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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          <p style="it">
            <s xml:id="echoid-s34763" xml:space="preserve">
              <pb o="540" file="0556" n="556" rhead="GNOMONICES"/>
            trum Horizontis ſecat, tanquam centro, interuallo vero d K, accipiendum eſt punctum M, be-
              <lb/>
              <note position="left" xlink:label="note-0556-01" xlink:href="note-0556-01a" xml:space="preserve">Horizontalis.</note>
            neficio circini in Meridiano, & </s>
            <s xml:id="echoid-s34764" xml:space="preserve">ex M, per L, recta ducenda M N, quæ, vt demonſtrauimus, ad B D,
              <lb/>
            perpendicularis eſt, Nam ſi ex M N, abſcindatur recta N Q, rectæ K L, æqualis, ducatur{q́ue} ex
              <lb/>
            centro E, per Q, recta ſecans circunferentiam Meridiani in S, erit A S, circunferentia borizon-
              <lb/>
            talis, initium habens in Analemmate à diametro Verticalis, ſeu gnomone A C, Si vero inuenien
              <lb/>
              <note position="left" xlink:label="note-0556-02" xlink:href="note-0556-02a" xml:space="preserve">Deſcenſiua.</note>
            da ſit circunferentia deſcenſiua, ducenda eſt per L, ad diametrum Verticalis A C, perpendicularis
              <lb/>
            P O, ſecans Meridiani circunferentiam in P: </s>
            <s xml:id="echoid-s34765" xml:space="preserve">Vel (quod idem eſt) ex puncton, vbi diameter paralleli
              <lb/>
            diametrum Verticalis ſecat, veluti centro, interuallo autem n K, accipiendum eſt beneficio circini in
              <lb/>
            Meridiano punctum P. </s>
            <s xml:id="echoid-s34766" xml:space="preserve">Nam A P, erit circunferentia deſcenſiua, cuius principium in Analemma-
              <lb/>
            te ſumitur à gnomone, ſeu diametro Verticalis. </s>
            <s xml:id="echoid-s34767" xml:space="preserve">Quod ſi deſideretur circunferentia Verticalis, du-
              <lb/>
              <note position="left" xlink:label="note-0556-03" xlink:href="note-0556-03a" xml:space="preserve">Verticalis.</note>
              <note position="left" xlink:label="note-0556-04" xlink:href="note-0556-04a" xml:space="preserve">10</note>
            cenda
              <unsure/>
            est per L, ad diamctrum Verticalis A C, perpendicularis P O: </s>
            <s xml:id="echoid-s34768" xml:space="preserve">Vel (quod idem eſt,) ex puncto
              <lb/>
            n, vbi par alleli diameter diametrum Horizontis diuidit, vt centro, at interuallo n K, accipiendum est
              <lb/>
            beneficio circini in Meridiano punctum P, & </s>
            <s xml:id="echoid-s34769" xml:space="preserve">ex P, per L, recta ducenda P O, quæ, vt demonstraui-
              <lb/>
            mus, ad A C, perpendicularis eſt, Nã ſiex O P, auferatur recta O R, rectæ K L, æqualis, ducatur{q́ue}
              <lb/>
            ex centro E, per R, recta ſecans Meridiani circunferentiam in T, erit A T, circunferentia Vertica-
              <lb/>
            lis, initiũ in Analemmate habens à gnomone, ſeu diametro Verticalis A C. </s>
            <s xml:id="echoid-s34770" xml:space="preserve">At voro ſi proponatur:</s>
            <s xml:id="echoid-s34771" xml:space="preserve">
              <unsure/>
            cir-
              <lb/>
            cunferentia horaria inueſtiganda, duccnda est per L, ad Horizontis diametrum B D, perpendicularis
              <lb/>
              <note position="left" xlink:label="note-0556-05" xlink:href="note-0556-05a" xml:space="preserve">Heratia
                <unsure/>
