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-s854" xml:space="preserve">
              <pb o="12" file="0032" n="32" rhead="GNOMONICES"/>
            lis, hoc eſt, contineat gradus 23. </s>
            <s xml:id="echoid-s855" xml:space="preserve">minuta 30. </s>
            <s xml:id="echoid-s856" xml:space="preserve">& </s>
            <s xml:id="echoid-s857" xml:space="preserve">coniungatur recta M N, ſecans H I, in O. </s>
            <s xml:id="echoid-s858" xml:space="preserve">Quoniã
              <lb/>
            verò ductis rectis E M, E N, latera O E, E M, trianguli O E M, lateribus O E, E N, triãguli O E N,
              <lb/>
            ſunt æqualia, continentq́; </s>
            <s xml:id="echoid-s859" xml:space="preserve">angulos ad centrum E, æquales, propterea quòd arcubus æqualibus
              <lb/>
              <note position="left" xlink:label="note-0032-01" xlink:href="note-0032-01a" xml:space="preserve">27. tertij.
                <lb/>
              4. primi.</note>
            H M, H N, inſiſtant, erunt & </s>
            <s xml:id="echoid-s860" xml:space="preserve">baſes O M, O N, æquales, & </s>
            <s xml:id="echoid-s861" xml:space="preserve">anguli ad O, ac proinde recti. </s>
            <s xml:id="echoid-s862" xml:space="preserve">Si igitur
              <lb/>
              <figure xlink:label="fig-0032-01" xlink:href="fig-0032-01a" number="10">
                <image file="0032-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0032-01"/>
              </figure>
            ex O, ad interuallũ O M, vel O N,
              <lb/>
            deſcribatur circulus M P N, ex-
              <lb/>
            tendaturq́; </s>
            <s xml:id="echoid-s863" xml:space="preserve">recta I H, ad Q, erunt
              <lb/>
            arcus M P, P N, N Q, Q M, qua-
              <lb/>
            drantes, propterea quòd, cum ip-
              <lb/>
            ſis inſiſtant æquales anguli ad cen
              <lb/>
              <note position="left" xlink:label="note-0032-02" xlink:href="note-0032-02a" xml:space="preserve">10</note>
            trum O, nẽpe recti, æquales ſint.
              <lb/>
            </s>
            <s xml:id="echoid-s864" xml:space="preserve">
              <note position="left" xlink:label="note-0032-03" xlink:href="note-0032-03a" xml:space="preserve">26. tertij.</note>
            Quod ſi ſinguli quadrãtes in ter-
              <lb/>
            nas partes æquales ſecentur (atq;
              <lb/>
            </s>
            <s xml:id="echoid-s865" xml:space="preserve">adeò totus circulus in partes 12. </s>
            <s xml:id="echoid-s866" xml:space="preserve">
              <lb/>
            æquales, inſtar Zodiaci, qui in 12. </s>
            <s xml:id="echoid-s867" xml:space="preserve">
              <lb/>
            ſigna æqualia diſtribuitur) in pun
              <lb/>
            ctis R, S, &</s>
            <s xml:id="echoid-s868" xml:space="preserve">c quorum bina à pun
              <lb/>
            ctis P, Q, æqualiter remota lineis
              <lb/>
            rectis iungantur (quæ quidem pa
              <lb/>
            rallelæ erunt & </s>
            <s xml:id="echoid-s869" xml:space="preserve">ipſi H I, & </s>
            <s xml:id="echoid-s870" xml:space="preserve">inter
              <lb/>
              <note position="left" xlink:label="note-0032-04" xlink:href="note-0032-04a" xml:space="preserve">20</note>
            ſe, ex ijs, quæ in ſcholio propoſ.
