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-div338" type="section" level="1" n="126">
          <p style="it">
            <s xml:id="echoid-s5584" xml:space="preserve">
              <pb o="98" file="0118" n="118" rhead="GNOMONICES"/>
            per Φ, ducamus ad A E, perpendicularem φ χ, accipiamuſ{q́ue} φ χ, vmbræ A B, æqualem, dabit recta
              <lb/>
            χ E, producta ad S, amplitudinem Solis ortiuam, vel occiduam C S. </s>
            <s xml:id="echoid-s5585" xml:space="preserve">Cum enim planum F D, ſit in plano
              <lb/>
            Meridiani, erit gnomon A E, pars communis ſectionis verticalis proprie dicti, & </s>
            <s xml:id="echoid-s5586" xml:space="preserve">Horizontis. </s>
            <s xml:id="echoid-s5587" xml:space="preserve">Si igitur
              <lb/>
            circulus A B C D, pro Horizonte ſumatur, intelligatur{q́ue} tabulæ F D, applicari, ita vt punctum φ, in
              <lb/>
              <figure xlink:label="fig-0118-01" xlink:href="fig-0118-01a" number="83">
                <image file="0118-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0118-01"/>
              </figure>
            A, & </s>
            <s xml:id="echoid-s5588" xml:space="preserve">χ, in B, cadat, ob æqua
              <lb/>
            litatẽ rectarum A B, φ χ, ca-
              <lb/>
            det centrũ E, in extremũ ſtyli
              <lb/>
            E, propter æqualitatẽ rectarũ
              <lb/>
            A E, φ E. </s>
            <s xml:id="echoid-s5589" xml:space="preserve">Quare linea recta
              <lb/>
            χ E, cõgruet radio Solis B
              <unsure/>
            E,
              <lb/>
              <note position="left" xlink:label="note-0118-01" xlink:href="note-0118-01a" xml:space="preserve">10</note>
            ac propterea producta cadet
              <lb/>
            in S, punctum ortus, vel occa-
              <lb/>
            ſus in Horizonte. </s>
            <s xml:id="echoid-s5590" xml:space="preserve">Igitur arcus
              <lb/>
            C S, amplitudo erit ortiua,
              <lb/>
            vel occidua. </s>
            <s xml:id="echoid-s5591" xml:space="preserve">Aduertendum ta
              <lb/>
            men est, ſi matutino tempore
              <lb/>
            obſeruatio fiat, vmbra{q́ue} cadat
              <lb/>
            in rectam A F, ſolem eſſe bo-
              <lb/>
            realẽ. </s>
            <s xml:id="echoid-s5592" xml:space="preserve">vnde amplitudo ſumen-
              <lb/>
            da tunc erit à C, verſus par-
              <lb/>
              <note position="left" xlink:label="note-0118-02" xlink:href="note-0118-02a" xml:space="preserve">20</note>
            tes ſeptentrionales, nempe ver
              <lb/>
            ſus D: </s>
            <s xml:id="echoid-s5593" xml:space="preserve">Si autem vmbra cadat
              <lb/>
            in rectam A G, Solem eſſe au
              <lb/>
            ſtralẽ. </s>
            <s xml:id="echoid-s5594" xml:space="preserve">Quare amplitudo nume
              <lb/>
            rãda erit à C, verſus auſtrales
              <lb/>
            partes, hoc eſt, uerſus B. </s>
            <s xml:id="echoid-s5595" xml:space="preserve">Con-
              <lb/>
            trariũ intelligatur, ſi obſerua-
              <lb/>
            tio fiat tẽpore veſpertino. </s>
            <s xml:id="echoid-s5596" xml:space="preserve">Vm-
              <lb/>
            bra enim cadẽte in rectã AG,
              <lb/>
            Sol borealis eſt, auſtralis vero,
              <lb/>
              <note position="left" xlink:label="note-0118-03" xlink:href="note-0118-03a" xml:space="preserve">30</note>
            umbra cadente in rectã A F,
              <lb/>
            vt perſpicuum eſt.</s>
            <s xml:id="echoid-s5597" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s5598" xml:space="preserve">POSTREMO, vt omnia hæc facili{us}, & </s>
            <s xml:id="echoid-s5599" xml:space="preserve">rectius fiant, ducendæ erunt in circulo A B C D, ante-
              <lb/>
            quam ſtylus infigatur, aliquot rectę lineæ pro communibus ſectionibus Verticalium circulorum, & </s>
            <s xml:id="echoid-s5600" xml:space="preserve">cir-
              <lb/>
            culi A B C D. </s>
            <s xml:id="echoid-s5601" xml:space="preserve">Vt in figura ducta eſt F G, diſtans ab A C, grad. </s>
            <s xml:id="echoid-s5602" xml:space="preserve">30. </s>
            <s xml:id="echoid-s5603" xml:space="preserve">& </s>
            <s xml:id="echoid-s5604" xml:space="preserve">K L, grad. </s>
            <s xml:id="echoid-s5605" xml:space="preserve">50. </s>
            <s xml:id="echoid-s5606" xml:space="preserve">& </s>
            <s xml:id="echoid-s5607" xml:space="preserve">γβ, grad. </s>
            <s xml:id="echoid-s5608" xml:space="preserve">6.
