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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        <div xml:id="echoid-div375" type="section" level="1" n="132">
          <head xml:id="echoid-head135" xml:space="preserve">PROBLEMA 12. PROPOSITIO 33.</head>
          <p>
            <s xml:id="echoid-s6382" xml:space="preserve">DATO arcu diurno, nocturnove, & </s>
            <s xml:id="echoid-s6383" xml:space="preserve">latitudine loci, declinationem
              <lb/>
            paralleli illius arcus ab Aequatore inquirere.</s>
            <s xml:id="echoid-s6384" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6385" xml:space="preserve">DIVIDATVR circulus quicunque A B C D, cuius centrũ P, & </s>
            <s xml:id="echoid-s6386" xml:space="preserve">in quo duæ diametri A C,
              <lb/>
              <note position="left" xlink:label="note-0126-01" xlink:href="note-0126-01a" xml:space="preserve">Declinatio pa-
                <lb/>
              talleli, cuius
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              arcus di@@nus
                <lb/>
              contineat quot-
                <lb/>
              cunque quis @@@
                <lb/>
              ras propoſu@ri@
                <lb/>
              quo artificio in
                <lb/>
              ueniatur per
                <lb/>
              Analemma.</note>
            B D, ſe mutuo ad angulos rectos ſecantes, in horas vigintiquatuor æquales vnà cum ſemihoris,
              <lb/>
              <figure xlink:label="fig-0126-01" xlink:href="fig-0126-01a" number="92">
                <image file="0126-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0126-01"/>
              </figure>
            & </s>
            <s xml:id="echoid-s6387" xml:space="preserve">quadrantibus, ſi placuerit, initio
              <lb/>
            facto à quouis punctorum A, B, C, D.
              <lb/>
            </s>
            <s xml:id="echoid-s6388" xml:space="preserve">Numerato autẽ à puncto B, hinc in-
              <lb/>
              <note position="left" xlink:label="note-0126-02" xlink:href="note-0126-02a" xml:space="preserve">10</note>
            de arcu ſemidiurno B E, B F, vel à D,
              <lb/>
            hinc inde arcu ſeminocturno D E,
              <lb/>
            D F, vt totus arcus E B F, ſit verbi gra-
              <lb/>
            tia arcus diurnus horarum 14. </s>
            <s xml:id="echoid-s6389" xml:space="preserve">vel
              <lb/>
            E D F, arcus nocturnus horarum 10.
              <lb/>
            </s>
            <s xml:id="echoid-s6390" xml:space="preserve">datus, ducatur recta E F, ſecans B D,
              <lb/>
            in G, quæ ipſi A C, ob æquales arcus
              <lb/>
            A E, C F, parallela erit, per ea, quæ ad
              <lb/>
            propoſ. </s>
            <s xml:id="echoid-s6391" xml:space="preserve">27. </s>
            <s xml:id="echoid-s6392" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s6393" xml:space="preserve">3. </s>
            <s xml:id="echoid-s6394" xml:space="preserve">Euclidis, demonſtra
              <lb/>
            uimus; </s>
            <s xml:id="echoid-s6395" xml:space="preserve">atque adeo ad B D, perpendi-
              <lb/>
              <note position="left" xlink:label="note-0126-03" xlink:href="note-0126-03a" xml:space="preserve">20</note>
            cularis. </s>
            <s xml:id="echoid-s6396" xml:space="preserve">Conſtituatur iam angulus
              <lb/>
              <note position="left" xlink:label="note-0126-04" xlink:href="note-0126-04a" xml:space="preserve">29. primi.</note>
            P G k, æqualis angulo altitudinis Ae-
              <lb/>
            quatoris, ſeu complementi altítudi-
              <lb/>
            nis poli; </s>
            <s xml:id="echoid-s6397" xml:space="preserve">ſecetq́; </s>
            <s xml:id="echoid-s6398" xml:space="preserve">recta G k, rectã A C,
              <lb/>
            in k, puncto, ex quo recta ducatur
              <lb/>
            K B. </s>