              <lb/>
            </s>
            <s xml:id="echoid-s871" xml:space="preserve">27. </s>
            <s xml:id="echoid-s872" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s873" xml:space="preserve">3. </s>
            <s xml:id="echoid-s874" xml:space="preserve">Euclidis demonſtrata
              <lb/>
            ſunt à nobis) ſecantibus arcus
              <lb/>
            H M, H N in punctis, β, γ, δ, @,
              <lb/>
            erunt arcus H β, H γ, H δ, H @,
              <lb/>
            declinationibus reliquorũ ſigno-
              <lb/>
            rum Zodiaci inter ♋, & </s>
            <s xml:id="echoid-s875" xml:space="preserve">♑,
              <lb/>
            æquales, vt mox oſtendemus@</s>
          </p>
          <p>
            <s xml:id="echoid-s876" xml:space="preserve">IAM verò ſi his arcubus æquales arcus abſcindantur I θ, I λ, I μ, I ξ, I π, I ρ, ducanturq́; </s>
            <s xml:id="echoid-s877" xml:space="preserve">rectæ
              <lb/>
            M θ, β λ, γ μ, δ ξ, ε π, N ρ, vel certè parallelæ X R, Y S, &</s>
            <s xml:id="echoid-s878" xml:space="preserve">c. </s>
            <s xml:id="echoid-s879" xml:space="preserve">producantur, (Nam & </s>
            <s xml:id="echoid-s880" xml:space="preserve">rectæ H I,
              <lb/>
              <note position="left" xlink:label="note-0032-05" xlink:href="note-0032-05a" xml:space="preserve">30</note>
            γ μ, β λ, M θ, parallelę ſunt, ex demonſcratis à nobis in ſcholio propoſ. </s>
            <s xml:id="echoid-s881" xml:space="preserve">27. </s>
            <s xml:id="echoid-s882" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s883" xml:space="preserve">3. </s>
            <s xml:id="echoid-s884" xml:space="preserve">Euclidis, pro-
              <lb/>
            pter æqualitatem arcuum H γ, I μ, & </s>
            <s xml:id="echoid-s885" xml:space="preserve">γ β, μ λ, &</s>
            <s xml:id="echoid-s886" xml:space="preserve">c.) </s>
            <s xml:id="echoid-s887" xml:space="preserve">erunt hæ, communes ſectiones parallelorũ
              <lb/>
            per initia ſignorum ductorum, ac Meridiani circuli. </s>
            <s xml:id="echoid-s888" xml:space="preserve">Sunt enim earum diſtantiæ à recta H I, com@
              <lb/>
            muni ſectione Aequatoris & </s>
            <s xml:id="echoid-s889" xml:space="preserve">Meridiani, proportionales diſtantijs ſectionum eorundem parallelo-
              <lb/>
            rum, & </s>
            <s xml:id="echoid-s890" xml:space="preserve">Meridiani, in ipſo Meridiano; </s>
            <s xml:id="echoid-s891" xml:space="preserve">cum rectæ ex centro E, per puncta M, β, γ, &</s>
            <s xml:id="echoid-s892" xml:space="preserve">c. </s>
            <s xml:id="echoid-s893" xml:space="preserve">emiſſæ au-
              <lb/>
            ferant ex Meridiano circa idem centrum E, deſcripto arcus ſimiles arcubus H M, H β, H γ, &</s>
            <s xml:id="echoid-s894" xml:space="preserve">c.
              <lb/>
            </s>
            <s xml:id="echoid-s895" xml:space="preserve">ex ijs, quæ in commentarijs in Sphæram ſcripſimus ad finem primi capitis.</s>
            <s xml:id="echoid-s896" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s897" xml:space="preserve">SVNT autem rectæ E M, E β, E γ, &</s>
            <s xml:id="echoid-s898" xml:space="preserve">c. </s>
            <s xml:id="echoid-s899" xml:space="preserve">communes ſectiones Meridiani, atque Eclipticæ va-
              <lb/>
              <note position="left" xlink:label="note-0032-06" xlink:href="note-0032-06a" xml:space="preserve">Variæ poſitio-
                <lb/>
              nes Eclipticæ.</note>
            rias poſitiones obtinen tis in ipſo Meridiano. </s>
            <s xml:id="echoid-s900" xml:space="preserve">Nam EM, eſt eiuſmodi ſectio, cum principiũ ♋
              <lb/>
            in Meridiano fuerit poſitum: </s>
            <s xml:id="echoid-s901" xml:space="preserve">At E β, cum fuerit principium ♊ aut ♌ in Meridiano poſitũ
              <unsure/>
            :
              <lb/>
            </s>
            <s xml:id="echoid-s902" xml:space="preserve">
              <note position="left" xlink:label="note-0032-07" xlink:href="note-0032-07a" xml:space="preserve">40</note>
            Et E γ, quando initium ♉, vel ♍ Meridianũ poſſederit, &</s>
            <s xml:id="echoid-s903" xml:space="preserve">c. </s>
            <s xml:id="echoid-s904" xml:space="preserve">vt conſtat, ſi Analemma in plano
              <lb/>
            Meridiani proprium intelligatur habere ſitum. </s>
            <s xml:id="echoid-s905" xml:space="preserve">quæ res perfacilis eſt etiam ex Sphæra materiali.</s>
            <s xml:id="echoid-s906" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s907" xml:space="preserve">HAS quoque rectas, cum de Horologiorum deſcriptionibus agemus, appellabimus radios
              <lb/>
              <note position="left" xlink:label="note-0032-08" xlink:href="note-0032-08a" xml:space="preserve">Radij ſignerũ,
                <lb/>
              vel Zodiaci qui
                <lb/>
              ſint.</note>
            ſignorum, vel Zodiaci, quoniam Sole exiſtente in ſignorum initijs, referunt radios, quos in me-
