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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[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)
[291.] PROBLEMA 24. PROPOSITIO 24.
Page: 368 (352)
[292.] DE HOROLOGIIS ad Horizontem inclinatis.
Page: 369 (353)
[293.] PROBLEMA 25. PROPOSITIO 25.
Page: 369 (353)
[294.] PRÆCEPTVM I.
Page: 369 (353)
[295.] PRAECEPTVM II.
Page: 369 (353)
[296.] PRAECEPTVM III.
Page: 370 (354)
[297.] PRAECEPTVM IIII.
Page: 370 (354)
[298.] PRAECEPTVM V.
Page: 370 (354)
[299.] PRAECEPTVM VI.
Page: 370 (354)
[300.] SCHOLIVM.
Page: 372 (356)
[301.] PROBLEMA 26. PROPOSITIO 26.
Page: 374 (358)
[302.] PROBLEMA 27. PROPOSITIO 27.
Page: 376 (360)
[303.] PROBLEMA 28. PROPOSITIO 28.
Page: 376 (360)
[304.] PROBLEMA 29. PROPOSITIO 29.
Page: 377 (361)
[305.] PROBLEMA 30. PROPOSITIO 30.
Page: 378 (362)
[306.] SEQVITVR FIGVRA.
Page: 378 (362)
[307.] PROBLEMA 31. PROPOSITIO 31.
Page: 379 (363)
[308.] PROBLEMA 32. PROPOSITIO 32.
Page: 379 (363)
[309.] PROBLEMA 33. PROPOSITIO 33.
Page: 381 (365)
[310.] SCHOLIVM.
Page: 382 (366)
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          <p>
            <s xml:id="echoid-s15708" xml:space="preserve">
              <pb o="231" file="0251" n="251" rhead="LIBER SECVNDVS."/>
            punctis in linea meridiana inuentis iungantur rectis lineis, deſcripta erunt aſcendentia ſigna, vt
              <lb/>
            prius, quemadmodum in horologio horizontali propoſ. </s>
            <s xml:id="echoid-s15709" xml:space="preserve">9. </s>
            <s xml:id="echoid-s15710" xml:space="preserve">huius libri diximus, quæ neceſſario
              <lb/>
            tranſibunt per puncta inuenta in linea horizontali.</s>
            <s xml:id="echoid-s15711" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15712" xml:space="preserve">EODEM modo eadẽ ſigna aſcendentia deſcribentur in horologio boreali, ſi pro punctis in li
              <lb/>
            nea meridiana, ſeu in linea horæ 12. </s>
            <s xml:id="echoid-s15713" xml:space="preserve">meridiei inueniẽdis, ſumantur in linea horę 12. </s>
            <s xml:id="echoid-s15714" xml:space="preserve">mediæ noctis
              <lb/>
            ex tabella ſexta propoſ. </s>
            <s xml:id="echoid-s15715" xml:space="preserve">9. </s>
            <s xml:id="echoid-s15716" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s15717" xml:space="preserve">declinationes angulorum terræ. </s>
            <s xml:id="echoid-s15718" xml:space="preserve">Pro punctis verò in linea ho-
              <lb/>
            ræ 6. </s>
            <s xml:id="echoid-s15719" xml:space="preserve">reperiendis capiantur ex tabella ſeptima eiuſdem propoſ. </s>
            <s xml:id="echoid-s15720" xml:space="preserve">9. </s>
            <s xml:id="echoid-s15721" xml:space="preserve">huius libri declinationes pun-
              <lb/>
            ctorum borealium in circulo horæ 6. </s>
            <s xml:id="echoid-s15722" xml:space="preserve">exiſtentium, &</s>
            <s xml:id="echoid-s15723" xml:space="preserve">c. </s>
            <s xml:id="echoid-s15724" xml:space="preserve">Sed ſatius eſt, ſi puncta in horologio auſtra-
              <lb/>
            li reperta transferantur in boreale, mutatis nominibus auſtralium in nomina borealium, & </s>
            <s xml:id="echoid-s15725" xml:space="preserve">con-
              <lb/>
            tra. </s>
            <s xml:id="echoid-s15726" xml:space="preserve">Cum enim habeant eaſdem declinationes, habebunt in vtroque horologio eundem ſitum,
              <lb/>
              <note position="left" xlink:label="note-0251-01" xlink:href="note-0251-01a" xml:space="preserve">10</note>
            & </s>
            <s xml:id="echoid-s15727" xml:space="preserve">diſtantiam.</s>
