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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[261.] SCHOLIVM.
Page: 338 (322)
[262.] PROBLEMA 5. PROPOSITIO 5.
Page: 338 (322)
[263.] PROBLEMA 6. PROPOSITIO 6.
Page: 339 (323)
[264.] PROBLEMA 7. PROPOSITIO 7.
Page: 340 (324)
[265.] PROBLEMA 8. PROPOSITIO 8.
Page: 340 (324)
[266.] PROBLEMA 9. PROPOSITIO 9.
Page: 342 (326)
[267.] SCHOLIVM.
Page: 344 (328)
[268.] PROBLEMA 10. PROPOSITIO 10.
Page: 345 (329)
[269.] PROBLEMA 11. PROPOSITIO 11.
Page: 347 (331)
[270.] SCHOLIVM.
Page: 347 (331)
[271.] PROBLEMA 12. PROPOSITIO 12.
Page: 348 (332)
[272.] SCHOLIVM.
Page: 350 (334)
[273.] DE HOROLOGIIS, QVAE ab Horizonte declinant. PROBLEMA 13. PROPOSITIO 13.
Page: 350 (334)
[274.] SCHOLIVM.
Page: 353 (337)
[275.] PROBLEMA 14. PROPOSITIO 14.
Page: 357 (341)
[276.] PROBLEMA 15. PROPOSITIO 15.
Page: 359 (343)
[277.] SCHOLIVM.
Page: 360 (344)
[278.] PROBLEMA 16. PROPOSITIO 16.
Page: 360 (344)
[279.] SCHOLIVM.
Page: 361 (345)
[280.] PROBLEMA 17. PROPOSITIO 17.
Page: 362 (346)
[281.] SCHOLIVM.
Page: 362 (346)
[282.] PROBLEMA 18. PROPOSITIO 18.
Page: 363 (347)
[283.] PROBLEMA 19. PROPOSITIO 19.
Page: 363 (347)
[284.] PROBLEMA 20. PROPOSITIO 20.
Page: 363 (347)
[285.] SCHOLIVM.
Page: 364 (348)
[286.] PROBLEMA 21. PROPOSITIO 21.
Page: 365 (349)
[287.] SCHOLIVM.
Page: 366 (350)
[288.] PROBLEMA 22. PROPOSITIO 22.
Page: 367 (351)
[289.] PROBLEMA 23. PROPOSITIO 23.
Page: 368 (352)
[290.] SCHOLIVM.
Page: 368 (352)
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          <p>
            <s xml:id="echoid-s21245" xml:space="preserve">
              <pb o="316" file="0332" n="332" rhead="GNOMONICES"/>
            toris facit, cõtinet gr. </s>
            <s xml:id="echoid-s21246" xml:space="preserve">48. </s>
            <s xml:id="echoid-s21247" xml:space="preserve">cũ tanta ſit declinatio paralleli maximi ſemper apparentiũ, fit vt addito
              <lb/>
            angulorecto G I C, conficiatur angulus contentus radio eiuſdem paralleli, & </s>
            <s xml:id="echoid-s21248" xml:space="preserve">axe I C, grad. </s>
            <s xml:id="echoid-s21249" xml:space="preserve">138.
              <lb/>
            </s>
            <s xml:id="echoid-s21250" xml:space="preserve">Cum ergo angulus I C G, altitudinis poli ſupra planum declinans comprehendat grad. </s>
            <s xml:id="echoid-s21251" xml:space="preserve">40. </s>
            <s xml:id="echoid-s21252" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s21253" xml:space="preserve">
              <lb/>
            3. </s>
            <s xml:id="echoid-s21254" xml:space="preserve">fient anguli interni, quos dictus radius, & </s>
            <s xml:id="echoid-s21255" xml:space="preserve">recta C G, cum axe faciunt, grad. </s>
            <s xml:id="echoid-s21256" xml:space="preserve">178. </s>
            <s xml:id="echoid-s21257" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s21258" xml:space="preserve">3. </s>
            <s xml:id="echoid-s21259" xml:space="preserve">hoc eſt,
              <lb/>
            minores duobus rectis. </s>
            <s xml:id="echoid-s21260" xml:space="preserve">Quare coibit linea C G, cum dicto radio; </s>
            <s xml:id="echoid-s21261" xml:space="preserve">ac proinde cum recta C G, ſe-
              <lb/>
            cet vtrumque radium, hoc eſt, eum, qui eſt paralleli maximi ſemper apparentium, & </s>
            <s xml:id="echoid-s21262" xml:space="preserve">eum, qui eſt
              <lb/>
              <note position="left" xlink:label="note-0332-01" xlink:href="note-0332-01a" xml:space="preserve">Quando linea
                <lb/>
              ſtyli vna eſt ex
                <lb/>
              horariis lineis,
                <lb/>
              vel æqualiter à
                <lb/>
              duabus hinc in
                <lb/>
              de diſtat, facili 9
                <lb/>
              arcus ſignorũ
                <lb/>
              deſcribuntur.</note>
            paralleli ſemper latentiũ maximus, fient duæ hyperbolæ oppoſitæ, & </s>
            <s xml:id="echoid-s21263" xml:space="preserve">æquales, vt ex dictis conſtat.</s>
