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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          <pb o="274" file="0290" n="290" rhead="GNOMONICES"/>
          <p>
            <s xml:id="echoid-s18599" xml:space="preserve">QVONIAM punctum F, extremum ſtyli idem eſt, quod centrum mundi, ex propoſ. </s>
            <s xml:id="echoid-s18600" xml:space="preserve">2. </s>
            <s xml:id="echoid-s18601" xml:space="preserve">ſupe-
              <lb/>
              <note position="left" xlink:label="note-0290-01" xlink:href="note-0290-01a" xml:space="preserve">Demonſtratio
                <lb/>
              conſtructionis
                <lb/>
              horologii æqui-
                <lb/>
              noctialis Aſtro
                <lb/>
              nomici.</note>
            rioris lib. </s>
            <s xml:id="echoid-s18602" xml:space="preserve">fit vt, ſi circa centrum mundi F, intelligatur æquinoctialis circulus, cui planum horolo-
              <lb/>
            gii æquidiſtat, in propria poſi-
              <lb/>
              <figure xlink:label="fig-0290-01" xlink:href="fig-0290-01a" number="201">
                <image file="0290-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0290-01"/>
              </figure>
            tione, ſtylus E F, ſit axis mundi.
              <lb/>
            </s>
            <s xml:id="echoid-s18603" xml:space="preserve">Cum enim axis mundi rectus
              <lb/>
            ſitad planũ Aequatoris in mun
              <lb/>
            di centro, ſitq́ue ſtylus E F, qui
              <lb/>
            rectus eſt ad planum horologij,
              <lb/>
            ad planum Aequatoris rectus,
              <lb/>
            vt in ſcholio propoſ. </s>
            <s xml:id="echoid-s18604" xml:space="preserve">14. </s>
            <s xml:id="echoid-s18605" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s18606" xml:space="preserve">11. </s>
            <s xml:id="echoid-s18607" xml:space="preserve">
              <lb/>
              <note position="left" xlink:label="note-0290-02" xlink:href="note-0290-02a" xml:space="preserve">10</note>
            Euclidis demõſtrauimus, quòd
              <lb/>
            duo hæc plana parallela ponan-
              <lb/>
            tur; </s>
            <s xml:id="echoid-s18608" xml:space="preserve">erit omnino ſtylus E F, pars
              <lb/>
            axis mundani. </s>
            <s xml:id="echoid-s18609" xml:space="preserve">Quia vero circu-
              <lb/>
            li horarum à meridie, vel me-
              <lb/>
            dia nocte ſecant maximum pa-
              <lb/>
            rallelorum ſemper apparentiũ,
              <lb/>
            atque adeò, ex propoſ. </s>
            <s xml:id="echoid-s18610" xml:space="preserve">10. </s>
            <s xml:id="echoid-s18611" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s18612" xml:space="preserve">2.
              <lb/>
            </s>
            <s xml:id="echoid-s18613" xml:space="preserve">Theodoſii, & </s>
            <s xml:id="echoid-s18614" xml:space="preserve">Aequatorem, qui
              <lb/>
            eſt omnium parallelorum maxi
              <lb/>
              <note position="left" xlink:label="note-0290-03" xlink:href="note-0290-03a" xml:space="preserve">20</note>
            mus, & </s>
            <s xml:id="echoid-s18615" xml:space="preserve">parallelum illum ſphæ-
              <lb/>
            ræ, in quo planum horologii
              <lb/>
            exiſtit, & </s>
            <s xml:id="echoid-s18616" xml:space="preserve">cuius centrum eſt E,
              <lb/>
            (quòd per propoſ. </s>
            <s xml:id="echoid-s18617" xml:space="preserve">10. </s>
            <s xml:id="echoid-s18618" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s18619" xml:space="preserve">1.
              <lb/>
            </s>
            <s xml:id="echoid-s18620" xml:space="preserve">Theodoſii, axis E F, per centrũ
              <lb/>
            ipſius neceſſario tranſit) in 24. </s>
            <s xml:id="echoid-s18621" xml:space="preserve">
              <lb/>
            partes æquales, tranſeuntq́ue
              <lb/>
            omnes per axem mundi, atque
              <lb/>
            adeo per punctum E, in quo, per propoſ. </s>
            <s xml:id="echoid-s18622" xml:space="preserve">18. </s>
            <s xml:id="echoid-s18623" xml:space="preserve">ſuperioris lib. </s>
            <s xml:id="echoid-s18624" xml:space="preserve">communes eorum, & </s>
            <s xml:id="echoid-s18625" xml:space="preserve">dicti paralleli ſe-
              <lb/>
            ctiones ſe interſecant; </s>
            <s xml:id="echoid-s18626" xml:space="preserve">erunt rectæ ex E, ad puncta diuiſionum illius paralleli, in quo horologium
              <lb/>
              <note position="left" xlink:label="note-0290-04" xlink:href="note-0290-04a" xml:space="preserve">30</note>
            exiſtit, eductæ, ſectiones communes circulorum horariorum à meridie, vel media nocte, & </s>
            <s xml:id="echoid-s18627" xml:space="preserve">dicti
              <lb/>
            paralleli. </s>
            <s xml:id="echoid-s18628" xml:space="preserve">Cum ergo hæ rectæ diuidant quoque, ex jis, quæ prope finem cap. </s>
            <s xml:id="echoid-s18629" xml:space="preserve">1. </s>
            <s xml:id="echoid-s18630" xml:space="preserve">ſphæræ demon-
              <lb/>
            ſtrauimus, circulum A C B D, illi parallelo ſphæræ concentricum, in 24. </s>
            <s xml:id="echoid-s18631" xml:space="preserve">partes æquales, erunt
              <lb/>
            eædem rectæ per centrum E, & </s>
            <s xml:id="echoid-s18632" xml:space="preserve">puncta diuiſionum circuli A C B D, emiſſæ, communes ſectiones
              <lb/>
            circulorum horarum à meridie, vel media nocte, & </s>
            <s xml:id="echoid-s18633" xml:space="preserve">plani horologij, hoc eſt, lineæ horarum à me-
              <lb/>
            ridie, vel media nocte; </s>
            <s xml:id="echoid-s18634" xml:space="preserve">ita vt A B, ſit ſectio Meridiani, & </s>
            <s xml:id="echoid-s18635" xml:space="preserve">plani horologij, recta deinde per ſequens
              <lb/>
            punctum ab A, verſus D, & </s>
            <s xml:id="echoid-s18636" xml:space="preserve">per centrum E, ducta communis ſectio plani horologij, & </s>
            <s xml:id="echoid-s18637" xml:space="preserve">circuli ho-
              <lb/>
            ræ 1. </s>
            <s xml:id="echoid-s18638" xml:space="preserve">à meridie, vel media nocte, & </s>
            <s xml:id="echoid-s18639" xml:space="preserve">ſic deinceps. </s>
            <s xml:id="echoid-s18640" xml:space="preserve">Horologium igitur Aſtronomicum æquinoctia-
              <lb/>
            le deſcripſimus, &</s>
            <s xml:id="echoid-s18641" xml:space="preserve">c. </s>
            <s xml:id="echoid-s18642" xml:space="preserve">Quod erat faciendum.
