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

Table of figures

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[Figure 241]
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[Figure 242]
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[Figure 243]
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[265] 1. figura
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[266] 2. figura.
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[267] 3. figura.
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[268] 4. figura
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[269] 5. figura
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[270] 6. figura
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            <s xml:id="echoid-s25849" xml:space="preserve">
              <pb o="392" file="0408" n="408" rhead="GNOMONICES"/>
            C D, angulum inclinationis, vt res poſtulat. </s>
            <s xml:id="echoid-s25850" xml:space="preserve">Quare Horizon plano horologij in C, occurret, & </s>
            <s xml:id="echoid-s25851" xml:space="preserve">propte-
              <lb/>
            rea per punctum C, linea horizontalis ducenda erit ad C D, perpendicularis. </s>
            <s xml:id="echoid-s25852" xml:space="preserve">Cum enim tam Horizon,
              <lb/>
            quàm planum horologij rectum ſit ad circulum maximum, qui inclinationem plani metitur, duciturq́, per
              <lb/>
            rectam C D, erit & </s>
            <s xml:id="echoid-s25853" xml:space="preserve">communis illorum ſectio, nempe linea horizontalis, ad eundem circulum maximum
              <lb/>
              <note position="left" xlink:label="note-0408-01" xlink:href="note-0408-01a" xml:space="preserve">19. vn
                <unsure/>
              dec
                <unsure/>
              .</note>
            recta, atque adeo, per defin. </s>
            <s xml:id="echoid-s25854" xml:space="preserve">3. </s>
            <s xml:id="echoid-s25855" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s25856" xml:space="preserve">11. </s>
            <s xml:id="echoid-s25857" xml:space="preserve">Eucl. </s>
            <s xml:id="echoid-s25858" xml:space="preserve">ad rectam C D, in illo circulo exiſtentem perpendicularis in
              <lb/>
            puncto C. </s>
            <s xml:id="echoid-s25859" xml:space="preserve">Rurſus quoniam tam circulus maximus inclinationem horologij metiens, quàm Meridianus ad
              <lb/>
            Horizontem rectus eſt, erit
              <lb/>
            quoque communis eorum ſe
              <lb/>
              <note position="left" xlink:label="note-0408-02" xlink:href="note-0408-02a" xml:space="preserve">19. vn
                <unsure/>
              dec
                <unsure/>
              .</note>
              <figure xlink:label="fig-0408-01" xlink:href="fig-0408-01a" number="268">
                <image file="0408-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0408-01"/>
                <caption xml:id="echoid-caption4" xml:space="preserve">4. figura</caption>
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            ctio ad euudẽ recta, ac pro- pterea, per defin. </s>
            <s xml:id="echoid-s25860" xml:space="preserve">3. </s>
            <s xml:id="echoid-s25861" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s25862" xml:space="preserve">11.</s>
            <s xml:id="echoid-s25863" xml:space="preserve">
              <note position="left" xlink:label="note-0408-03" xlink:href="note-0408-03a" xml:space="preserve">10</note>
            Eucl. </s>
            <s xml:id="echoid-s25864" xml:space="preserve">ad rectam β C, in Ho rizonte exiſtentem perpen- dicularis in centro mundi β, per quod omnes circuli maximi ducuntur. </s>
            <s xml:id="echoid-s25865" xml:space="preserve">Cum er- go recta β D, ſit in plano cir culi maximi inclinationem borologij metiẽtis, rectum{q́ue} faciat angulum cum β C, vt diximus, erit ipſa β D, com
              <note position="left" xlink:label="note-0408-04" xlink:href="note-0408-04a" xml:space="preserve">20</note>