            <s xml:id="echoid-s21264" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s21265" xml:space="preserve">QVANDO linea ſtyli eſt vna ex lineis horarijs, vel æqualiter à duabus horis hinc inde po-
              <lb/>
            ſitis diſtat, transferenda erunt ſingula interualla prædicta in binas lineas horarias æqualiter à linea
              <lb/>
            ſtyli in horologio remotas, vt in horizontali etiam horologio, Verticaliq́; </s>
            <s xml:id="echoid-s21266" xml:space="preserve">factum eſt.</s>
            <s xml:id="echoid-s21267" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">10</note>
          <p>
            <s xml:id="echoid-s21268" xml:space="preserve">VT autem accuratius ſignorum arcus delineari poſſint, quando linea ſtyli inæqualiter à dua-
              <lb/>
              <note position="left" xlink:label="note-0332-03" xlink:href="note-0332-03a" xml:space="preserve">Quando linea
                <lb/>
              ſtyli inæquali-
                <lb/>
              ter à duabus
                <lb/>
              horis hinc inde
                <lb/>
              diſtat, quid fa-
                <lb/>
              ciendum, vt ac-
                <lb/>
              cura@us arcus
                <lb/>
              ſignorũ deſcri-
                <lb/>
              bantur.</note>
            bus horarijs lineis hinc inde collocatis fuerit remota, transferri poterunt omnia puncta horaria
              <lb/>
            lineæ æquinoctialis ad ſiniſtram, vel dextram lineæ indicis poſita, in alteram partem æquinoctia-
              <lb/>
            lis lineæ, nempe dextram, vel ſiniſtram eiuſdẽ lineæ ſtyli, initio ſemper facto à linea ſtyli: </s>
            <s xml:id="echoid-s21269" xml:space="preserve">Vel certè
              <lb/>
            (quod ego magis probo, quoniã aliquæ lineæ horariæ vix, aut nunquã æquinoctialẽ lineam ſecãt)
              <lb/>
            deſcripto arcu circuli ex centro C, poterunt eius portiones inter lineã indicis, & </s>
            <s xml:id="echoid-s21270" xml:space="preserve">horarias lineas ex
              <lb/>
            vna parte lineę indicis transferri in eundẽ arcũ ex altera parte eiuſdem lineæ indicis. </s>
            <s xml:id="echoid-s21271" xml:space="preserve">Si enim per
              <lb/>
            puncta ſiue in linea æquinoctiali, ſiue in illo arcu (quod magis probatur) notata, ex cẽtro C, lineas
              <lb/>
            occultas duxerimus, quales in proxima figura ſunt lineæ minutis illis lineis diſtinctæ ad dextram
              <lb/>
            ipſius lineæ indicis exiſtẽtes, habebimus ſemper binas lineas æqualiter à linea indicis hinc inde re
              <lb/>
              <note position="left" xlink:label="note-0332-04" xlink:href="note-0332-04a" xml:space="preserve">20</note>
            motas, in quas vnum, & </s>
            <s xml:id="echoid-s21272" xml:space="preserve">idem ſpatiũ horarium inter C, & </s>
            <s xml:id="echoid-s21273" xml:space="preserve">radiũ cuiuslibet ſigni interceptũ tranſ-
              <lb/>
            ferri poteſt, vt in horizontali horologio, & </s>
            <s xml:id="echoid-s21274" xml:space="preserve">Verticali. </s>
            <s xml:id="echoid-s21275" xml:space="preserve">Quod quidem ſi fiat, ſatis erit, ſi in figura ra-
              <lb/>
              <note position="left" xlink:label="note-0332-05" xlink:href="note-0332-05a" xml:space="preserve">Qua ratione ſa
                <lb/>
              tis ſit, ſi in figu
                <lb/>
              ra radiorũ du-
                <lb/>
              cãtur lineæ ho-
                <lb/>
              rariæ reſpondẽ
                <lb/>
              tes ho ris cõten
                <lb/>
              tis in horolo-
                <lb/>
              gio ex altera dũ
                <lb/>
              taxat parte li-
                <lb/>
              neę ſtyli.</note>
            diorum ex C, ducamus lineas horarias reſpondentes horis contentis in horologio ex vna dunta-
              <lb/>
            xat parte, dextra vel ſiniſtra, lineæ indicis. </s>
            <s xml:id="echoid-s21276" xml:space="preserve">Nam ſi puncta horarum illarum in æquinoctiali linea,