              <lb/>
            ridie Sol per centrũ mundi E, proijcit. </s>
            <s xml:id="echoid-s908" xml:space="preserve">At verò rectæ M θ, β λ, γ μ, &</s>
            <s xml:id="echoid-s909" xml:space="preserve">c. </s>
            <s xml:id="echoid-s910" xml:space="preserve">diametri ſunt parallelo-
              <lb/>
              <note position="left" xlink:label="note-0032-09" xlink:href="note-0032-09a" xml:space="preserve">Diametri paral
                <lb/>
              lelorũ per pun-
                <lb/>
              cta Zodiaci du-
                <lb/>
              ctorum.</note>
            rum, qui per initia ſignorum Zodiaci incedunt, nempe H I, diameter Aequatoris; </s>
            <s xml:id="echoid-s911" xml:space="preserve">γ μ, diame-
              <lb/>
            ter paralleli ♉, & </s>
            <s xml:id="echoid-s912" xml:space="preserve">♍, &</s>
            <s xml:id="echoid-s913" xml:space="preserve">c. </s>
            <s xml:id="echoid-s914" xml:space="preserve">quemadmodum & </s>
            <s xml:id="echoid-s915" xml:space="preserve">B D, diameter eſt Horizontis, & </s>
            <s xml:id="echoid-s916" xml:space="preserve">A D, Ver-
              <lb/>
            ticalis, &</s>
            <s xml:id="echoid-s917" xml:space="preserve">c.</s>
            <s xml:id="echoid-s918" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s919" xml:space="preserve">ALII has diametros M θ, β λ, &</s>
            <s xml:id="echoid-s920" xml:space="preserve">c. </s>
            <s xml:id="echoid-s921" xml:space="preserve">hac ratione ducunt, & </s>
            <s xml:id="echoid-s922" xml:space="preserve">rectè quidem, meo iudicio, quia vna
              <lb/>
              <note position="left" xlink:label="note-0032-10" xlink:href="note-0032-10a" xml:space="preserve">Alia deſcriptio
                <lb/>
              parallelorum
                <lb/>
              Aequatoris per
                <lb/>
              ſignorum ini-
                <lb/>
              tia tranſeun-
                <lb/>
              tium.</note>
            opera, vnoq́ue labore & </s>
            <s xml:id="echoid-s923" xml:space="preserve">declinationes parallelorum reperiunt, & </s>
            <s xml:id="echoid-s924" xml:space="preserve">diametros eorundem rectę H I,
              <lb/>
              <note position="left" xlink:label="note-0032-11" xlink:href="note-0032-11a" xml:space="preserve">50</note>
            æquidiſtantes ducunt. </s>
            <s xml:id="echoid-s925" xml:space="preserve">Sumptis arcubus H M, H N, I θ, I ρ, quorum quiſque maximæ Solis de-
              <lb/>
            clinationi æqualis ſit, coniungunt rectas M N, θ ρ, ſecantes rectam H I, in O, & </s>
            <s xml:id="echoid-s926" xml:space="preserve">e. </s>
            <s xml:id="echoid-s927" xml:space="preserve">Deinde ex O, & </s>
            <s xml:id="echoid-s928" xml:space="preserve">
              <lb/>
            e, deſcribunt circa diametros M N, θ ρ, ſe
              <unsure/>
            micirculos duntaxat M Q N, θ f ρ, quia vt ſupra de-
              <lb/>
            monſtratum eſt, recta M N, in O, atque adeo eadem ratione & </s>
            <s xml:id="echoid-s929" xml:space="preserve">θ ρ in e, ſecatur bifariam, & </s>
            <s xml:id="echoid-s930" xml:space="preserve">ad
              <lb/>
            angulos rectos. </s>
            <s xml:id="echoid-s931" xml:space="preserve">Diſtributis uerò his ſemicirculis in ſex partes æquales in punctis α, z, x, Y,
              <lb/>
            g, h, m, n, connectunt lineis rectis reſpondentia puncta, qualia ſunt M, θ Y, g; </s>
            <s xml:id="echoid-s932" xml:space="preserve">X, h, &</s>
            <s xml:id="echoid-s933" xml:space="preserve">c. </s>
            <s xml:id="echoid-s934" xml:space="preserve">Hæ enim
              <lb/>
            dabunt parallelorum diametros, vt prius, quia inter ſe parallelæ erunt, vt rectę Y S, X R, &</s>
            <s xml:id="echoid-s935" xml:space="preserve">c. </s>
            <s xml:id="echoid-s936" xml:space="preserve">cum
              <lb/>
            ſemicirculus θ f ρ
              <unsure/>
            , eundem ſitum habeat reſpectu ſemicirculi M Q N, quem ſemicirculus M P N,
              <lb/>
              <note position="left" xlink:label="note-0032-12" xlink:href="note-0032-12a" xml:space="preserve">Deſcriptio pa-
                <lb/>
              rall@lorum Ae-
                <lb/>
              quatoris per ſin
                <lb/>
              gulos grad
                <emph style="sub">9</emph>
              Ecli
                <lb/>
              pticæ ductorũ.</note>
            vt manifeſtum eſt.</s>
            <s xml:id="echoid-s937" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s938" xml:space="preserve">QVOD ſi ſinguli arcus Q X, X Y, &</s>
            <s xml:id="echoid-s939" xml:space="preserve">c. </s>
            <s xml:id="echoid-s940" xml:space="preserve">bifariam ſecentur, & </s>
            <s xml:id="echoid-s941" xml:space="preserve">eadem fiant, quæ prius, habebun-
              <lb/>
            tur communes ſectiones parallelorum, qui per dimidia ſignorum, id eſt, per quindenos </s>
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