            munis ſectio dicti circuli maximi, & </s>
            <s xml:id="echoid-s25866" xml:space="preserve">Meridiani. </s>
            <s xml:id="echoid-s25867" xml:space="preserve">Oc- currit igitur Meridianus plano horologij in pũcto D.</s>
            <s xml:id="echoid-s25868" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s25869" xml:space="preserve">MOVEATVR quo-
              <lb/>
            que triangulum α F E, cir-
              <lb/>
            ca rectam α E, donec cum
              <lb/>
            plano Horizontis coniunga
              <lb/>
            tur, punctumq́, F, cum cen-
              <lb/>
            tro mundi β, ob æqualitatẽ
              <lb/>
              <note position="left" xlink:label="note-0408-05" xlink:href="note-0408-05a" xml:space="preserve">30</note>
            rectarum C F, C β. </s>
            <s xml:id="echoid-s25870" xml:space="preserve">Quo
              <lb/>
            facto, cũ C F E, ſit angulus
              <lb/>
            declinationis plani à Verti-
              <lb/>
            cali, erit C E F, angulus complementi eiuſdem declinationis, qualem nimirum cõmunis ſectio plani horo
              <lb/>
            logij & </s>
            <s xml:id="echoid-s25871" xml:space="preserve">Horizoutis cum communi ſectione Horizontis ac Meridiani facit. </s>
            <s xml:id="echoid-s25872" xml:space="preserve">Cum igitur Meridian{us} per
              <lb/>
            F, ducatur, hoc eſt, per centrum mundi, in quo punctum F, poſuimus, erit recta F E, faciens cum linea
              <lb/>
            horizontali C E, angulum complementi declinationis, communis ſectio Horizontis ac Meridiani, cum
              <lb/>
            exiſtat in Horizonte per centrum mundi F, & </s>
            <s xml:id="echoid-s25873" xml:space="preserve">punctum E, ducto. </s>
            <s xml:id="echoid-s25874" xml:space="preserve">Quare Meridianus plano horologij
              <lb/>
            occurret in puncto E: </s>
            <s xml:id="echoid-s25875" xml:space="preserve">Occurrit autem eidem in puncto D, vt oſtendimus. </s>
            <s xml:id="echoid-s25876" xml:space="preserve">Igitur recta D E, in vtram-
              <lb/>
            que partem eiecta erit linea meridiana. </s>
            <s xml:id="echoid-s25877" xml:space="preserve">Quoniam vero tam Aequator, quàm Horizon ad Meridianum
              <lb/>
            rectus eſt, erit etiam eorum communis ſectio ad eundem recta, ac proinde, per defin. </s>
            <s xml:id="echoid-s25878" xml:space="preserve">3. </s>
            <s xml:id="echoid-s25879" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s25880" xml:space="preserve">11. </s>
            <s xml:id="echoid-s25881" xml:space="preserve">Eucl. </s>
            <s xml:id="echoid-s25882" xml:space="preserve">ad
              <lb/>
              <note position="left" xlink:label="note-0408-06" xlink:href="note-0408-06a" xml:space="preserve">@@. vn
                <unsure/>
              dec.</note>
              <note position="left" xlink:label="note-0408-07" xlink:href="note-0408-07a" xml:space="preserve">40</note>
            rectam F E, in Meridiano exiſtentem perpendicularis in F, centro mundi. </s>
            <s xml:id="echoid-s25883" xml:space="preserve">Quocirca cum recta F α, ſit
              <lb/>
            in Horizonte per centrum mundi F, & </s>
            <s xml:id="echoid-s25884" xml:space="preserve">punctum α, ducto, faciat{q́ue} cum F E, in Meridiano exiſtentem an
              <lb/>
            gulum rectum in F, ob quadrantem circuli ex F, deſcripti inter rectas F E, F α, interiectum, erit ipſa
              <lb/>
            F α, communis ſectio Horizontis & </s>
            <s xml:id="echoid-s25885" xml:space="preserve">Aequatoris: </s>
            <s xml:id="echoid-s25886" xml:space="preserve">Quamobrem Aequator plano horologii occurret in
              <lb/>
            α, ac idcirco per α, ducenda erit linea æquinoctialis.</s>