              <lb/>
            vel arcu ex centro C, deſcripto, transferantur in alteram partem lineæ æquinoctialis, vel dicti ar-
              <lb/>
            cus, principio ſemper facto à linea indicis, & </s>
            <s xml:id="echoid-s21277" xml:space="preserve">reliqua perficiantur, vt proximè præcepimus, deſcri
              <lb/>
            bentur arcus ſignorum, vt in horizontali horologio. </s>
            <s xml:id="echoid-s21278" xml:space="preserve">Atque hac ratione vitaretur confuſio linea-
              <lb/>
            rum ex C, per radium Aequatoris ductarum in figura radiorum. </s>
            <s xml:id="echoid-s21279" xml:space="preserve">Id quod in deſcriptione arcuum
              <lb/>
            ſignorum in horologio declinante ab Horizonte propoſ. </s>
            <s xml:id="echoid-s21280" xml:space="preserve">14. </s>
            <s xml:id="echoid-s21281" xml:space="preserve">huius libri obſeruatum eſſe videbis.
              <lb/>
            </s>
            <s xml:id="echoid-s21282" xml:space="preserve">Rurſus ſi portiones rectæ C A, inter C, & </s>
            <s xml:id="echoid-s21283" xml:space="preserve">radios ſignorum transferantur in horologium ex C, in
              <lb/>
              <note position="left" xlink:label="note-0332-06" xlink:href="note-0332-06a" xml:space="preserve">30</note>
            rectam C d, ex vtraque parte centri C, habebimus in recta C d, puncta, per quæ arcus ſignorum
              <lb/>
            ducendi ſunt, velut in linea horæ 6. </s>
            <s xml:id="echoid-s21284" xml:space="preserve">horizontalis horologij, & </s>
            <s xml:id="echoid-s21285" xml:space="preserve">Verticalis factum eſt.</s>
            <s xml:id="echoid-s21286" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s21287" xml:space="preserve">PERTINENT autem in horologijs declinantibus à meridie arcus ſupra lineam æquino-
              <lb/>
              <note position="left" xlink:label="note-0332-07" xlink:href="note-0332-07a" xml:space="preserve">Qui arcus ſi-
                <lb/>
              gnorum in ho-
                <lb/>
              rologio declinã
                <lb/>
              re à Verticali
                <lb/>
              pertineant ad
                <lb/>
              ſigna auſtralia,
                <lb/>
              & qui ad borea
                <lb/>
              lia.</note>
            ctialem verſus centrum deſcripti ad ſigna auſtralia: </s>
            <s xml:id="echoid-s21288" xml:space="preserve">reliqui verò ad borealia, veluti in Verticalibus
              <lb/>
            horologijs. </s>
            <s xml:id="echoid-s21289" xml:space="preserve">In declinantibus autem à ſeptentrione contrarium intelligatur. </s>
            <s xml:id="echoid-s21290" xml:space="preserve">Vt facile quiuis per-
              <lb/>
            cipere poteſt, ſi rectè concipiat animo poſitionem vtriuſque horologij, & </s>
            <s xml:id="echoid-s21291" xml:space="preserve">ſitum parallelorum per
              <lb/>
            ſignorum initia ductorum.</s>
            <s xml:id="echoid-s21292" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s21293" xml:space="preserve">CAETERVM quando arcus ſignorum hyperbolæ ſunt oppoſitæ, & </s>
            <s xml:id="echoid-s21294" xml:space="preserve">æquales, (quod quan-
              <lb/>
              <note position="left" xlink:label="note-0332-08" xlink:href="note-0332-08a" xml:space="preserve">Quo pacto hy-
                <lb/>
              perbolæ borea-
                <lb/>
              lium ſignorum
                <lb/>
              ex hyperbolis
                <lb/>
              oppoſitis ſigno
                <lb/>
              rum auſtraliũ
                <lb/>
              deſcribantur.</note>
            do fiat, paulò ante docuimus) multò accuratius in horologijs à meridie declinantibus deſcribe-
              <lb/>
            mus arcus ſignorum borealium ex arcubus auſtralium ſignorum tribus illis modis, quos ad finem
              <lb/>
              <note position="left" xlink:label="note-0332-09" xlink:href="note-0332-09a" xml:space="preserve">40</note>