              <lb/>
            </s>
          </p>
        </div>
        <div xml:id="echoid-div953" type="section" level="1" n="232">
          <head xml:id="echoid-head239" style="it" xml:space="preserve">SCHOLIVM.</head>
          <p style="it">
            <s xml:id="echoid-s18643" xml:space="preserve">SI in plano aliquo ſtabili, quod Aequatori æquidiſtet, horologium ſit deſcribendum, datus ſit lo-
              <lb/>
              <note position="left" xlink:label="note-0290-06" xlink:href="note-0290-06a" xml:space="preserve">Quo pacto idẽ
                <lb/>
              horologiã ęqui
                <lb/>
              noctiale con-
                <lb/>
              ſtruendũ ſit in
                <lb/>
              plano ſtabili, in
                <lb/>
              quo locus ſtyli
                <lb/>
              datus ſit.</note>
            cus ſtyli cuiusuis in puncto E, ducenda erit beneficio libellæ, & </s>
            <s xml:id="echoid-s18644" xml:space="preserve">perpendiculi per E, recta C D, Horizonti
              <lb/>
            æquidiſtans, quam in E, ad angulos rectos ſecet recta A B. </s>
            <s xml:id="echoid-s18645" xml:space="preserve">Hæc enim erit linea meridiana. </s>
            <s xml:id="echoid-s18646" xml:space="preserve">Reliqua om-
              <lb/>
            nia perficienda erunt, vt prius.</s>
            <s xml:id="echoid-s18647" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div955" type="section" level="1" n="233">
          <head xml:id="echoid-head240" xml:space="preserve">PROBLEMA 50. PROPOSITIO 50.</head>
          <p>
            <s xml:id="echoid-s18648" xml:space="preserve">PARALLELOS, ſiue arcus ſignorum Zodiaci in prædicto ho-
              <lb/>
              <note position="left" xlink:label="note-0290-07" xlink:href="note-0290-07a" xml:space="preserve">50</note>
            rologio æquinoctiali deſignare.</s>
            <s xml:id="echoid-s18649" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s18650" xml:space="preserve">REPETATVR prima figura propoſ. </s>
            <s xml:id="echoid-s18651" xml:space="preserve">26. </s>
            <s xml:id="echoid-s18652" xml:space="preserve">huius libri, in qua ex axe E G, abſcindatur recta
              <lb/>
              <note position="left" xlink:label="note-0290-08" xlink:href="note-0290-08a" xml:space="preserve">Arcus ſignorũ
                <lb/>
              in horologio ę
                <lb/>
              quinoctiali quo
                <lb/>
              modo deſcribã
                <lb/>
              tur ex Analem-
                <lb/>
              mate.</note>
            E a, ſtylo cuiuſuis magnitudinis aſſumpto æqualis, & </s>
            <s xml:id="echoid-s18653" xml:space="preserve">per a, Æquatoris diametro HI, parallela
              <lb/>
            agatur, quæ erit communis ſectio plani horologii, ac Meridiani, cum planum horologii per illam
              <lb/>
            parallelam ductum plano Aequatoris per rectam HI, ducto æquidiſtet ſecundum magnitudinem
              <lb/>
            ſtyli E a. </s>
            <s xml:id="echoid-s18654" xml:space="preserve">Productis autem diametris Zodiaci ſigna oppoſita connectentibus, vt fiant triangula per
              <lb/>
            axem in conis, quorum baſes ſunt paralleli Aequatoris, & </s>
            <s xml:id="echoid-s18655" xml:space="preserve">vertex communis centrum E, erunt por
              <lb/>
            tiones parallelæ per a, ductæ, interceptæ inter latera triangulorum per axem, diametri conicarum
              <lb/>
            ſectionum, quæ quidem ex coroll. </s>
            <s xml:id="echoid-s18656" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s18657" xml:space="preserve">4. </s>
            <s xml:id="echoid-s18658" xml:space="preserve">ſuperioris lib circuli ſunt habentes centra in </s>
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