              .</note>
            M N, ſecans circunferentiam Meridiani in M: </s>
            <s xml:id="echoid-s34772" xml:space="preserve">Vel (quod idem eſt) beneficio circini ex puncto d, vbi
              <lb/>
            diameter paralleli diametrum Horizontis ſecat, vt centro, interuallo vero d K, accipiendum eſt in Me-
              <lb/>
            ridiano punctum M. </s>
            <s xml:id="echoid-s34773" xml:space="preserve">Nam B M, erit circunferentia horaria, habens principium à diametro Horizon-
              <lb/>
              <note position="left" xlink:label="note-0556-06" xlink:href="note-0556-06a" xml:space="preserve">20</note>
            tis B D, in Analemmate. </s>
            <s xml:id="echoid-s34774" xml:space="preserve">Vt autem habeatur circunferentia meridiana, ducenda eſt ex E, centro
              <lb/>
              <note position="left" xlink:label="note-0556-07" xlink:href="note-0556-07a" xml:space="preserve">Meridiana.</note>
            per L, recta ſecans circunferentiam Meridiani in γ. </s>
            <s xml:id="echoid-s34775" xml:space="preserve">Nam recta B γ, erit circunferentia meridiana.
              <lb/>
            </s>
            <s xml:id="echoid-s34776" xml:space="preserve">Pro hectemoria denique circunferentia ducenda eſt ex centro E, per L, recta E γ, & </s>
            <s xml:id="echoid-s34777" xml:space="preserve">ad eam ex E,
              <lb/>
              <note position="left" xlink:label="note-0556-08" xlink:href="note-0556-08a" xml:space="preserve">Hectemoria.</note>
            & </s>
            <s xml:id="echoid-s34778" xml:space="preserve">L, excitandæ duæ perpendiculares E g, L f: </s>
            <s xml:id="echoid-s34779" xml:space="preserve">ſecantes Meridiani circunferentiam in g, f: </s>
            <s xml:id="echoid-s34780" xml:space="preserve">Vel (quod
              <lb/>
            idem est) ducta E G, ad E γ, perpendiculari, ſumendum eſt ex L, vt centro, & </s>
            <s xml:id="echoid-s34781" xml:space="preserve">interuallo L K, bene-
              <lb/>
            ficio circini in Meridiano punctum f. </s>
            <s xml:id="echoid-s34782" xml:space="preserve">Nam g f, erit circunferentia hecto
              <unsure/>
            moria.</s>
            <s xml:id="echoid-s34783" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s34784" xml:space="preserve">PORRO confecimus pro parallelo boreali quinque figuras, vt omnis varietas, quæ accidere potest,
              <lb/>
              <note position="left" xlink:label="note-0556-09" xlink:href="note-0556-09a" xml:space="preserve">Cur pro paralle
                <lb/>
              lo boreali con-
                <lb/>
              fectæ ſint quin-
                <lb/>
              que figuræ, pro
                <lb/>
              auſtrali vero
                <lb/>
              vnica.</note>
            explicaretur. </s>
            <s xml:id="echoid-s34785" xml:space="preserve">Nam in ſecunda figura huius cap. </s>
            <s xml:id="echoid-s34786" xml:space="preserve">exiſtit Sol vltra Verticalem circulum, propterea{q́ue} per-
              <lb/>
            pendicularis K L, vltra diametrum A C, Verticalis circuli verſus auſtrũ cadit: </s>
            <s xml:id="echoid-s34787" xml:space="preserve">In tertia vero ponitur
              <lb/>
            Sol in Verticali circulo; </s>
            <s xml:id="echoid-s34788" xml:space="preserve">vnde perpendicularis K L, cadit in punctũ n, vbi diameter Vertie
              <unsure/>
            alis à diame-
              <lb/>
              <note position="left" xlink:label="note-0556-10" xlink:href="note-0556-10a" xml:space="preserve">30</note>
