xml:space="preserve">♍, & </s>
            <s xml:id="echoid-s18705" xml:space="preserve">gradus 5. </s>
            <s xml:id="echoid-s18706" xml:space="preserve">♈; </s>
            <s xml:id="echoid-s18707" xml:space="preserve">in inferiori autẽ gradus 25. </s>
            <s xml:id="echoid-s18708" xml:space="preserve">♓, & </s>
            <s xml:id="echoid-s18709" xml:space="preserve">gradus 5. </s>
            <s xml:id="echoid-s18710" xml:space="preserve">♎, &</s>
            <s xml:id="echoid-s18711" xml:space="preserve">c.
              <lb/>
            </s>
            <s xml:id="echoid-s18712" xml:space="preserve">quoniam circa æquinoctiorum tempora longiſſima efficitur vmbra ſtyli, in ipſis verò æquinoctiis
              <lb/>
            infinita, & </s>
            <s xml:id="echoid-s18713" xml:space="preserve">plano horologij æquidiſtans, vt ex dicto ſcholio propoſ. </s>
            <s xml:id="echoid-s18714" xml:space="preserve">11. </s>
            <s xml:id="echoid-s18715" xml:space="preserve">ſuperioris lib. </s>
            <s xml:id="echoid-s18716" xml:space="preserve">perſpicuum
              <lb/>
            eſt. </s>
            <s xml:id="echoid-s18717" xml:space="preserve">Idem de horis ab ortu, & </s>
            <s xml:id="echoid-s18718" xml:space="preserve">occaſu intelligendum eſt, de quibus propoſ. </s>
            <s xml:id="echoid-s18719" xml:space="preserve">58. </s>
            <s xml:id="echoid-s18720" xml:space="preserve">& </s>
            <s xml:id="echoid-s18721" xml:space="preserve">59. </s>
            <s xml:id="echoid-s18722" xml:space="preserve">huius li-
              <lb/>
            bri agemus.</s>
            <s xml:id="echoid-s18723" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s18724" xml:space="preserve">LINEA horizontalis, in quam, Sole oriente, vel occidente, vmbra ſtyli proiicitur, ita deſcri-
              <lb/>
              <note position="left" xlink:label="note-0292-01" xlink:href="note-0292-01a" xml:space="preserve">Horizontalis li
                <lb/>
              nea quo pacto
                <lb/>
              in æquinoctia-
                <lb/>
              li horologio de
                <lb/>
              ſcribatur.</note>
            bitur. </s>
            <s xml:id="echoid-s18725" xml:space="preserve">In prima figura propoſ. </s>
            <s xml:id="echoid-s18726" xml:space="preserve">26. </s>
            <s xml:id="echoid-s18727" xml:space="preserve">huius libri notentur puncta h, i, in quibus Horizontis diame-
              <lb/>
            ter B D, parallelas per a, & </s>
            <s xml:id="echoid-s18728" xml:space="preserve">e, ductas ſecat, & </s>
            <s xml:id="echoid-s18729" xml:space="preserve">recta a h, vel e i, transferatur in lineam meridianã ho-
              <lb/>
            rologii ſuperioris ſupra locum ſtyli ex E, vſque ad m, infra verò locum ſtyli in horologio inferiori,
              <lb/>
              <note position="left" xlink:label="note-0292-02" xlink:href="note-0292-02a" xml:space="preserve">10</note>
            atque per m, ducatur lineæ horæ ſextæ parallela. </s>
            <s xml:id="echoid-s18730" xml:space="preserve">Hæc enim erit horizontalis linea. </s>
            <s xml:id="echoid-s18731" xml:space="preserve">Cum enim
              <lb/>
            Horizon per B D, ductus plano horologij ſuperioris per a h, lineam meridianam ducto in puncto
              <lb/>
            h, plano verò horologij inferioris per lineam meridianam e i, ducto in puncto i, occurrat; </s>
            <s xml:id="echoid-s18732" xml:space="preserve">mani-
              <lb/>
            feſtum eſt, ſi rectam a h, ex loco ſtyli in ſuperiori horologio transferamus in lineam meridianam
              <lb/>