            <s xml:id="echoid-s25887" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s25888" xml:space="preserve">CONCIPIATVR rurſum per polum plani horologii, atque adeo per ſtylum K β, qui portio
              <lb/>
            eſt axis eiuſdem plani, & </s>
            <s xml:id="echoid-s25889" xml:space="preserve">per polum Meridiani duci circul{us} maximus faciens in horologio ſectionem li-
              <lb/>
            ueam rectam, quæneceſſario per α, punctum tranſibit. </s>
            <s xml:id="echoid-s25890" xml:space="preserve">Quoniam enim Aequator, & </s>
            <s xml:id="echoid-s25891" xml:space="preserve">Horizon tranſeũt
              <lb/>
            quoque per polos Meridiani, habebunt Aequator, Horizon, & </s>
            <s xml:id="echoid-s25892" xml:space="preserve">dictus circulus maximus eandem commu
              <lb/>
            nem ſectionem. </s>
            <s xml:id="echoid-s25893" xml:space="preserve">Quare in horologio facient tres ſectiones, lineas rectas, in eo puncto coeuntes, per pro-
              <lb/>
              <note position="left" xlink:label="note-0408-08" xlink:href="note-0408-08a" xml:space="preserve">50</note>
            poſ. </s>
            <s xml:id="echoid-s25894" xml:space="preserve">18. </s>
            <s xml:id="echoid-s25895" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s25896" xml:space="preserve">1. </s>
            <s xml:id="echoid-s25897" xml:space="preserve">in quod communis eorum ſectio cadit. </s>
            <s xml:id="echoid-s25898" xml:space="preserve">Cum ergo communis ſectio Horizontis, & </s>
            <s xml:id="echoid-s25899" xml:space="preserve">Aequa-
              <lb/>
            toris cadat in punctum α, quòd ibi ſe mutuo ſecent horizontalis linea, & </s>
            <s xml:id="echoid-s25900" xml:space="preserve">ęquinoctialis, vt oſtendimus,
              <lb/>
            tranſibit quoque communis ſectio prędicti circuli maximi, & </s>
            <s xml:id="echoid-s25901" xml:space="preserve">plani horologii per punctum α: </s>
            <s xml:id="echoid-s25902" xml:space="preserve">Tranſit
              <lb/>
            autem idem circulus maximus per K, locum ſtyli. </s>
            <s xml:id="echoid-s25903" xml:space="preserve">Igitur recta α K, communis ſectio eſt plani horologii,
              <lb/>
            & </s>
            <s xml:id="echoid-s25904" xml:space="preserve">dicti circuli maximi. </s>
            <s xml:id="echoid-s25905" xml:space="preserve">Quia vero dictus circulus rectus eſt, per propoſ. </s>
            <s xml:id="echoid-s25906" xml:space="preserve">15. </s>
            <s xml:id="echoid-s25907" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s25908" xml:space="preserve">1. </s>
            <s xml:id="echoid-s25909" xml:space="preserve">Theod. </s>
            <s xml:id="echoid-s25910" xml:space="preserve">ad Meridia-
              <lb/>
            num, & </s>
            <s xml:id="echoid-s25911" xml:space="preserve">ad planum horologii, cum per horum polos ducatur, erit viciſſim tam planum horologii, quàm
              <lb/>
            planum Meridiani ad dictum circulum rectum. </s>
            <s xml:id="echoid-s25912" xml:space="preserve">Igitur & </s>
            <s xml:id="echoid-s25913" xml:space="preserve">communis illorum ſectio, hoc eſt, linea meri-
              <lb/>
            diana E ρ, ad eundem circulum recta erit, ac proinde & </s>
            <s xml:id="echoid-s25914" xml:space="preserve">ad rectam α K, in illo circulo exiſtentem per-
              <lb/>
              <note position="left" xlink:label="note-0408-09" xlink:href="note-0408-09a" xml:space="preserve">@@. vndec.</note>
            pendicularis. </s>
            <s xml:id="echoid-s25915" xml:space="preserve">Secabit ergo neceſſario recta α K, meridianam lineam ad angulos rectos in puncto a. </s>
            <s xml:id="echoid-s25916" xml:space="preserve">Hinc
              <lb/>
            fit eandem rectam α K, tranſire omnino per punctum H, vbi ſe interſecant arcus deſcripti ex D, E, </s>
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