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-s9608" xml:space="preserve">
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            trum H, ducta, & </s>
            <s xml:id="echoid-s9609" xml:space="preserve">vtrumque in ſuo circulo quatuor horis abeſt à linca meridiana) & </s>
            <s xml:id="echoid-s9610" xml:space="preserve">per F, punctum ex-
              <lb/>
            terioris circuli ducatur diametro S T, quæ meridianam lineam ad rectos angulos ſecat, parallela occulta
              <lb/>
            F L; </s>
            <s xml:id="echoid-s9611" xml:space="preserve">quod facile fiet, ſi recta occulta ducatur ex F, ad punctum M, quod tanto interuallo abſit à punct@
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              <figure xlink:label="fig-0170-01" xlink:href="fig-0170-01a" number="125">
                <image file="0170-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0170-01"/>
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              <note position="left" xlink:label="note-0170-01" xlink:href="note-0170-01a" xml:space="preserve">10</note>
              <note position="left" xlink:label="note-0170-02" xlink:href="note-0170-02a" xml:space="preserve">20</note>
              <note position="left" xlink:label="note-0170-03" xlink:href="note-0170-03a" xml:space="preserve">30</note>
            S, quanto punctum F, à puncto T, abeſt. </s>
            <s xml:id="echoid-s9612" xml:space="preserve">Rectæ enim F M, T S, parallelę erunt, ex ſcholio propoſ. </s>
            <s xml:id="echoid-s9613" xml:space="preserve">27.
              <lb/>
            </s>
            <s xml:id="echoid-s9614" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s9615" xml:space="preserve">3. </s>
            <s xml:id="echoid-s9616" xml:space="preserve">Eucl. </s>
            <s xml:id="echoid-s9617" xml:space="preserve">ob æqualitatem arcuum F T, M S: </s>
            <s xml:id="echoid-s9618" xml:space="preserve">Item per K, punctum circuli interioris agatur meridianæ
              <lb/>
            lineę H B, parallela occulta K L; </s>
            <s xml:id="echoid-s9619" xml:space="preserve">quod facile etiã fiet, ſi recta occulta ducatur ex K, ad punctum N, quod
              <lb/>
              <note position="left" xlink:label="note-0170-04" xlink:href="note-0170-04a" xml:space="preserve">40</note>
            tanto ſpatio diſtet à puncto R, quanto abeſt ab eodem punctum K: </s>
            <s xml:id="echoid-s9620" xml:space="preserve">Secet autem recta K L, rectam F L,
              <lb/>
            in L. </s>
            <s xml:id="echoid-s9621" xml:space="preserve">Quod ſi idem fiat cum reliquis binis punctis diuiſionum reſpondentibus, vt in figura apparet, inuenta
              <lb/>
            erunt puncta ellipſis, cuius maior diameter eſt B V, & </s>
            <s xml:id="echoid-s9622" xml:space="preserve">minor R X, centrum autem H, vt ex coroll. </s>
            <s xml:id="echoid-s9623" xml:space="preserve">propoſ.