            propoſ. </s>
            <s xml:id="echoid-s21295" xml:space="preserve">2. </s>
            <s xml:id="echoid-s21296" xml:space="preserve">ſuperioris libri tradidimus poſt demonſtrationem ſecundi modi deſcribendorum ar-
              <lb/>
            cuum ſignorum Zodiaci in horologio horizontali, qui ex figura, in qua radij omnium ſignorum
              <lb/>
            Zodiaci continentur, abſoluitur. </s>
            <s xml:id="echoid-s21297" xml:space="preserve">Nam in primo illorum modorum nulla eſt difficultas, ſi in li-
              <lb/>
            nea ſtyli inueniatur diameter tranſuerſa oppoſitarum hyperbolarum, earumq́ue centrum, nempe
              <unsure/>
              <lb/>
            punctum medium tranſuerſæ diametri, & </s>
            <s xml:id="echoid-s21298" xml:space="preserve">reliqua perficiantur, vt in dicta propoſ. </s>
            <s xml:id="echoid-s21299" xml:space="preserve">2. </s>
            <s xml:id="echoid-s21300" xml:space="preserve">præcedentis
              <lb/>
            lib. </s>
            <s xml:id="echoid-s21301" xml:space="preserve">docuimus. </s>
            <s xml:id="echoid-s21302" xml:space="preserve">Quod verò ad ſecundum illorum modorum ſpectat, axis hyperbolarum in his ho
              <lb/>
            rologijs declinantibus eſt ipſamet linea ſtyli. </s>
            <s xml:id="echoid-s21303" xml:space="preserve">Portiones autem arcuum ſignorum auſtralium vſq;
              <lb/>
            </s>
            <s xml:id="echoid-s21304" xml:space="preserve">ad axem hyperbolarum oppoſitarum, ſeu lineam ſtyli, deſcribendæ ſunt ad partes horæ 6. </s>
            <s xml:id="echoid-s21305" xml:space="preserve">quia eæ
              <lb/>
            commodius deſcribi poſlunt, quàm aliæ verſus horam 12. </s>
            <s xml:id="echoid-s21306" xml:space="preserve">& </s>
            <s xml:id="echoid-s21307" xml:space="preserve">ex eis vno labore non ſolum reliquæ
              <lb/>
            portiones ex altera parte, verum etiam toti arcus ſignorum borealium, qui illis opponuntur, facili
              <lb/>
              <note position="left" xlink:label="note-0332-10" xlink:href="note-0332-10a" xml:space="preserve">50</note>
            negotio delineabuntur, vt in prædicto modo oſtendimus ſuo loco. </s>
            <s xml:id="echoid-s21308" xml:space="preserve">Eſt porrò ſecundus hic modus
              <lb/>
            valde accommodatus ad arcus ſignorum borealium, & </s>
            <s xml:id="echoid-s21309" xml:space="preserve">oppoſitorum rectè deſcribendos, hoc eſt,
              <lb/>
            qui à centro horologii remotiores ſunt. </s>
            <s xml:id="echoid-s21310" xml:space="preserve">Nam, vt vides, horariæ lineę ex C, in figura radiorum ca-
              <lb/>
            dentes, quò longius protenduntur, eò maiorem errandi prębent occaſionem in deſcribendis arcu-
              <lb/>
            bus per radios ſignorum ad ſiniſtram radij Aequatoris in illa figura collocatos, quales hic ſunt ra-
              <lb/>
            dij ſignorum borealium; </s>
            <s xml:id="echoid-s21311" xml:space="preserve">propterea quòd vix fieri poteſt, vt ſine errore accipiantur puncta, vbi di-
              <lb/>
            cti radij à lineis horarijs ſecantur, niſi ſumma diligentia dictæ omnes lineæ ductæ ſint. </s>
            <s xml:id="echoid-s21312" xml:space="preserve">At vero
              <lb/>
            puncta in radijs ſignorum, qui ad dextram radij Aequatoris ponuntur, vicinioresq́ue ſunt puncto
              <lb/>
            C, quales hic ſunt radij auſtralium ſignorum, facilius deprehendi poſſunt, propter breuitatem li-
              <lb/>
            nearum ex C, cadentium, quæ inter C, & </s>
            <s xml:id="echoid-s21313" xml:space="preserve">dictos radios comprehenduntur, ſi conferantur cum eiſ-
              <lb/>
            dem rectis inter C, & </s>
            <s xml:id="echoid-s21314" xml:space="preserve">radios ſignorum borealium comprehenſis. </s>
            <s xml:id="echoid-s21315" xml:space="preserve">Vnde certius arcus </s>
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