            <s xml:id="echoid-s6399" xml:space="preserve">Dico P B k, æqualem eſſe angu-
              <lb/>
            lo declinationis paralleli illius, cuius
              <lb/>
            arcus diurnus tot horas cõplectitur,
              <lb/>
            quot ſunt in arcu E B F, nempe 14. </s>
            <s xml:id="echoid-s6400" xml:space="preserve">Ducta enim recta K D, deſcribatur circulus B O M N, ex cen-
              <lb/>
            tro K, interualloq́; </s>
            <s xml:id="echoid-s6401" xml:space="preserve">k B, vel K D. </s>
            <s xml:id="echoid-s6402" xml:space="preserve">Sunt enim rectæ K B, K D, inter ſe æquales. </s>
            <s xml:id="echoid-s6403" xml:space="preserve">Nam cum latera
              <lb/>
              <note position="left" xlink:label="note-0126-05" xlink:href="note-0126-05a" xml:space="preserve">30</note>
            B P, P K, lateribus D P, P K, in triangulis B P K, D P K, ęqualia ſint, angulosq́; </s>
            <s xml:id="echoid-s6404" xml:space="preserve">contineant æqua-
              <lb/>
            les, vtpote rectos, ęquales erunt rectæ K B, K D. </s>
            <s xml:id="echoid-s6405" xml:space="preserve">Deinde per K, ipſi B D, parallela agatur diame-
              <lb/>
              <note position="left" xlink:label="note-0126-06" xlink:href="note-0126-06a" xml:space="preserve">4. primi.</note>
            ter L M. </s>
            <s xml:id="echoid-s6406" xml:space="preserve">Extendatur quoque recta G K, hinc inde. </s>
            <s xml:id="echoid-s6407" xml:space="preserve">Quoniam igitur P G K, ex conſtructione, an-
              <lb/>
            gulus eſt complementi altitudinis poli, erit P
              <emph style="sc">K</emph>
            G, angulus altitudinis poli. </s>
            <s xml:id="echoid-s6408" xml:space="preserve">Quare arcus I N, alti-
              <lb/>
            tudinem poli ſupra Horizontem metietur, atque adeo ſi circulus N L O M, ponatur eſſe Meridia
              <lb/>
            nus, erit recta HI, communis ſectio Meridiani, & </s>
            <s xml:id="echoid-s6409" xml:space="preserve">Horizontis; </s>
            <s xml:id="echoid-s6410" xml:space="preserve">N O, axis mundi; </s>
            <s xml:id="echoid-s6411" xml:space="preserve">L M, commu-
              <lb/>
            nis ſectio Meridiani, & </s>
            <s xml:id="echoid-s6412" xml:space="preserve">Acquatoris; </s>
            <s xml:id="echoid-s6413" xml:space="preserve">B D, communis ſectio Meridiani, & </s>
            <s xml:id="echoid-s6414" xml:space="preserve">paralleli A B C D, cuius
              <lb/>
            arcus diurnus E B F, datus. </s>
            <s xml:id="echoid-s6415" xml:space="preserve">Eſt enim E F, communis ſectio Horizontis, & </s>
            <s xml:id="echoid-s6416" xml:space="preserve">paralleli A B C D, quod
              <lb/>
            ita planum fiet. </s>
            <s xml:id="echoid-s6417" xml:space="preserve">Quoniam tam Horizon per HI, ductus, quàm parallelus A B C D, ad Meridianũ
              <lb/>
            N L O M, rectus eſt, ſi hi circuli propriã cõcipiantur habere poſitionẽ in ſphæra, erit quoque com
              <lb/>
              <note position="left" xlink:label="note-0126-07" xlink:href="note-0126-07a" xml:space="preserve">40</note>
            munis eorũ ſectio, quæ quidẽ in G, cadit, vbi ſe interſecãt Horizon & </s>
            <s xml:id="echoid-s6418" xml:space="preserve">dictus parallelus, ad Meridia
              <lb/>
              <note position="left" xlink:label="note-0126-08" xlink:href="note-0126-08a" xml:space="preserve">19. vndec.</note>
            num recta, atque adeo per defin. </s>
            <s xml:id="echoid-s6419" xml:space="preserve">3. </s>
            <s xml:id="echoid-s6420" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s6421" xml:space="preserve">11. </s>
            <s xml:id="echoid-s6422" xml:space="preserve">Eucl. </s>
            <s xml:id="echoid-s6423" xml:space="preserve">perpendicularis ad rectam B D, in Meridiano exi-
              <lb/>
            ftentem. </s>
