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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            <s xml:id="echoid-s10431" xml:space="preserve">
              <pb o="162" file="0182" n="182" rhead="GNOMONICES"/>
            lia ſunt lateribus H D, D F, trianguli H D F, in horologio, quòd D F, ipſi E F, cui æqualis eſt ſum
              <lb/>
            pta D C, in radio Aequatoris, æqualis ſit; </s>
            <s xml:id="echoid-s10432" xml:space="preserve">(Cum enim latera E I, I F, trianguli E I F, lateribus D I,
              <lb/>
            I F, trianguli D I F, æqualia ſint, angulosq́; </s>
            <s xml:id="echoid-s10433" xml:space="preserve">contineant æquales, nempe rectos; </s>
            <s xml:id="echoid-s10434" xml:space="preserve">Nam E I F, rectus eſt
              <lb/>
            ex conſtructione, at F I D, rectus eſt, ex defin. </s>
            <s xml:id="echoid-s10435" xml:space="preserve">3. </s>
            <s xml:id="echoid-s10436" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s10437" xml:space="preserve">11. </s>
            <s xml:id="echoid-s10438" xml:space="preserve">Euclidis, quòd F I, communis ſectio Aequa
              <lb/>
              <figure xlink:label="fig-0182-01" xlink:href="fig-0182-01a" number="134">
                <image file="0182-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0182-01"/>
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            toris, & </s>
            <s xml:id="echoid-s10439" xml:space="preserve">plani horolo
              <lb/>
            gii ad Meridianum,
              <lb/>
              <note position="left" xlink:label="note-0182-01" xlink:href="note-0182-01a" xml:space="preserve">19. vndec.</note>
            hoc eſt, ad triãgulum
              <lb/>
            D H I, in plano Meri-
              <lb/>
            diani ſitũ, atq; </s>
            <s xml:id="echoid-s10440" xml:space="preserve">adeo
              <lb/>
            ad rectã D I, perpen-
              <lb/>
              <note position="left" xlink:label="note-0182-02" xlink:href="note-0182-02a" xml:space="preserve">10</note>
            dicularis eſt, in pun-
              <lb/>
            cto I; </s>
            <s xml:id="echoid-s10441" xml:space="preserve">æquales erunt
              <lb/>
              <note position="left" xlink:label="note-0182-03" xlink:href="note-0182-03a" xml:space="preserve">4. primi.</note>
            baſes E F, D F,) angu
              <lb/>
            losq́, continent æqua
              <lb/>
            les, vtpote rectos; </s>
            <s xml:id="echoid-s10442" xml:space="preserve">Nã
              <lb/>
            H D C, in proxima
              <lb/>
            figura rectus eſt, ex
              <lb/>
            cõſtructione, at vero
              <lb/>
            & </s>
            <s xml:id="echoid-s10443" xml:space="preserve">H D F, in horo-
              <lb/>
            logio rectus eſt, pro-
              <lb/>
              <note position="left" xlink:label="note-0182-04" xlink:href="note-0182-04a" xml:space="preserve">20</note>
            pterea quòd axis HD,
              <lb/>
            rectus ad planũ Ae-
              <lb/>
            quatoris, ad rectam
              <lb/>
            F D, in eo exiſtentem
              <lb/>
            perpendicularis eſt,
              <lb/>
            in pũcto D, ex defin.