            ſupra locum ſtyli, vſque ad punctum m, lineam horizontalem per m, tranſire; </s>
            <s xml:id="echoid-s18733" xml:space="preserve">propterea quòd in
              <lb/>
            horologio ſuperiori in puncto h, coeant communes ſectiones Horizontis, & </s>
            <s xml:id="echoid-s18734" xml:space="preserve">Meridiani factæ à
              <lb/>
            plano horologij illos ſecante, ex propoſ. </s>
            <s xml:id="echoid-s18735" xml:space="preserve">18. </s>
            <s xml:id="echoid-s18736" xml:space="preserve">ſuperioris lib. </s>
            <s xml:id="echoid-s18737" xml:space="preserve">quandoquidem communis ſectio Hori
              <lb/>
            zontis, & </s>
            <s xml:id="echoid-s18738" xml:space="preserve">Meridiani, hoc eſt, recta B D, plano horologij ſuperioris occurrit in h; </s>
            <s xml:id="echoid-s18739" xml:space="preserve">cuiuſmodi ſectio-
              <lb/>
            nes ſunt linea horizontalis, & </s>
            <s xml:id="echoid-s18740" xml:space="preserve">linea meridiana. </s>
            <s xml:id="echoid-s18741" xml:space="preserve">Quia verò Horizon, circulus horæ 6. </s>
            <s xml:id="echoid-s18742" xml:space="preserve">à meridie,
              <lb/>
            vel media nocte, & </s>
            <s xml:id="echoid-s18743" xml:space="preserve">Aequator vnam habent, & </s>
            <s xml:id="echoid-s18744" xml:space="preserve">eandem communem ſectionem, cui æquidiſtat pla-
              <lb/>
              <note position="left" xlink:label="note-0292-03" xlink:href="note-0292-03a" xml:space="preserve">20</note>
            num horologij, quòd Aequatori, in quo illa communis ſectio eſt, æquidiſtet; </s>
            <s xml:id="echoid-s18745" xml:space="preserve">erunt reliquorum
              <lb/>
            circulorum communes ſectiones cum plano horologii parallelæ, nempe linea horizontalis, & </s>
            <s xml:id="echoid-s18746" xml:space="preserve">li-
              <lb/>
            nea horæ 6. </s>
            <s xml:id="echoid-s18747" xml:space="preserve">ex propoſ. </s>
            <s xml:id="echoid-s18748" xml:space="preserve">18. </s>
            <s xml:id="echoid-s18749" xml:space="preserve">vel ex ſcholio propoſ. </s>
            <s xml:id="echoid-s18750" xml:space="preserve">22. </s>
            <s xml:id="echoid-s18751" xml:space="preserve">præcedentis lib. </s>
            <s xml:id="echoid-s18752" xml:space="preserve">Quamobrem recta per m, du-
              <lb/>
            cta lineæ horæ 6. </s>
            <s xml:id="echoid-s18753" xml:space="preserve">parallela, horizontalis linea eſt, hoc eſt, communis ſectio Horizontis, & </s>
            <s xml:id="echoid-s18754" xml:space="preserve">plani
              <lb/>
            horologii. </s>
            <s xml:id="echoid-s18755" xml:space="preserve">Eodem modo, ſi rectam e
              <unsure/>
            i, in lineam meridianam horologii inferioris infra locũ gno-
              <lb/>
            monis transferamus, habebimus punctum, per quod linea horizontalis eſt ducenda. </s>
            <s xml:id="echoid-s18756" xml:space="preserve">Sed quia re-
              <lb/>
            cta e i, rectæ a h, eſt æqualis, (quoniam enim in triangulis E a h, E e i, anguli ad a, e, recti ſunt, & </s>
            <s xml:id="echoid-s18757" xml:space="preserve">
              <lb/>
            anguli ad verticem E, æquales, lateraq́ue E a, E e, æqualia; </s>
            <s xml:id="echoid-s18758" xml:space="preserve">erunt & </s>
            <s xml:id="echoid-s18759" xml:space="preserve">latera a h, e i, æqualia) idcirco
              <lb/>
              <note position="left" xlink:label="note-0292-04" xlink:href="note-0292-04a" xml:space="preserve">15. primi.</note>
