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-s3121" xml:space="preserve">
              <pb o="47" file="0067" n="67" rhead="LIBER PRIMVS."/>
            rectæ L I, S T, parallelæ. </s>
            <s xml:id="echoid-s3122" xml:space="preserve">Eademq́; </s>
            <s xml:id="echoid-s3123" xml:space="preserve">ratione H k, P Q, parallelæ erunt, cum ſint communes ſectio-
              <lb/>
              <note position="right" xlink:label="note-0067-01" xlink:href="note-0067-01a" xml:space="preserve">16. vndec.</note>
            nes planorum parallelorum F G, M N, factæ à parallelo B C. </s>
            <s xml:id="echoid-s3124" xml:space="preserve">Tangat quoque circulus aliquis
              <lb/>
            horarius ab ortu, vel occaſu parallelos B C, D E, in H, I, punctis, atque adeo & </s>
            <s xml:id="echoid-s3125" xml:space="preserve">conicas ſuperficies
              <lb/>
              <figure xlink:label="fig-0067-01" xlink:href="fig-0067-01a" number="49">
                <image file="0067-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0067-01"/>
              </figure>
              <note position="left" xlink:label="note-0067-02" xlink:href="note-0067-02a" xml:space="preserve">10</note>
              <note position="left" xlink:label="note-0067-03" xlink:href="note-0067-03a" xml:space="preserve">20</note>
              <note position="left" xlink:label="note-0067-04" xlink:href="note-0067-04a" xml:space="preserve">30</note>
            in recta H I, per propoſ. </s>
            <s xml:id="echoid-s3126" xml:space="preserve">13. </s>
            <s xml:id="echoid-s3127" xml:space="preserve">huius lib, faciens in plano horologii lineam horariam V X. </s>
            <s xml:id="echoid-s3128" xml:space="preserve">Dico re-
              <lb/>
            ctam V X, eſſe ἀσύμπτοτον, id eſt, non conuenire vnquam cum hyperbolis O P Q, R S T, fieri ta-
              <lb/>
            men ipſis ſemper propinquiorem, ſi tam recta, quàm hyperbolæ producantur. </s>
            <s xml:id="echoid-s3129" xml:space="preserve">Cum enim cir-
              <lb/>
            culus H I V X, conicas ſuperficies tangat in recta H I, tantum, ita vt omnia alia puncta circuli
              <lb/>
              <note position="left" xlink:label="note-0067-05" xlink:href="note-0067-05a" xml:space="preserve">40</note>
            H I V X, exiſtentia extra rectam H I, ſint extra conicas ſuperficies, erit horaria linea V X, tota ex-
              <lb/>
            tra conicas ſuperficies, propterea quod non coire poteſt cum recta H I, quandoquidem plana F G,
              <lb/>
            M N, parallela ponuntur, ac propterea rectæ H I, V X, ipſorum communes ſectiones factæ à pla-
              <lb/>
            no H I V X, parallelæ ſunt. </s>
            <s xml:id="echoid-s3130" xml:space="preserve">Non igitur conueniet recta V X, cum hyperbolis O P Q, R S T, etiã
              <lb/>
              <note position="right" xlink:label="note-0067-06" xlink:href="note-0067-06a" xml:space="preserve">16. vndec.</note>
            ſi recta V X, & </s>
            <s xml:id="echoid-s3131" xml:space="preserve">hyperbolæ in eodem ſint plano horologii. </s>
            <s xml:id="echoid-s3132" xml:space="preserve">Eodem modo erit V X, extra conicas
              <lb/>
            ſuperficies, etiamſi producantur in infinitum. </s>
            <s xml:id="echoid-s3133" xml:space="preserve">Idemq́ dices de linea horaria, cuius circulus tan-
              <lb/>
            git ſuperficies conicas in recta K L.</s>