              <lb/>
            </s>
            <s xml:id="echoid-s10444" xml:space="preserve">3. </s>
            <s xml:id="echoid-s10445" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s10446" xml:space="preserve">11. </s>
            <s xml:id="echoid-s10447" xml:space="preserve">Euclidis; </s>
            <s xml:id="echoid-s10448" xml:space="preserve">æquales erunt baſes H C, H F, & </s>
            <s xml:id="echoid-s10449" xml:space="preserve">anguli D H C, D H F. </s>
            <s xml:id="echoid-s10450" xml:space="preserve">Quare ſi triangulum
              <lb/>
              <note position="left" xlink:label="note-0182-05" xlink:href="note-0182-05a" xml:space="preserve">4. primi.</note>
            H D C, circa axem H D, in horologio moueri concipiatur, donec cum triangulo H D F, coniun-
              <lb/>
            tur, & </s>
            <s xml:id="echoid-s10451" xml:space="preserve">recta H C, rectæ H F, in plano horologij congruat, cadet radii æquinoctialis punctum C, in
              <lb/>
            punctum F, ob æqualitatem angulorum C H D; </s>
            <s xml:id="echoid-s10452" xml:space="preserve">F H D, & </s>
            <s xml:id="echoid-s10453" xml:space="preserve">linearum H C, H F, & </s>
            <s xml:id="echoid-s10454" xml:space="preserve">radii ♋, punctũ
              <lb/>
              <note position="left" xlink:label="note-0182-06" xlink:href="note-0182-06a" xml:space="preserve">30</note>
            Z, cadet in punctum α, propterea quod & </s>
            <s xml:id="echoid-s10455" xml:space="preserve">recta H α, æqualis ſumpta eſt rectæ H Z, per conſtru-
              <lb/>
            ctionem, vel F α, ipſi C Z. </s>
            <s xml:id="echoid-s10456" xml:space="preserve">Per punctum ergo α, horæ quintæ à meridie incedit ſectio conica ♋,
              <lb/>
            cum in ipſum radius cancri incidat in illa reuolutione trianguli D H C, circa axem D H, in horo-
              <lb/>
            logio, vt oſtendimus. </s>
            <s xml:id="echoid-s10457" xml:space="preserve">Non aliter probabimus & </s>
            <s xml:id="echoid-s10458" xml:space="preserve">punctum T, in illa circumlatione radiorum Zo-
              <lb/>
            diaci cadere in R; </s>
            <s xml:id="echoid-s10459" xml:space="preserve">& </s>
            <s xml:id="echoid-s10460" xml:space="preserve">β, punctum radii ♋, in γ; </s>
            <s xml:id="echoid-s10461" xml:space="preserve">& </s>
            <s xml:id="echoid-s10462" xml:space="preserve">ſic de cæteris lineis horariis, quæ æquinoctia-
              <lb/>
            lem lineam interſecant, dicendum eſt.</s>
            <s xml:id="echoid-s10463" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10464" xml:space="preserve">PRO hora vero ſexta à mer. </s>
            <s xml:id="echoid-s10465" xml:space="preserve">vel med. </s>
            <s xml:id="echoid-s10466" xml:space="preserve">noc. </s>
            <s xml:id="echoid-s10467" xml:space="preserve">quæ lineam æquinoctialem non ſecat, ſed ei ęqui-
              <lb/>
            diſtat, ducenda eſt H V, ad axem H D, perpendicularis in figura radiorum Zodiaci, ſiue radio Ae-
              <lb/>
            quatoris D C, parallela; </s>
            <s xml:id="echoid-s10468" xml:space="preserve">quia hac ratione, in illa circumductione radiorum, recta H V, recte H δ,
              <lb/>
            in horologio congruet, propter æqualitatem angulorum rectorum D H V, D H δ; </s>
            <s xml:id="echoid-s10469" xml:space="preserve">Eſt enim angu
              <lb/>
              <note position="left" xlink:label="note-0182-07" xlink:href="note-0182-07a" xml:space="preserve">40</note>
            lus D H V, rectus, ex conſtructione, angulus vero D H δ
              <unsure/>
            , ad axem conſtitutus rectus quoque eſt,
              <lb/>
            per defin. </s>
            <s xml:id="echoid-s10470" xml:space="preserve">3. </s>
            <s xml:id="echoid-s10471" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s10472" xml:space="preserve">11. </s>
            <s xml:id="echoid-s10473" xml:space="preserve">Euclidis, propterea quòd H δ, linea ſextæ horæ, communis nimirum ſectio pla
              <lb/>
            ni horologii, & </s>
            <s xml:id="echoid-s10474" xml:space="preserve">circuli horæ ſextæ, ad Meridianum, (ad quem vtrumque illorum rectum eſt) hoc
              <lb/>