            <s xml:id="echoid-s15728" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15729" xml:space="preserve">IMMO lineæ rectæ ductæ ex punctis in linea meridiana inuentis tangentes tropicos erunt
              <lb/>
              <note position="right" xlink:label="note-0251-02" xlink:href="note-0251-02a" xml:space="preserve">Quo pacto rur-
                <lb/>
              ſum aſcenden-
                <lb/>
              tia ſigna per el@
                <lb/>
              men@a conica
                <lb/>
              deſcribantur.</note>
            ſigna aſcendentia, vt demonſtratum eſt propoſ. </s>
            <s xml:id="echoid-s15730" xml:space="preserve">9. </s>
            <s xml:id="echoid-s15731" xml:space="preserve">huius libri. </s>
            <s xml:id="echoid-s15732" xml:space="preserve">Ducentur autem huiuſmodi lineæ
              <lb/>
            contingentes, vt docuimus in coroll. </s>
            <s xml:id="echoid-s15733" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s15734" xml:space="preserve">37. </s>
            <s xml:id="echoid-s15735" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s15736" xml:space="preserve">1. </s>
            <s xml:id="echoid-s15737" xml:space="preserve">Apollonii. </s>
            <s xml:id="echoid-s15738" xml:space="preserve">Itaque ſigna Zodiaci aſcenden-
              <lb/>
            tia in eodem Verticali horologio deſcripſimus. </s>
            <s xml:id="echoid-s15739" xml:space="preserve">Quod faciendum erat.</s>
            <s xml:id="echoid-s15740" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div803" type="section" level="1" n="191">
          <head xml:id="echoid-head194" style="it" xml:space="preserve">SCHOLIVM.</head>
          <p style="it">
            <s xml:id="echoid-s15741" xml:space="preserve">EX Andrea Schonero eadem ſigna aſcendentia hoc pacto delineabimus. </s>
            <s xml:id="echoid-s15742" xml:space="preserve">In prima figura ſcholij
              <lb/>
              <note position="right" xlink:label="note-0251-03" xlink:href="note-0251-03a" xml:space="preserve">Quomodo eadé
                <unsure/>
                <lb/>
              ſigna aſcenden-
                <lb/>
              tia deſcribãtur
                <lb/>
              ſecundum pra-
                <lb/>
              xim Andreæ
                <lb/>
              Schoneri.</note>
            propoſ. </s>
            <s xml:id="echoid-s15743" xml:space="preserve">9. </s>
            <s xml:id="echoid-s15744" xml:space="preserve">huius libri abſcindatur ex E B, recta E a, æqualis meridianæ lineæ E I, horologij interceptæ
              <lb/>
              <note position="left" xlink:label="note-0251-04" xlink:href="note-0251-04a" xml:space="preserve">20</note>
            inter E, centrum Aequatoris, & </s>
            <s xml:id="echoid-s15745" xml:space="preserve">lineam æquinoctialem; </s>
            <s xml:id="echoid-s15746" xml:space="preserve">& </s>
            <s xml:id="echoid-s15747" xml:space="preserve">per a, ipſi A C, parallela agatur; </s>
            <s xml:id="echoid-s15748" xml:space="preserve">adeo
              <lb/>
            vt poſito centro E, in centro Aequatoris, & </s>
            <s xml:id="echoid-s15749" xml:space="preserve">puncto a, in puncto I, parallela per a, ducta congruat li-
              <lb/>
            neæ æquinoctiali. </s>
            <s xml:id="echoid-s15750" xml:space="preserve">Secabit parallela per a, ducta lineas ſignorum ex E, emiſſas in punctis, quæ ex a, ac-
              <lb/>
            cepta beneficio circini, & </s>
            <s xml:id="echoid-s15751" xml:space="preserve">in æquinoctialem lineam ex I, in vtramque partem translata dabunt puncta in
              <lb/>
            æquinoctiali linea, per quæ ſi ex puncto G, vbi meridiana linea horizontalem lineã interſecat, rectæ emit-
              <lb/>
