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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[471.] DEMONSTRATIO EORVM, QV AE dicta ſunt in antecedenti cap. de inuentione prædictarum ſex circunferentiarum. CAP. III.
Page: 549 (533)
[472.] INVENTIO CIRCVNFERENTIAE HECTEMORIAE, horariæ, deſcenſiuæ, meridianæ, Verticalis, atque horizontalis, ex Analemmate, Sole exiſtente in quouis parallelo extra æquinoctialem circulum, ad quamcunque latitudinem. C A P. IIII.
Page: 552 (536)
[473.] SCHOLIVM.
Page: 555 (539)
[474.] DEMONSTR ATIO EORVM, QV AE IN ANTECEDENTI cap. dicta ſunt de inuentione prædictarum ſex circun-ferentiarum. CAP. V.
Page: 556 (540)
[475.] DIVISIO ANALEMMATIS IN HORAS, pro quib{us} prædictę circunferentiæ ſunt inueſtigandæ, vt ex illis horo- logium horizontale, Verticale, ac Meridianum con- ſtruatur. CAP. VI.
Page: 557 (541)
[476.] INVENTIO CIRCVNFERENTIAE HECTEMORIAE, horariæ, deſcenſiuæ, meridianæ, Verticalis, atque horizontalis, ex doctrina ſinuum, Sole exiſtente ſiue in Aequatore, ſiue in alio quouis parallelo, ad quamcunque latitudinem. CAP. VII.
Page: 560 (544)
[477.] INVENTIO SVPRADICT ARVM SEX CIRCVNFEREN-tiarum in ſphæra recta tam Geometrice ex Analemmate, quàm per numeros ex doctrina ſinuum, ſiue Sol exiſtat in Aequatore, ſiue in alio quouis parallelo. CAP. VIII.
Page: 571 (555)
[478.] CONSTRVCTIO HOROLOGII HORIZONT ALIS, Verticalis, ac Meridiani, ex ſupradictis ſex circun-ferentijs. CAP. IX.
Page: 575 (559)
[479.] SCHOLIVW.
Page: 576 (560)
[480.] DE HOROLOGIIS DECLINANTIBVS VEL AVERTICALI, vel ab Horizonte, & inclinatis ad Horizontem, & ijs, quæ à Ver-ticali declinant, & ſimul ad Horizontem ſunt inclinata. CAP. X.
Page: 579 (563)
[481.] SCHOLIVM.
Page: 583 (567)
[482.] FINIS SEXTI LIBRI.
Page: 590 (574)
[483.] GNOMONICES LIBER SEPTIMVS.
Page: 591 (575)
[484.] AVCTORE
Page: 591 (575)
[485.] CHRISTOPHORO CLAVIO BAMBERGENSI SOCIETATIS IESV.
Page: 591 (575)
[486.] DE HOROLOGIO HORIZONTALI Aſtronomico. CAP. I.
Page: 591 (575)
[487.] DE ARCVBVS SIGNORVM IN HOROLOGIO horizontali deſcribendis. CAP. II.
Page: 593 (577)
[488.] DE ARCVBVS LONGITVDINVM DIERVM in eodem horologio horizontali deſcribendis. CAP. III.
Page: 596 (580)
[489.] DE HOROLOGIO HORIZONTALI Italico, & Babylonico. CAP. IIII.
Page: 597 (581)
[490.] Horæ ab or. vel occ. & à mer. vel med. noc. ſe mutuo ſecantes in vno \\ eodem puncto lineæ æquinoctialis.
Page: 598 (582)
[491.] DE HOROLOGIO HORIZONT ALI Antiquo. CAP. V.
Page: 600 (584)
[492.] DE HOROLOGIO VERTICALI Aſtronomico. CAP. VI.
Page: 601 (585)
[493.] DE ARCVBVS SIGNORVM IN HOROLOGIO Verticali. CAP. VII.
Page: 602 (586)
[494.] DE ARCVBVS LONGITVDINVM DIERVM in eodem Verticali horologio. CAP. VIII.
Page: 604 (588)
[495.] DE HOROLOGIO VERTIC ALI IT ALICO, & Babylonico. CAP. IX
Page: 604 (588)
[496.] DE HOROLOGIO VERTICALI Antiquo. CAP. X.
