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>
            <s xml:id="echoid-s4390" xml:space="preserve">
              <pb o="80" file="0100" n="100" rhead="GNOMONICES"/>
            nationis plani à Verticali circulo proprie dicto, ita vt tanta ſit declinatio plani, quantus eſt angu-
              <lb/>
            lus E I G, atque adeo arcus circuli ex centro I, deſcripti inter rectas I E, I G, comprehenſus conti-
              <lb/>
            neat gradus declinationis. </s>
            <s xml:id="echoid-s4391" xml:space="preserve">Ducatur enim G K, in plano inſtrumẽti A B C D, perpendicularis ad
              <lb/>
            G H, ita vt G K, ſit communis ſectio Verticalis circuli proprie dicti, & </s>
            <s xml:id="echoid-s4392" xml:space="preserve">plani, in quo eſt inſtrumen
              <lb/>
              <figure xlink:label="fig-0100-01" xlink:href="fig-0100-01a" number="63">
                <image file="0100-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0100-01"/>
              </figure>
            tum A B C D. </s>
            <s xml:id="echoid-s4393" xml:space="preserve">Erit igitur
              <lb/>
            E G K, angulus declinationis
              <lb/>
            plani propoſiti per rectã A B,
              <lb/>
            ducti à Verticali per rectam
              <lb/>
            G k, ducto. </s>
            <s xml:id="echoid-s4394" xml:space="preserve">Nam cum & </s>
            <s xml:id="echoid-s4395" xml:space="preserve">Ver
              <lb/>
            ticalis circuli planũ per G K,
              <lb/>
              <note position="left" xlink:label="note-0100-01" xlink:href="note-0100-01a" xml:space="preserve">10</note>
            & </s>
            <s xml:id="echoid-s4396" xml:space="preserve">planum propoſitum per
              <lb/>
            A B, ductum, rectum ſit ad Ho
              <lb/>
            rizontem, erit quoque com-
              <lb/>
            munis ſectio Verticalis, & </s>
            <s xml:id="echoid-s4397" xml:space="preserve">pla
              <lb/>
            ni propoſiti perpendicularis
              <lb/>
              <note position="left" xlink:label="note-0100-02" xlink:href="note-0100-02a" xml:space="preserve">19. vndec.</note>
            ad Horizontem, atque adeo
              <lb/>
            & </s>
            <s xml:id="echoid-s4398" xml:space="preserve">ad rectas G k, A B, in Ho-
              <lb/>
            rizonte exiſtentes, ex deſin.
              <lb/>
            </s>
            <s xml:id="echoid-s4399" xml:space="preserve">3. </s>
            <s xml:id="echoid-s4400" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s4401" xml:space="preserve">11. </s>
            <s xml:id="echoid-s4402" xml:space="preserve">Euclidis. </s>
            <s xml:id="echoid-s4403" xml:space="preserve">Igitur ex
              <lb/>
            definitione 6. </s>
            <s xml:id="echoid-s4404" xml:space="preserve">eiuſdem libri,
              <lb/>
              <note position="left" xlink:label="note-0100-03" xlink:href="note-0100-03a" xml:space="preserve">20</note>
            erit E G K, angulus decli-
              <lb/>
            nationis, ſiue inclinationis
              <lb/>
            plani propoſiti per A B, ducti
              <lb/>
            ad Verticalem circulum per
              <lb/>
            G k, ductum; </s>
            <s xml:id="echoid-s4405" xml:space="preserve">quandoquidem
              <lb/>
            rectæ G K, G E, ad idem pun
              <lb/>
            ctũ G, cõmunis ſectionis pla-
              <lb/>
            ni ꝓpoſiti, & </s>
            <s xml:id="echoid-s4406" xml:space="preserve">Verticalis, rectos
              <lb/>
            cũ cõmuni ſectione angulos