            præcepimus, eandem a h, vel e i, in vtroque horologio transferendam eſſe in lineam meridianam
              <lb/>
              <note position="left" xlink:label="note-0292-05" xlink:href="note-0292-05a" xml:space="preserve">26. primi.</note>
            ſupra vel infra locum ſtyli.</s>
            <s xml:id="echoid-s18760" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">30</note>
          <p>
            <s xml:id="echoid-s18761" xml:space="preserve">IDEM punctum m, per quod ducenda eſt linea horizontalis lineæ horæ 6. </s>
            <s xml:id="echoid-s18762" xml:space="preserve">parallela, hac arte
              <lb/>
              <note position="left" xlink:label="note-0292-07" xlink:href="note-0292-07a" xml:space="preserve">Alia deſcriptio
                <lb/>
              horizontalis li-
                <lb/>
              neæ in horolo-
                <lb/>
              gio æquino-
                <lb/>
              ctiali.</note>
            inuenietur. </s>
            <s xml:id="echoid-s18763" xml:space="preserve">In linea horæ 6. </s>
            <s xml:id="echoid-s18764" xml:space="preserve">horologii accipiatur E l, æqualis ſtylo, & </s>
            <s xml:id="echoid-s18765" xml:space="preserve">ſiat angulus E l m, altitudi-
              <lb/>
            ni poli æqualis, ita vt recta l m, ſecans lineam meridianam in m, cadat ſurſum verſus in ſuperiori
              <lb/>
            horologio, deorſum autem verſus in inferiori. </s>
            <s xml:id="echoid-s18766" xml:space="preserve">Quod facile fiet, ſi ex l, arcus circuli deſcribatur
              <lb/>
            ſiue ſupra rectam C D, ſiue infra, verſus meridianam lineam, & </s>
            <s xml:id="echoid-s18767" xml:space="preserve">in eo numeretur à recta C D, ar-
              <lb/>
            cus altitudinis poli, à cuius extremo puncto ad l, recta ducatur ſecans meridianam lineam in pun-
              <lb/>
            cto m. </s>
            <s xml:id="echoid-s18768" xml:space="preserve">Per punctum enim m, ducenda eſt linea horizontalis, vt prius. </s>
            <s xml:id="echoid-s18769" xml:space="preserve">Intelligatur enim trian-
              <lb/>
            gulum E l m, circa lineam meridianam conuerti, donec rectum ſit ad planum horologij, & </s>
            <s xml:id="echoid-s18770" xml:space="preserve">in pla-
              <lb/>
            no Meridiani exiſtat, atque adeò punctum l, cum vertice ſtvli, ſeu centro mundi coniungatur, & </s>
            <s xml:id="echoid-s18771" xml:space="preserve">
              <lb/>
            recta E l, cum ſtylo, ſeu axe mundi. </s>
            <s xml:id="echoid-s18772" xml:space="preserve">tranſibit Horizon per l, verticem ſtyli, ac proinde per rectam
              <lb/>
              <note position="left" xlink:label="note-0292-08" xlink:href="note-0292-08a" xml:space="preserve">40</note>
            l m; </s>
            <s xml:id="echoid-s18773" xml:space="preserve">propterea quòd angulus E l m, altitudini poli æqualis eſt, qualem nimitum cum axe in cen-
              <lb/>
            tro mundi l, facit communis ſectio Horizontis, ac Meridiani. </s>
            <s xml:id="echoid-s18774" xml:space="preserve">Immo & </s>
            <s xml:id="echoid-s18775" xml:space="preserve">reliquus E m l, comple-
              <lb/>
            mento altitudinis poli æqualis eſt, qualem nimirum facit Horizon cum Aequatore in plano Meri
              <lb/>
            diani circuli; </s>
            <s xml:id="echoid-s18776" xml:space="preserve">qui quidem angulus æqual@s eſt angulo, quem Horizon cum plano horologii, quod
              <lb/>
            Aequatori parallelum eſt, in eodem Meridiani plano conſtituit. </s>
            <s xml:id="echoid-s18777" xml:space="preserve">Quoniam enim ſectiones Meri-
              <lb/>