            <s xml:id="echoid-s6424" xml:space="preserve">Cum ergo E F, per G, ducta, ſit oſtenſa perpendicularis ad B D, erit E F, communis ſectio
              <lb/>
            Horizontis & </s>
            <s xml:id="echoid-s6425" xml:space="preserve">paralleli A B C D. </s>
            <s xml:id="echoid-s6426" xml:space="preserve">Eſt ergo B L, in Meridiano N L O M, arcus declinationis paral-
              <lb/>
            leli A B C D, ab Aequatore, atque adeo B K L, angulus eiuſdem declinationis, cui quidem æqua-
              <lb/>
            lis eſt angulus P B K, alternus, quod eſt propoſitum.</s>
            <s xml:id="echoid-s6427" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">29. primi.</note>
          <p>
            <s xml:id="echoid-s6428" xml:space="preserve">EODEM modo inueniemus Q B P, angulum declinationis paralleli, cuius arcus diurnus con
              <lb/>
            tinet horas 13. </s>
            <s xml:id="echoid-s6429" xml:space="preserve">Item R B P, angulum declinationis paralleli, cuius arcus diurnus horas 15. </s>
            <s xml:id="echoid-s6430" xml:space="preserve">comple
              <lb/>
            ctitur, &</s>
            <s xml:id="echoid-s6431" xml:space="preserve">c. </s>
            <s xml:id="echoid-s6432" xml:space="preserve">Simili ratione reperiemus angulum declinationis paralleli auſtralis, cuius arcus diur-
              <lb/>
            nus continet pauciores hotas, quàm 12. </s>
            <s xml:id="echoid-s6433" xml:space="preserve">nempe 9, vel 8, &</s>
            <s xml:id="echoid-s6434" xml:space="preserve">c. </s>
            <s xml:id="echoid-s6435" xml:space="preserve">Nam in eadem figura, ſi à puncto D,
              <lb/>
              <note position="left" xlink:label="note-0126-10" xlink:href="note-0126-10a" xml:space="preserve">50</note>
            vtrinque numeretur exempli gratia arcus ſemidiurnus D E, D F, horarum 5. </s>
            <s xml:id="echoid-s6436" xml:space="preserve">& </s>
            <s xml:id="echoid-s6437" xml:space="preserve">cætera fiant, vt
              <lb/>
            prius, erit HI, communis ſectio Horizontis, & </s>
            <s xml:id="echoid-s6438" xml:space="preserve">Meridiani, arcusq́; </s>
            <s xml:id="echoid-s6439" xml:space="preserve">H O, numerabit altitudinẽ po-
              <lb/>
            li ſupra Horizontem, & </s>
            <s xml:id="echoid-s6440" xml:space="preserve">B D, erit parallelus auſtralis; </s>
            <s xml:id="echoid-s6441" xml:space="preserve">angulus declinationis P D K, vel D K M, & </s>
            <s xml:id="echoid-s6442" xml:space="preserve">
              <lb/>
            ſic de reliquis.</s>
            <s xml:id="echoid-s6443" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6444" xml:space="preserve">IDEM parallelus auſtralis, cuius arcus diurnus datus eſt, nempe horarũ 10. </s>
            <s xml:id="echoid-s6445" xml:space="preserve">inuenietur hac ra-
              <lb/>
            tione. </s>
            <s xml:id="echoid-s6446" xml:space="preserve">Numeretur à puncto B, in vtramque partẽ arcus ſemidiurnus, nimirũ hor. </s>
            <s xml:id="echoid-s6447" xml:space="preserve">5. </s>
            <s xml:id="echoid-s6448" xml:space="preserve">in dato exem
              <lb/>
            plo. </s>
            <s xml:id="echoid-s6449" xml:space="preserve">Deinde per extremitates horum arcuum ſemidiurnorum ducatur recta linea ſecans rectam
              <lb/>
            B D, in puncto, per quod ſi agatur ipſi H I, parallela, conſtituens nimirum cum B D, angulum cõ-
              <lb/>
            plementi altitudinis poli angulo B G H, æqualem, ſecabitur recta A P, in puncto, ad quod ducta
              <lb/>
            recta ex B, continebit cum recta B D, angulum declinationis quæſitum, qui omnino æqualis erit
              <lb/>
            angulo P D K, vel P B K. </s>
            <s xml:id="echoid-s6450" xml:space="preserve">Atque ſic de cæteris. </s>
            <s xml:id="echoid-s6451" xml:space="preserve">Exemplum huius inuenies in ſecunda figura </s>
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