Page: 605 (589)
[497.] DE HOROLOGIO MERIDIANO Aſtronomico. CAP. XI.
Page: 606 (590)
[498.] DE ARCVBVS SIGNORVM IN ME- ridiano horologio. CAP. XII.
Page: 607 (591)
[499.] DE ARCVBVS LONGITVDINVM DIERVM in horologio Meridiano. CAP. XIII.
Page: 609 (593)
[500.] DE HOROLOGIO MERIDIANO ITALICO, & Babylonico. CAP. XIIII.
Page: 609 (593)
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          <pb o="431" file="0447" n="447" rhead="LIBER QVARTVS."/>
          <p style="it">
            <s xml:id="echoid-s28301" xml:space="preserve">HAEC omnia alijs quoque horologijs conueniunt, prout altitudo poli ſuper circulos maximos, qui-
              <lb/>
              <note position="right" xlink:label="note-0447-01" xlink:href="note-0447-01a" xml:space="preserve">Quomodo idé
                <lb/>
              ſciatur in aliis
                <lb/>
              horologiis.</note>
            bus eorum plana æquidiſtant, maior fuerit, æqualiſue, aut minor maxima Solis declinatione, aut denique
              <lb/>
            nulla. </s>
            <s xml:id="echoid-s28302" xml:space="preserve">Ita k
              <unsure/>
            ides in horologijs, quæ lib. </s>
            <s xml:id="echoid-s28303" xml:space="preserve">2. </s>
            <s xml:id="echoid-s28304" xml:space="preserve">& </s>
            <s xml:id="echoid-s28305" xml:space="preserve">3. </s>
            <s xml:id="echoid-s28306" xml:space="preserve">deſcripſimus, nempe in horizontali, verticali, Aequinoctia
              <lb/>
            li, Declinante à verticali, Declinante ab Horizonte, Inclinato ad Horizontem, & </s>
            <s xml:id="echoid-s28307" xml:space="preserve">in Declinante ſimul
              <lb/>
            ac inclinato, in quo propoſ. </s>
            <s xml:id="echoid-s28308" xml:space="preserve">38. </s>
            <s xml:id="echoid-s28309" xml:space="preserve">ſuperioris lib. </s>
            <s xml:id="echoid-s28310" xml:space="preserve">arcus ſignorum delineauimus, locum ſtyli extra tropicos
              <lb/>
            eſſe conſtitutum; </s>
            <s xml:id="echoid-s28311" xml:space="preserve">quia altitudo poli ſupra maximos circulos, quibus ea horologia ſunt parallela, maximã
              <lb/>
            Solis declinationem ſuperat: </s>
            <s xml:id="echoid-s28312" xml:space="preserve">In horologio autem horizontali, quod in ſcholio propoſ. </s>
            <s xml:id="echoid-s28313" xml:space="preserve">2. </s>
            <s xml:id="echoid-s28314" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s28315" xml:space="preserve">2. </s>
            <s xml:id="echoid-s28316" xml:space="preserve">contine-
              <lb/>
            tur, locum ſtyli intra tropicum cadere; </s>
            <s xml:id="echoid-s28317" xml:space="preserve">quoniã altitudo poli ſupra illum Horizontem minor eſt maxima
              <lb/>
            declinatione Solis: </s>
            <s xml:id="echoid-s28318" xml:space="preserve">In horologio denique Meridiano, Polari, Declinante ſimul ac inclinato, quod tertio
              <lb/>
            loco conſtruximus propoſ. </s>
            <s xml:id="echoid-s28319" xml:space="preserve">37. </s>
            <s xml:id="echoid-s28320" xml:space="preserve">ſuperioris lib. </s>
            <s xml:id="echoid-s28321" xml:space="preserve">& </s>
            <s xml:id="echoid-s28322" xml:space="preserve">in horologiis ſphæræ rectæ hoc lib. </s>
            <s xml:id="echoid-s28323" xml:space="preserve">compoſitis, ſtylum ca-
              <lb/>
              <note position="left" xlink:label="note-0447-02" xlink:href="note-0447-02a" xml:space="preserve">10</note>
            dere in ipſam lineam æquinoctialem, propterea quòd nulla eſt altitudo poli ſupra circulos maximos, qui-
              <lb/>
            bus ca horologia æquidiſtant.</s>
            <s xml:id="echoid-s28324" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1461" type="section" level="1" n="354">
          <head xml:id="echoid-head367" xml:space="preserve">PROBLEMA 12. PROPOSITIO 12.</head>