            tro paralleli ſecatur: </s>
            <s xml:id="echoid-s34789" xml:space="preserve">Deinde in quarta conſtituitur Sol citra Verticalem circulum, ita tamen, vt eius
              <lb/>
            diſtantia à Meridiano minor ſit quadrante, ſiue ſex horis; </s>
            <s xml:id="echoid-s34790" xml:space="preserve">ex quo fit vt perpendicularis K L, cadat
              <lb/>
            citra diametrum Verticalis, ſed ſupra centrum paralleli m: </s>
            <s xml:id="echoid-s34791" xml:space="preserve">Rurſus in quinta Sol abeſt ſex horis à Me-
              <lb/>
            ridiano, ac idcirco perpendicularis K L, in m, centrum paralleli cadit: </s>
            <s xml:id="echoid-s34792" xml:space="preserve">In ſexta denique Sol à Meridia-
              <lb/>
            no maiorem diſtantiam habet, quam ſex horarum, ideoque perpendicularis infra m, centrum paralleli
              <lb/>
            cadit. </s>
            <s xml:id="echoid-s34793" xml:space="preserve">In omnibus tamen iſtis figuris idem ſemper modus eſt inueſtigandi dictas circunferentias, vt pa-
              <lb/>
            tet. </s>
            <s xml:id="echoid-s34794" xml:space="preserve">Pro parallelo autem australi vnicam figuram, nempe primam, deſcripſimus, quia Sol tunc ſupra
              <lb/>
            Horizontem ſemper vltra Verticalem exiſtit, minorem{q́ue} diſtantiam babet à Meridiano, quam ſex ho-
              <lb/>
            rarum, vt patet.</s>
            <s xml:id="echoid-s34795" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">40</note>
        </div>
        <div xml:id="echoid-div1756" type="section" level="1" n="474">
          <head xml:id="echoid-head503" style="it" xml:space="preserve">DEMONSTR ATIO EORVM, QV AE IN ANTECEDENTI
            <lb/>
          cap. dicta ſunt de inuentione prædictarum ſex circun-
            <lb/>
          ferentiarum. CAP. V.</head>
          <p>
            <s xml:id="echoid-s34796" xml:space="preserve">IN qualibet figura præcedentis cap. </s>
            <s xml:id="echoid-s34797" xml:space="preserve">(in qua tamen axis mundi, & </s>
            <s xml:id="echoid-s34798" xml:space="preserve">diameter Aequatoris non du-
              <lb/>
              <note position="left" xlink:label="note-0556-12" xlink:href="note-0556-12a" xml:space="preserve">Demonſtratio
                <lb/>
              iuuentionis ſex
                <lb/>
              dictarum circũ-
                <lb/>
              ferentiarum, So
                <lb/>
              le conſtituto in
                <lb/>
              qu@liber paral-
                <lb/>
              lelo.</note>
            cantur, ne multitudo linearum confuſionem pariat) intelligatur circa a b, diametrum paralleli
              <lb/>
            ſemicirculus paralleli a e b, ad propriam poſitionem conuerſus, ita vt rectus ſit ad Meridianum,
              <lb/>
            tranſeatq́ue per K, centrum Solis. </s>
            <s xml:id="echoid-s34799" xml:space="preserve">Et quoniam K L, per defin. </s>
            <s xml:id="echoid-s34800" xml:space="preserve">4 lib. </s>
            <s xml:id="echoid-s34801" xml:space="preserve">11. </s>
            <s xml:id="echoid-s34802" xml:space="preserve">Eucl. </s>
            <s xml:id="echoid-s34803" xml:space="preserve">ad planum Meridia-
              <lb/>
            ni recta eſt in eo ſitu, extendatur recta Y E, vſque ad Z, ducaturq́ue per rectas Y Z, K L, planum
              <lb/>
            faciens in ſuperficie ſphæræ, per propoſ. </s>
            <s xml:id="echoid-s34804" xml:space="preserve">1. </s>
            <s xml:id="echoid-s34805" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s34806" xml:space="preserve">1. </s>