              <lb/>
            </s>
            <s xml:id="echoid-s5609" xml:space="preserve">Min. </s>
            <s xml:id="echoid-s5610" xml:space="preserve">30. </s>
            <s xml:id="echoid-s5611" xml:space="preserve">& </s>
            <s xml:id="echoid-s5612" xml:space="preserve">c. </s>
            <s xml:id="echoid-s5613" xml:space="preserve">Nam cadente vmbrę extremitate in aliquam dictarum linearum, ſciemus, in quonam Ver-
              <lb/>
            ticali circulo Sol ſit. </s>
            <s xml:id="echoid-s5614" xml:space="preserve">Vnde accepta tunc eius altitudine, progrediemur vt prius. </s>
            <s xml:id="echoid-s5615" xml:space="preserve">Hoc autem idcirco
              <lb/>
            fieri debet, quoniam ſtylus, ſi prius infigatur, antequàm lineæ per centrum ducantur ex puncto extremo in
              <lb/>
            vmbra notato, impedimento eſt, ne per centrum dictæ lineæ rectę duci poſſint. </s>
            <s xml:id="echoid-s5616" xml:space="preserve">At vero ſi pro ſtylo vſur-
              <lb/>
            pemus inſtrumentum in principio ſcholij propoſ. </s>
            <s xml:id="echoid-s5617" xml:space="preserve">23. </s>
            <s xml:id="echoid-s5618" xml:space="preserve">hui{us} lib. </s>
            <s xml:id="echoid-s5619" xml:space="preserve">deſcriptum, hac cautione opus non erit,
              <lb/>
              <note position="left" xlink:label="note-0118-04" xlink:href="note-0118-04a" xml:space="preserve">40</note>
            cum illud instrumentum poſt obſeruationem vmbrę amoueri queat, vt lineæ per centrum E, poſſint duci
              <lb/>
            ſine impedimento.</s>
            <s xml:id="echoid-s5620" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s5621" xml:space="preserve">IAM verò ſi per doctrinam ſinuum quantitatem anguli P R Q, altitudinis poli metiri volueri-
              <lb/>
              <note position="left" xlink:label="note-0118-05" xlink:href="note-0118-05a" xml:space="preserve">Altitudo poli
                <lb/>
              ſupra Horizon-
                <lb/>
              tem qua ratio-
                <lb/>
              ne ſupputetur
                <lb/>
              per ſinus</note>
            mus, efficiemus id hoc modo. </s>
            <s xml:id="echoid-s5622" xml:space="preserve">Quoniam arcus G H, altitudinis Solis notus eſt, cognitus erit eius comple-
              <lb/>
            menti ſinus E I. </s>
            <s xml:id="echoid-s5623" xml:space="preserve">Quia verò & </s>
            <s xml:id="echoid-s5624" xml:space="preserve">angulus C E G, notus eſt, ex vmbræ obſeruatione, (Cum enim vmbra ca-
              <lb/>
            dat in E F, metientur gradus arcus A F, angulum A E F, hoc eſt, C E G,) erit & </s>
            <s xml:id="echoid-s5625" xml:space="preserve">alternus E I O, il
              <lb/>
              <note position="left" xlink:label="note-0118-06" xlink:href="note-0118-06a" xml:space="preserve">29. primi.</note>
            li æqualis, in triangulo rectangulo E I O, notus. </s>
            <s xml:id="echoid-s5626" xml:space="preserve">Igitur & </s>
            <s xml:id="echoid-s5627" xml:space="preserve">E O, ſinus anguli E I O, notus erit in parti-
              <lb/>
            bus ſinus totius E I. </s>
            <s xml:id="echoid-s5628" xml:space="preserve">Quòd ſi fiat, vt E I, ſinus totus ad E I, quatenus nota eſt in partibus ſinus totius