          <p>
            <s xml:id="echoid-s28325" xml:space="preserve">GNOMONEM cuiuſcunque horologii proprio in loco ita col-
              <lb/>
            locare, vt ad planum horologij rectus ſit, eiuſq́; </s>
            <s xml:id="echoid-s28326" xml:space="preserve">verticem in propriam
              <lb/>
            ſedem, ſi quando ab ea deflexerit, reſtituere.</s>
            <s xml:id="echoid-s28327" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">20</note>
          <p>
            <s xml:id="echoid-s28328" xml:space="preserve">SIT ſtylus, ſiue gnomon cuiuſuis horologii A B, eiuſq́ue locus in puncto A, in quo ita eum
              <lb/>
            oporteat horologio infigere, vt ad planum horologii rectus ſit, &</s>
            <s xml:id="echoid-s28329" xml:space="preserve">c. </s>
            <s xml:id="echoid-s28330" xml:space="preserve">Ex A, loco ſtyli circulus in
              <lb/>
              <note position="right" xlink:label="note-0447-04" xlink:href="note-0447-04a" xml:space="preserve">Qua ratione
                <lb/>
              ſlylus rectus ad
                <lb/>
              planum horelo
                <lb/>
              gii fit colloc@@-
                <lb/>
              dus.</note>
            horologii plano deſcribatur C D E, cuiuslibet magnitudinis, in quo tria puncta eligantur vtcun-
              <lb/>
            que C, D, E. </s>
            <s xml:id="echoid-s28331" xml:space="preserve">Deinde in A, erigatur ſtylus A B, eiuſq́ue vertex B, hinc inde moueatur, donec be-
              <lb/>
            neficio circini deprehendantur æquales tres rectæ, quæ ex punctis C, D, E, ad verticem B, perti-
              <lb/>
            nent. </s>
            <s xml:id="echoid-s28332" xml:space="preserve">Dico tunc gnomonem A B, ad
              <lb/>
            planum horologii, in quo circulus
              <lb/>
              <figure xlink:label="fig-0447-01" xlink:href="fig-0447-01a" number="296">
                <image file="0447-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0447-01"/>
              </figure>
            C D E, exiſtit, rectum eſſe. </s>
            <s xml:id="echoid-s28333" xml:space="preserve">Si enim
              <lb/>
            nõ dicatur eſſe rectus, demitti intel-
              <lb/>
            ligatur ex vertice B, ad planũ horo-
              <lb/>
              <note position="left" xlink:label="note-0447-05" xlink:href="note-0447-05a" xml:space="preserve">30</note>
            logii alia linea perpendicularis B F,
              <lb/>
            ſi fieri poteſt, cadens in punctum F,
              <lb/>
            diuerſum ab A. </s>
            <s xml:id="echoid-s28334" xml:space="preserve">Ductis rectis C F,
              <lb/>
            D F, E F, erit per defin. </s>
            <s xml:id="echoid-s28335" xml:space="preserve">3. </s>
            <s xml:id="echoid-s28336" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s28337" xml:space="preserve">11. </s>
            <s xml:id="echoid-s28338" xml:space="preserve">Eu
              <lb/>
            clidis ad omnes has recta B F, per-
              <lb/>
            pendicularis, atque adeo triangula
              <lb/>
            B F C, B F D, B F E, rectãgula erunt;
              <lb/>
            </s>
            <s xml:id="echoid-s28339" xml:space="preserve">ac propterea & </s>
            <s xml:id="echoid-s28340" xml:space="preserve">quadratum ex B C,
              <lb/>
            quadratis ex B F, F C, & </s>
            <s xml:id="echoid-s28341" xml:space="preserve">quadratũ ex
              <lb/>
            B D, quadratis ex B F, F D, & </s>
            <s xml:id="echoid-s28342" xml:space="preserve">quadra-
              <lb/>
            tũ ex B E, quadratis ex B F, F E, ęqua-
              <lb/>
              <note position="left" xlink:label="note-0447-06" xlink:href="note-0447-06a" xml:space="preserve">40</note>
              <note position="right" xlink:label="note-0447-07" xlink:href="note-0447-07a" xml:space="preserve">49. primi.</note>