            <s xml:id="echoid-s34807" xml:space="preserve">Theod. </s>
            <s xml:id="echoid-s34808" xml:space="preserve">ſemicirculum Y K H Z, qui rectus erit
              <lb/>
              <note position="left" xlink:label="note-0556-13" xlink:href="note-0556-13a" xml:space="preserve">18. vndec.</note>
              <note position="left" xlink:label="note-0556-14" xlink:href="note-0556-14a" xml:space="preserve">50</note>
            ad planum Meridiani, atque adeo Hectemorion referet, cum hic etiã per centrum Solis ducatur,
              <lb/>
            rectusq́ue ſit ad Meridianum, per propoſ. </s>
            <s xml:id="echoid-s34809" xml:space="preserve">15. </s>
            <s xml:id="echoid-s34810" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s34811" xml:space="preserve">1. </s>
            <s xml:id="echoid-s34812" xml:space="preserve">Theod. </s>
            <s xml:id="echoid-s34813" xml:space="preserve">vtpote qui per polos Meridiani tran-
              <lb/>
            ſeat, vt ſupra dictum eſt. </s>
            <s xml:id="echoid-s34814" xml:space="preserve">Reliqua in figura conſtruantur, vt in figura cap. </s>
            <s xml:id="echoid-s34815" xml:space="preserve">3. </s>
            <s xml:id="echoid-s34816" xml:space="preserve">Quoniam igitur re-
              <lb/>
              <note position="left" xlink:label="note-0556-15" xlink:href="note-0556-15a" xml:space="preserve">Demonſtratio
                <lb/>
              circunferentiæ
                <lb/>
              hectemoriæ.</note>
            cta L f, æqualis eſt rectæ L K, ex conſtructione, vel ex demonſtratis in antecedenti cap. </s>
            <s xml:id="echoid-s34817" xml:space="preserve">(Dixi-
              <lb/>
            mus enim ad interuallum L K, ſumendum eſſe ex L, vt centro, punctum f, in Meridiano, pro in-
              <lb/>
            uentione circunferentiæ hectemoriæ. </s>
            <s xml:id="echoid-s34818" xml:space="preserve">Item ſi ex L, ducatur ad E L Y, perpendicularis L f, de-
              <lb/>
            monſtrauimus L f, rectæ L K, æqualem eſſe) erunt duo latera E f, f L, trianguli E f L, in plano
              <lb/>
            Meridiani duobus lateribus E
              <emph style="sc">K</emph>
            ,
              <emph style="sc">K</emph>
            L, trianguli E K L, in plano Hectemorij æqualia: </s>
            <s xml:id="echoid-s34819" xml:space="preserve">Habent au-
              <lb/>
            tem & </s>
            <s xml:id="echoid-s34820" xml:space="preserve">baſim E L, communem. </s>
            <s xml:id="echoid-s34821" xml:space="preserve">Igitur angulus E f L, angulo E K L, æqualis erit. </s>
            <s xml:id="echoid-s34822" xml:space="preserve">Eſtautem
              <lb/>
              <note position="left" xlink:label="note-0556-16" xlink:href="note-0556-16a" xml:space="preserve">8. primi.</note>
            angulo E f L, æqualis alternus angulus f E g; </s>
            <s xml:id="echoid-s34823" xml:space="preserve">propterea quòd, cum anguli f L E, g E L, recti ſint,
              <lb/>
              <note position="left" xlink:label="note-0556-17" xlink:href="note-0556-17a" xml:space="preserve">29. primi.</note>
            rectæ f L, g E, parallelæ ſunt. </s>
            <s xml:id="echoid-s34824" xml:space="preserve">Item angulo E K L, eadem ratione æqualis eſt angulus alternus
              <lb/>
              <note position="left" xlink:label="note-0556-18" xlink:href="note-0556-18a" xml:space="preserve">28. primi.</note>
            </s>
          </p>
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