            tantur, ſecabuntur duo tropici in punctis, per quæ lineæ ſignorum aſcendentium ducendæ erunt, eo tamen
              <lb/>
            ordine, quem in horizontali horologio præſcripſimus.</s>
            <s xml:id="echoid-s15752" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s15753" xml:space="preserve">QVOD ſi quando recta ex puncto G, educta non ſecet tropicum ♋, vt in exemplo contingit in ſi-
              <lb/>
            gno ♌, & </s>
            <s xml:id="echoid-s15754" xml:space="preserve">♐, argumento id eſt, huiuſmodi ſigna non oriri, Sole exiſtente in principio ♋, illuminante{q́ue} fa-
              <lb/>
            ciem circuli Verticalis auſtralem, ſed dum partem borealem illuſtrat; </s>
            <s xml:id="echoid-s15755" xml:space="preserve">atque ita lineæ illæ ex G, emiſſæ
              <lb/>
              <note position="left" xlink:label="note-0251-05" xlink:href="note-0251-05a" xml:space="preserve">30</note>
            ſecabunt tropicum ♋, in horologio boreali, quod à linea horizontali abſcinditur.</s>
            <s xml:id="echoid-s15756" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s15757" xml:space="preserve">RVRSVS inſecunda figura eiuſdem ſcholij propoſ. </s>
            <s xml:id="echoid-s15758" xml:space="preserve">9. </s>
            <s xml:id="echoid-s15759" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s15760" xml:space="preserve">ſumatur in E B, recta E a, eidem
              <lb/>
            lineæ meridianæ E I, æqualis ex horologio, agatur{q́ue} per a, ipſi A C, parallela, ita vt poſito centro E, in
              <lb/>
            E, centro Aequatoris, & </s>
            <s xml:id="echoid-s15761" xml:space="preserve">puncto a, in puncto I, parallela per a, ducta lineæ æquinoctiali congruat. </s>
            <s xml:id="echoid-s15762" xml:space="preserve">Se-
              <lb/>
            cabit parallela per a, ducta ſignorum lineas ex E, emiſſas in punctis, quæ ex α, accepta, & </s>
            <s xml:id="echoid-s15763" xml:space="preserve">in lineam ęqui
              <lb/>
            noctialem ab I, translata dabunt in æquinoctiali linea puncta, per quæ lineæ aſcendentium ſignor um in-
              <lb/>
            cedere debent, ordine in horologio horizontali tradito. </s>
            <s xml:id="echoid-s15764" xml:space="preserve">Si igitur hæc puncta æquinoctialis lineæ cum
              <lb/>
            punctis tropicorum reſpondentibus iungantur, habebuntur lineæ ſignorum aſcendentium, vt prius. </s>
            <s xml:id="echoid-s15765" xml:space="preserve">Hu-
              <lb/>
            ius deſcriptionis exemplum non poſuimus, quia, vt confuſio linearum vitaretur, tropicos in horologio
              <lb/>
            non deſcripſimus.</s>
            <s xml:id="echoid-s15766" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">40</note>
          <p style="it">
            <s xml:id="echoid-s15767" xml:space="preserve">IAM vcrò ſi lineæ ſignorum aſcendentium vltra horizontalem lineam extendantur, habebuntur
              <lb/>
              <note position="right" xlink:label="note-0251-07" xlink:href="note-0251-07a" xml:space="preserve">Lineæ ſignor@
                <lb/>
              aſcendentiũ vl-
                <lb/>
              tra horizontalé
                <lb/>
              lineam produ-
                <lb/>
              ctæ efficiunt ho
                <lb/>
              rologium bore@
                <lb/>
              le.</note>
            eadem ſigna aſcendentia in horologio boreali, quod ab horizontali linea abſcinditur; </s>
            <s xml:id="echoid-s15768" xml:space="preserve">dummodo ita collo-
              <lb/>
            cetur, vt horizontalis linea in ſuperiori loco ſtatuatur, & </s>
            <s xml:id="echoid-s15769" xml:space="preserve">pars, quæ tunc in eo ſitu nobis ad horologium