            diani, quas cum Aequatore, & </s>
            <s xml:id="echoid-s18778" xml:space="preserve">plano horologij illi parallelo facit, ſunt parallelæ, faciet communis
              <lb/>
              <note position="left" xlink:label="note-0292-09" xlink:href="note-0292-09a" xml:space="preserve">16. vndec.</note>
            ſectio Horizontis & </s>
            <s xml:id="echoid-s18779" xml:space="preserve">Meridiani angulos æquales cum dictis ſectionibus, quarum vna eſt linea me-
              <lb/>
              <note position="left" xlink:label="note-0292-10" xlink:href="note-0292-10a" xml:space="preserve">29. primi.</note>
            ridiana in Aequatore, & </s>
            <s xml:id="echoid-s18780" xml:space="preserve">altera in horologii plano, externũ ſcilicet, & </s>
            <s xml:id="echoid-s18781" xml:space="preserve">internũ. </s>
            <s xml:id="echoid-s18782" xml:space="preserve">Quare Horizon pla
              <lb/>
            num horologij ſecabit in m; </s>
            <s xml:id="echoid-s18783" xml:space="preserve">ac idcirco pet m, linea horizontalis ducẽda eſt. </s>
            <s xml:id="echoid-s18784" xml:space="preserve">Parallelos igitur, ſiue
              <lb/>
            arcus ſignorum Zodiaci in prædicto horologio ęquinoctiali deſignauimus. </s>
            <s xml:id="echoid-s18785" xml:space="preserve">Quod faciendũ erat.</s>
            <s xml:id="echoid-s18786" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">50</note>
        </div>
        <div xml:id="echoid-div961" type="section" level="1" n="234">
          <head xml:id="echoid-head241" style="it" xml:space="preserve">SCHOLIVM.</head>
          <note position="left" xml:space="preserve">Pottio horolo-
            <lb/>
          gii æquinoctia-
            <lb/>
          lis abſciſſa à li-
            <lb/>
          nea horizonra
            <lb/>
          li, quo pacto ho
            <lb/>
          rologium Infe-
            <lb/>
          rius efficiatur.</note>
          <p style="it">
            <s xml:id="echoid-s18787" xml:space="preserve">PARS ea horologij, quam linea horizont alis abſcindit, erit ipſum horologium inferius, ſi omnia in-
              <lb/>
            uertantur, vt in præcedentibus factum eſt, hoc eſt, ſi linea horizontalis in infcriori facie plani ſuperiorẽ
              <lb/>
            teneat locum, & </s>
            <s xml:id="echoid-s18788" xml:space="preserve">pars, quæ in eo ſitu dextra eſt, mutetur in ſiniſtram, vt in ſcholio propoſ. </s>
            <s xml:id="echoid-s18789" xml:space="preserve">14. </s>
            <s xml:id="echoid-s18790" xml:space="preserve">huius
              <lb/>
            libri ostendimus. </s>
            <s xml:id="echoid-s18791" xml:space="preserve">Verum arcus ſignorum borealium mutantur in arcus oppoſitorum ſignorum au-
              <lb/>
            ſtralium; </s>
            <s xml:id="echoid-s18792" xml:space="preserve">propterea quòd vmbra ſtyli cadit in inferius horologium, Sole exiſtente in ſignis auſtralibus,
              <lb/>
              <note position="left" xlink:label="note-0292-13" xlink:href="note-0292-13a" xml:space="preserve">Eadem pottio
                <lb/>
              abſciſſa in ſupe
                <lb/>
              riori horologio
                <lb/>
              eſt hotologium
                <lb/>
              @octuinum.</note>
            vt conſtat.</s>
            <s xml:id="echoid-s18793" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s18794" xml:space="preserve">PORTIO quoque abſciſſa à linea horizontali exhibet nobis horologium nocturnum, vt in præce-
              <lb/>
            dentibus dictum eſt.</s>
            <s xml:id="echoid-s18795" xml:space="preserve"/>
          </p>
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