            eſt, ad triangulum D H I, ac proinde & </s>
            <s xml:id="echoid-s10475" xml:space="preserve">ad rectam D H, in puncto H, perpendicularis eſt. </s>
            <s xml:id="echoid-s10476" xml:space="preserve">Quam-
              <lb/>
              <note position="left" xlink:label="note-0182-08" xlink:href="note-0182-08a" xml:space="preserve">19. vndec.</note>
            obrem punctum θ, radij ♋, cadet in δ, ob ęqualitatem, ex conſtructione, rectarum H θ, H δ:
              <lb/>
            </s>
            <s xml:id="echoid-s10477" xml:space="preserve">Sumpta enim eſt in horologio recta H δ, rectæ H θ, in figura radiorum æqualis. </s>
            <s xml:id="echoid-s10478" xml:space="preserve">Pro hora deni-
              <lb/>
            que ſeptima à meridie, vel quinta à med. </s>
            <s xml:id="echoid-s10479" xml:space="preserve">noc. </s>
            <s xml:id="echoid-s10480" xml:space="preserve">& </s>
            <s xml:id="echoid-s10481" xml:space="preserve">aliis, quæ æquinoctialem lineam nõ ſecant, ſi opus
              <lb/>
            fuerit, (In noſtro exemplo nulla alia hora indigemus, cum arcus ♋, ſecet lineas horarum ſeptimæ à
              <lb/>
            mer. </s>
            <s xml:id="echoid-s10482" xml:space="preserve">& </s>
            <s xml:id="echoid-s10483" xml:space="preserve">quintæ à med. </s>
            <s xml:id="echoid-s10484" xml:space="preserve">noc. </s>
            <s xml:id="echoid-s10485" xml:space="preserve">in punctis ualde remotis à centro H) ducendæ ſunt lineæ, quæ ex alte-
              <lb/>
            ra parte, nempe ſiniſtra, cum linea H V, horæ ſextæ angulos faciant æquales angulis, quos lineæ ra-
              <lb/>
              <note position="left" xlink:label="note-0182-09" xlink:href="note-0182-09a" xml:space="preserve">50</note>
            dium Aequatoris ex parte dextra ſecantes, & </s>
            <s xml:id="echoid-s10486" xml:space="preserve">quæ ad horas æquinoctialem lineam ſecantes in ho-
              <lb/>
            rologio pertinent, cum eadem linea horæ ſextæ faciunt, quales ſunt H X, H Y, &</s>
            <s xml:id="echoid-s10487" xml:space="preserve">c. </s>
            <s xml:id="echoid-s10488" xml:space="preserve">Nam hoc mo.
              <lb/>
            </s>
            <s xml:id="echoid-s10489" xml:space="preserve">do facient huiuſmodi lineæ cum axe H D, in figura radiorum Zodiaci angulos X H D, Y H D,
              <lb/>
            æquales angulis, quos lineæ horariæ reſpondentes in horologio cum axe H D, faciunt: </s>
            <s xml:id="echoid-s10490" xml:space="preserve">nimirum
              <lb/>
            angulum X H D, in dicta figura æqualem angulo κ H D, in horologio. </s>
            <s xml:id="echoid-s10491" xml:space="preserve">Cum enim duo anguli
              <lb/>
            X H λ, X H D, in figura radiorum æquales ſint duobus angulis D H k, D H κ, in horologio; </s>
            <s xml:id="echoid-s10492" xml:space="preserve">quòd
              <lb/>
            tam hi, quàm illi duobus ſint rectis æquales: </s>
            <s xml:id="echoid-s10493" xml:space="preserve">Sit autem angulus X H λ, in dicta figura angulo
              <lb/>
              <note position="left" xlink:label="note-0182-10" xlink:href="note-0182-10a" xml:space="preserve">13. primi.</note>
            D H K, in horologio æqualis; </s>
            <s xml:id="echoid-s10494" xml:space="preserve">(Nam angulus X H λ, in eadem figura æqualis eſt angulo C H D,
              <lb/>
            eiuſdem figuræ, per pronunciatum 3. </s>
            <s xml:id="echoid-s10495" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s10496" xml:space="preserve">1. </s>
            <s xml:id="echoid-s10497" xml:space="preserve">Euclidis, quòd & </s>
            <s xml:id="echoid-s10498" xml:space="preserve">anguli toti recti V H λ, V H D, in-
              <lb/>
            ter ſe, & </s>
            <s xml:id="echoid-s10499" xml:space="preserve">ablati V H X, V H C, inter ſe, per conſtructionem, æquales ſint; </s>
            <s xml:id="echoid-s10500" xml:space="preserve">angulus autem C H D,
              <lb/>
            dictæ figuræ æqualis eſt angulo D H F, in horologio, vt demõſtratũ eſt, atq; </s>
            <s xml:id="echoid-s10501" xml:space="preserve">adeò & </s>
            <s xml:id="echoid-s10502" xml:space="preserve">angulo D H </s>
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