              <lb/>
            </s>
            <s xml:id="echoid-s9624" xml:space="preserve">26. </s>
            <s xml:id="echoid-s9625" xml:space="preserve">ſuperioris lib. </s>
            <s xml:id="echoid-s9626" xml:space="preserve">perſpicuum eſt. </s>
            <s xml:id="echoid-s9627" xml:space="preserve">Dico rectas ex H, per hæc puncta ellipſis inuenta ductas, eſſe lineas ho-
              <lb/>
            rarias, ita vt quælibet eam horam referat, quam puncta diuiſionum reſpondentia in circulis referunt. </s>
            <s xml:id="echoid-s9628" xml:space="preserve">Vt
              <lb/>
            quoniam punctum F, refert quartam horam poſt meridiem, idcirco recta H L, ducta dabit horam quar-
              <lb/>
            tam à meridie, & </s>
            <s xml:id="echoid-s9629" xml:space="preserve">ſic de cæteris. </s>
            <s xml:id="echoid-s9630" xml:space="preserve">Atque hac ratione commodiſſime horas ducemus, quia ſemper terna pun
              <lb/>
            cta pro ſingulis horis habemus, quorum duo ſunt oppoſita in ellipſi, qualia ſunt L, & </s>
            <s xml:id="echoid-s9631" xml:space="preserve">a, tertium autem
              <lb/>
            eſt ipſum centrum H. </s>
            <s xml:id="echoid-s9632" xml:space="preserve">Inuenietur autem punctum oppoſitum a, in ellipſi hoc modo. </s>
            <s xml:id="echoid-s9633" xml:space="preserve">Sumantur arcus S β,
              <lb/>
            X γ, oppoſiti arcubus T F, R K, æquales, ducantur{q́ue} rectæ β α, γ α, diametris S T, B V, parallelæ ſe-
              <lb/>
              <note position="left" xlink:label="note-0170-05" xlink:href="note-0170-05a" xml:space="preserve">50</note>
            cantes ſeſe in α. </s>
            <s xml:id="echoid-s9634" xml:space="preserve">Punctum enim α, oppoſitum erit puncto L. </s>
            <s xml:id="echoid-s9635" xml:space="preserve">Iam vero ſi dimidiatas horas, & </s>
            <s xml:id="echoid-s9636" xml:space="preserve">quadran-
              <lb/>
            tes earundem deſcribere lubeat, diuidendæ erunt ſingulæ partes circulorum bifariam, & </s>
            <s xml:id="echoid-s9637" xml:space="preserve">in quatuor par-
              <lb/>
            tes, & </s>
            <s xml:id="echoid-s9638" xml:space="preserve">c. </s>
            <s xml:id="echoid-s9639" xml:space="preserve">Hanc deſcriptionem, quæ omnium elegantiſſima eſt, hoc modo demonſtrabimus.</s>
            <s xml:id="echoid-s9640" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s9641" xml:space="preserve">INTELLIGATVR triangulum A B H, circa rectam B H, moueri, donec rectum ſit ad pla-
              <lb/>
              <note position="left" xlink:label="note-0170-06" xlink:href="note-0170-06a" xml:space="preserve">Denion ſtratio
                <lb/>
              huius deſcri-
                <lb/>
              ptionis.</note>
            num horologij, & </s>
            <s xml:id="echoid-s9642" xml:space="preserve">cum plano Meridiani circuli coniunctum: </s>
            <s xml:id="echoid-s9643" xml:space="preserve">& </s>
            <s xml:id="echoid-s9644" xml:space="preserve">ex A, quod centrum mundi refert, ad
              <lb/>
            interuallum A B, concipiatur deſcriptus circulus θ Y B Z, Aequatori concentricus, & </s>
            <s xml:id="echoid-s9645" xml:space="preserve">in plano Aequa
              <lb/>
            toris, qui propterea, vt Aequator, in 24. </s>
            <s xml:id="echoid-s9646" xml:space="preserve">partes æquales à communibus ſectionibus circulorum horariorũ
              <lb/>
            & </s>
            <s xml:id="echoid-s9647" xml:space="preserve">Aequatoris diuidetur. </s>
            <s xml:id="echoid-s9648" xml:space="preserve">Diſtent quoque puncta O, P, quatuor horis à puncto B, meridiei, quemadmo-
              <lb/>
            dum & </s>
            <s xml:id="echoid-s9649" xml:space="preserve">puncta F, K, M, δ, quatuor horis distant ab eodem puncto B, meridiei. </s>
            <s xml:id="echoid-s9650" xml:space="preserve">Quamuis enim punctum
              <lb/>
            P, in Aequatore pertineat ad horam 4. </s>
            <s xml:id="echoid-s9651" xml:space="preserve">à med. </s>
            <s xml:id="echoid-s9652" xml:space="preserve">noc. </s>
            <s xml:id="echoid-s9653" xml:space="preserve">(vt conſtat, ſi circulus θ Y B Z, in proprio ſitu pona-
              <lb/>
            tur, ita vt ſemicirculus θ Y B, ſit occidentalis, & </s>
            <s xml:id="echoid-s9654" xml:space="preserve">B Z θ, oriẽtalis) tamen quia A, ponitur centrum </s>
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