            le erit. </s>
            <s xml:id="echoid-s28343" xml:space="preserve">Quia verò quadrata trium li-
              <lb/>
            nearum B C, B D, B E, quæ æquales
              <lb/>
            ponuntur, æqualia ſunt, erunt qua-
              <lb/>
            drata ex B F, F C, tam quadratis ex
              <lb/>
            B F, F D, quàm quadratis ex B F,
              <lb/>
            F E, æqualia. </s>
            <s xml:id="echoid-s28344" xml:space="preserve">Ablato ergo commu-
              <lb/>
            ni quadrato rectę B F, æqualia remanebunt quadrata rectarum F C, F D, F E; </s>
            <s xml:id="echoid-s28345" xml:space="preserve">ac idcirco & </s>
            <s xml:id="echoid-s28346" xml:space="preserve">ipſę
              <lb/>
            rectæ æquales erunt. </s>
            <s xml:id="echoid-s28347" xml:space="preserve">Punctum ergo F, centrum erit circuli C D E, quod eſt abſurdum. </s>
            <s xml:id="echoid-s28348" xml:space="preserve">Eſt enim
              <lb/>
              <note position="right" xlink:label="note-0447-08" xlink:href="note-0447-08a" xml:space="preserve">9. tertij.</note>
            A, centrum dicti circuli. </s>
            <s xml:id="echoid-s28349" xml:space="preserve">Non igitur ex B, vertice ſtyli ad planum horologii perpendicularis de-
              <lb/>
              <note position="left" xlink:label="note-0447-09" xlink:href="note-0447-09a" xml:space="preserve">50</note>
            miſſa cadet in F, punctum ab A, diuerſum, ac proinde in A, cadet. </s>
            <s xml:id="echoid-s28350" xml:space="preserve">Quare recta A B, ita erecta, ut
              <lb/>
            tres rectæ C B, D B, E B, ſint æquales, ad planum propoſitum perpendicularis erit.</s>
            <s xml:id="echoid-s28351" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">Quantum in-
            <lb/>
          ter ſe diſtare de
            <lb/>
          beant erura eir
            <lb/>
          cini, vt benefi-
            <lb/>
          cio circuli ſty-
            <lb/>
          lus ad planum
            <lb/>
          horologii re-
            <lb/>
          ctus ſtatuatur.</note>
          <p>
            <s xml:id="echoid-s28352" xml:space="preserve">VT autem ſciamus, quanto interuallo inter ſe diſtare debeãt circini crura, vt vno crure poſito
              <lb/>
            in tribus quibuſcunque punctis circunferentię C D E, altero verticem ſtyli B, ad horologii planũ
              <lb/>
            recti attingamus, deſcribemus triangulum rectangulum G H I, cuius latus G H, ſtylo, & </s>
            <s xml:id="echoid-s28353" xml:space="preserve">G I, ſemi-
              <lb/>
            diametro A E, ſit æquale. </s>
            <s xml:id="echoid-s28354" xml:space="preserve">Nam interuallum rectæ I H, æquale erit ſingulis interuallis inter pun-
              <lb/>
            cta C, D, E, & </s>
            <s xml:id="echoid-s28355" xml:space="preserve">verticem B, ſi ſtylus ad planum horologii rectus fuerit. </s>
            <s xml:id="echoid-s28356" xml:space="preserve">Cum enim duo latera
              <lb/>
            G H, G I, trianguli G H I, æqualia ſint duobus lateribus A B, A E, trianguli A B E, habeantq́ue
              <lb/>
            angulos G, A, æquales, vtpote rectos, erunt quoque baſes I H, E B, æquales inter ſe; </s>
            <s xml:id="echoid-s28357" xml:space="preserve">& </s>
            <s xml:id="echoid-s28358" xml:space="preserve">eadem ra-
              <lb/>
              <note position="right" xlink:label="note-0447-11" xlink:href="note-0447-11a" xml:space="preserve">4. primi.</note>
            tione I H, rectis D B, C B, æqualis oſtendetur. </s>
            <s xml:id="echoid-s28359" xml:space="preserve">Itaque vt ſtylum A B, in puncto A, ita figamus, vt
              <lb/>
            rectus ſit ad planum horologii, neceſſe eſt, vt vno pede circini in quouis puncto </s>
          </p>
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