              <lb/>
            E G, ita E O, quatenus ſinus eſt anguli E I O, ad aliud, nota fiet E O, in partibus ſinus totius E G, vel
              <lb/>
            E B. </s>
            <s xml:id="echoid-s5629" xml:space="preserve">Eadem ratione in eiſdem partibus not a fiet E P. </s>
            <s xml:id="echoid-s5630" xml:space="preserve">Detracta ergo E O, ex E P, nota fiet O P, in eiſ-
              <lb/>
              <note position="left" xlink:label="note-0118-07" xlink:href="note-0118-07a" xml:space="preserve">50</note>
            dem partibus. </s>
            <s xml:id="echoid-s5631" xml:space="preserve">Ducta autem recta Q ω, ex Q, ad P R, perpendiculari, erit tam Q ω, ipſi O P, quàm
              <lb/>
              <note position="left" xlink:label="note-0118-08" xlink:href="note-0118-08a" xml:space="preserve">34. primi.</note>
            P ω, ipſi O Q, æqualis. </s>
            <s xml:id="echoid-s5632" xml:space="preserve">Igitur & </s>
            <s xml:id="echoid-s5633" xml:space="preserve">Q ω, in partibus ſinus totius E B, not a erit. </s>
            <s xml:id="echoid-s5634" xml:space="preserve">Sunt autem in eiſdem par
              <lb/>
            tibus notæ rectæ O Q, hoc eſt, P ω, & </s>
            <s xml:id="echoid-s5635" xml:space="preserve">P R, cum ſint æquales ſinubus rectis I H, N M, altitudinum So-
              <lb/>
            lis notarum. </s>
            <s xml:id="echoid-s5636" xml:space="preserve">Detracta ergo recta P ω, ex P R, erit & </s>
            <s xml:id="echoid-s5637" xml:space="preserve">reliqua ω R, in eiſdem partib{us} nota. </s>
            <s xml:id="echoid-s5638" xml:space="preserve">Cum igi-
              <lb/>
            tur quadrata rectarum ω Q, ω R, æqualia ſint quadrato rectæ Q R, fiet quoque Q R, in eiſdem parti-
              <lb/>
              <note position="left" xlink:label="note-0118-09" xlink:href="note-0118-09a" xml:space="preserve">47. primi.</note>
            bus nota. </s>
            <s xml:id="echoid-s5639" xml:space="preserve">Quapropter ſi fiat, vt Q R, quatenus nota in partibus ſinus totius E B, ad ſe ipſam, quatenus
              <lb/>
            eſt ſinus totus, ita Q ω, quatenus nota in partibus ſinus totius E B, ad aliud, nota fiet Q ω, in partibus
              <lb/>
            ſinus totius Q R, hoc eſt, quatenus ſinus est anguli Q R ω, altitudinis poli quæſitæ, & </s>
            <s xml:id="echoid-s5640" xml:space="preserve">c.</s>
            <s xml:id="echoid-s5641" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s5642" xml:space="preserve">QVOD ſi vnum punctum inuentum ſit ex vmbra in recta E B, vt P, alterum autem in recta
              <lb/>
            E D, vt θ, addenda erit E θ, ipſi E P, vt tota θ P, not a fiat. </s>
            <s xml:id="echoid-s5643" xml:space="preserve">Hinc enim & </s>
            <s xml:id="echoid-s5644" xml:space="preserve">λ a, ipſi θ P, æqualis not a
              <lb/>
              <note position="left" xlink:label="note-0118-10" xlink:href="note-0118-10a" xml:space="preserve">34. primi.</note>
            erit. </s>
            <s xml:id="echoid-s5645" xml:space="preserve">Ex θ λ, autem vel P a, nota erit a R. </s>
            <s xml:id="echoid-s5646" xml:space="preserve">Igitur vt prius, angulus a R λ, in triangulo a R λ, </s>
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