            <s xml:id="echoid-s3134" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3135" xml:space="preserve">DICO iam rectam V X, productam in vtramque partem fieri ſemper hyperbolis pro pinquio
              <lb/>
            rem. </s>
            <s xml:id="echoid-s3136" xml:space="preserve">Augeatur enim conica ſuperficies A B C, & </s>
            <s xml:id="echoid-s3137" xml:space="preserve">auctæ baſis ſit Y Z; </s>
            <s xml:id="echoid-s3138" xml:space="preserve">& </s>
            <s xml:id="echoid-s3139" xml:space="preserve">protrahantur rectæ I H,
              <lb/>
            F G, M N, V X, ad puncta α, β, γ, δ, vnà cum planis F G, M N, H I V X; </s>
            <s xml:id="echoid-s3140" xml:space="preserve">augeaturq́ue hyper-
              <lb/>
              <note position="left" xlink:label="note-0067-07" xlink:href="note-0067-07a" xml:space="preserve">50</note>
            bole O P Q, vt fiat O ε θ. </s>
            <s xml:id="echoid-s3141" xml:space="preserve">Secentur quoque conicæ ſuperficies plano, in quo circulus maximus
              <lb/>
            D B C E, per diametros D E, B C, quæ ad diametros L I, H K, atque ob id & </s>
            <s xml:id="echoid-s3142" xml:space="preserve">ad rectas S T, P Q,
              <lb/>
            illis æquidiſtantes, perpendiculares ſint. </s>
            <s xml:id="echoid-s3143" xml:space="preserve">Poſtremo ſint H λ, α δ, communes ſectiones planorum
              <lb/>
            B C, Y Z, & </s>
            <s xml:id="echoid-s3144" xml:space="preserve">plani, in quo circulus H I V X, quæ tangent circulos B C, Y Z, in punctis H, α, per
              <lb/>
            definitionem lib. </s>
            <s xml:id="echoid-s3145" xml:space="preserve">2. </s>
            <s xml:id="echoid-s3146" xml:space="preserve">Theod. </s>
            <s xml:id="echoid-s3147" xml:space="preserve">ſecabuntq́ue ſe mutuo tres rectæ V X, Q P, H λ, extra ſuperficies co-
              <lb/>
            nicas in puncto λ. </s>
            <s xml:id="echoid-s3148" xml:space="preserve">Quælibet enim duæ ſe mutuo ſecant. </s>
            <s xml:id="echoid-s3149" xml:space="preserve">Nam cum H I, V X, parallelæ ſint oſten
              <lb/>
            ſæ, ſitq́ue H λ, in eodem cum ipſis plano, nempe in plano circuli H I V X; </s>
            <s xml:id="echoid-s3150" xml:space="preserve">ſecet autem H λ, ip-
              <lb/>
            ſam H I, in H, ſecabit quoque eadem H λ, rectam V X, vt ad 28, propoſ. </s>
            <s xml:id="echoid-s3151" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s3152" xml:space="preserve">1. </s>
            <s xml:id="echoid-s3153" xml:space="preserve">Euclidis demon-
              <lb/>
            ſtrauimus. </s>
            <s xml:id="echoid-s3154" xml:space="preserve">Secant ergo ſe mutuo rectæ H λ, V X. </s>
            <s xml:id="echoid-s3155" xml:space="preserve">Rurſus eadem H λ, ipſam P Q, ſecabit. </s>
            <s xml:id="echoid-s3156" xml:space="preserve">Nam
              <lb/>
            cum H K, P Q, parallelæ ſint, vt ſupra oſtenſum eſt, ſecet autem H λ, ipſam H K, ſecabit quo-
              <lb/>
            que ipſam P Q, ex iis, quæ ad propoſ. </s>
            <s xml:id="echoid-s3157" xml:space="preserve">28. </s>
            <s xml:id="echoid-s3158" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s3159" xml:space="preserve">1. </s>
            <s xml:id="echoid-s3160" xml:space="preserve">Eucl. </s>
            <s xml:id="echoid-s3161" xml:space="preserve">oſtendimus. </s>
            <s xml:id="echoid-s3162" xml:space="preserve">Quòd autem & </s>
            <s xml:id="echoid-s3163" xml:space="preserve">P Q, V X, </s>
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