              <lb/>
            conuerſis dextra eſt, fiat ſinistra, & </s>
            <s xml:id="echoid-s15770" xml:space="preserve">contra, vt in ſcholio propoſ. </s>
            <s xml:id="echoid-s15771" xml:space="preserve">14. </s>
            <s xml:id="echoid-s15772" xml:space="preserve">huius libri demonſtrauimus.</s>
            <s xml:id="echoid-s15773" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s15774" xml:space="preserve">POTERVNT tamen, ſi libet, ſigna aſcendentia in horologio Boreali deſcribi non ſecus, acin
              <lb/>
            auſtrali deſcripta ſunt: </s>
            <s xml:id="echoid-s15775" xml:space="preserve">ſed facilius multo, & </s>
            <s xml:id="echoid-s15776" xml:space="preserve">expeditius ea ex auſtrali horologio deducemus, productis
              <lb/>
            lineis aſcendentium ſignorum vltra lineam horizontalem, & </s>
            <s xml:id="echoid-s15777" xml:space="preserve">c. </s>
            <s xml:id="echoid-s15778" xml:space="preserve">vt diximus.</s>
            <s xml:id="echoid-s15779" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div807" type="section" level="1" n="192">
          <head xml:id="echoid-head195" xml:space="preserve">PROBLEMA 22. PROPOSITIO 22.</head>
          <note position="left" xml:space="preserve">50</note>
          <p>
            <s xml:id="echoid-s15780" xml:space="preserve">HOROLOGIVM Italicum Verticale conſtituere.</s>
            <s xml:id="echoid-s15781" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15782" xml:space="preserve">HOC non aliter deſcribetur, quàm horizontale; </s>
            <s xml:id="echoid-s15783" xml:space="preserve">ſi tamen in primo modo pro auſtrali horo-
              <lb/>
              <note position="right" xlink:label="note-0251-09" xlink:href="note-0251-09a" xml:space="preserve">Italici horolo-
                <lb/>
              gii Verticalis
                <lb/>
              conſtructio.</note>
            logio arcus diurni tropicorum ♋, & </s>
            <s xml:id="echoid-s15784" xml:space="preserve">♑, in circulo M a N b, ſint a N b, d N e: </s>
            <s xml:id="echoid-s15785" xml:space="preserve">quia punctum N,
              <lb/>
            ad meridiem pertinet, cum vergat ad Meridianum circulum in hemiſphærio ſuperiori; </s>
            <s xml:id="echoid-s15786" xml:space="preserve">diuiſio
              <lb/>
            quoque circuli initium ſumat à punctis b, & </s>
            <s xml:id="echoid-s15787" xml:space="preserve">e, quæ occidentalia ſunt, ſi horologium, & </s>
            <s xml:id="echoid-s15788" xml:space="preserve">circulus
              <lb/>
            M a N b, in proprio ſitu collocentur. </s>
            <s xml:id="echoid-s15789" xml:space="preserve">Sumendus etiam erit nocturnus arcus ♑, ſupra lineam
              <lb/>
            horizontalem, vt in eo reperiantur puncta horarum 15. </s>
            <s xml:id="echoid-s15790" xml:space="preserve">14. </s>
            <s xml:id="echoid-s15791" xml:space="preserve">13. </s>
            <s xml:id="echoid-s15792" xml:space="preserve">& </s>
            <s xml:id="echoid-s15793" xml:space="preserve">c. </s>
            <s xml:id="echoid-s15794" xml:space="preserve">quæ in circulo continentur
              <lb/>
            in arcu nocturno ♑. </s>
            <s xml:id="echoid-s15795" xml:space="preserve">Pro horologio verò boreali, arcus diurni tropicorum ♋, & </s>
            <s xml:id="echoid-s15796" xml:space="preserve">♑, erunt d M e,
              <lb/>
            @ M b; </s>
            <s xml:id="echoid-s15797" xml:space="preserve">quoniam horologio, & </s>
            <s xml:id="echoid-s15798" xml:space="preserve">circulo M a N b, in proprio ſitu collocatis, punctum M, </s>
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