              <lb/>
            efficiunt, vt dictum eſt. </s>
            <s xml:id="echoid-s4407" xml:space="preserve">Quòd
              <lb/>
              <note position="left" xlink:label="note-0100-04" xlink:href="note-0100-04a" xml:space="preserve">30</note>
            ſi planum per A B, ductum
              <lb/>
            non ſit rectum ad Horizontẽ,
              <lb/>
            erit nihilominus E G K, angulus declinationis, licet impropriè. </s>
            <s xml:id="echoid-s4408" xml:space="preserve">oſtendit enim declinationem li-
              <lb/>
            neæ A B, quæ Horizonti æquidiſtat, à Verticali circulo. </s>
            <s xml:id="echoid-s4409" xml:space="preserve">Quamobrem, cum angulo E G K, ęqualis
              <lb/>
            ſit angulus E I G, (cum enim angulus I G K, rectus ęqualis ſit duobus angulis ſimul I G E, E I G,
              <lb/>
            quòd hi vhi angulo recto æquales ſint, ob rectum angulum G E I; </s>
            <s xml:id="echoid-s4410" xml:space="preserve">ſi dematur communis angu-
              <lb/>
              <note position="left" xlink:label="note-0100-05" xlink:href="note-0100-05a" xml:space="preserve">32. primi.</note>
            lus I G E, remanebuntęquales anguli E G K, E I G.) </s>
            <s xml:id="echoid-s4411" xml:space="preserve">erit quoque E I G, angulus declinationis pla-
              <lb/>
            ni dati à Verticali circulo. </s>
            <s xml:id="echoid-s4412" xml:space="preserve">Quod eſt propoſitum.</s>
            <s xml:id="echoid-s4413" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4414" xml:space="preserve">IAM vero, num planum propoſitum ad ortum declinet, an ad occaſum, ita cognoſcemus. </s>
            <s xml:id="echoid-s4415" xml:space="preserve">Si
              <lb/>
              <note position="left" xlink:label="note-0100-06" xlink:href="note-0100-06a" xml:space="preserve">An planũ pro-
                <lb/>
              poſitum in or-
                <lb/>
              tum, an uerò
                <lb/>
              in occaſum de-
                <lb/>
              clinet, qua ra-
                <lb/>
              tione cognoſca-
                <lb/>
              tur.</note>
            planum ad meridiem vergat, & </s>
            <s xml:id="echoid-s4416" xml:space="preserve">meridiana linea ſecet rectam E B, ipſum declinabit à meridie in
              <lb/>
              <note position="left" xlink:label="note-0100-07" xlink:href="note-0100-07a" xml:space="preserve">40</note>
            ortum: </s>
            <s xml:id="echoid-s4417" xml:space="preserve">ſi verò linea meridiana ſecet rectam E A, & </s>
            <s xml:id="echoid-s4418" xml:space="preserve">planum ſpectet ad meridiem, ipſum à meri-
              <lb/>
            die in occaſum declinabit. </s>
            <s xml:id="echoid-s4419" xml:space="preserve">Contra verò, ſi planum ad Septentrionem vergat. </s>
            <s xml:id="echoid-s4420" xml:space="preserve">Nam linea meridia-
              <lb/>
            na ſecante rectam E B, planum à Septentrione in occaſum, ſecante autem recram E A, in ortum
              <lb/>
            declinabit, vt ex figura apparet. </s>
            <s xml:id="echoid-s4421" xml:space="preserve">Iam vero, ſi ex I, circulum deſcribas ad quodcunque interuallum,
              <lb/>
            dabit arcus inter rectas I E, I G, comprehenſus, gradus declinationis, vt etiam ante diximus.</s>
            <s xml:id="echoid-s4422" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4423" xml:space="preserve">IDEM hoc modo diſcemus. </s>
            <s xml:id="echoid-s4424" xml:space="preserve">Quoniam linea meridiana G H, dum ipſam E F, ſecat oblique,
              <lb/>
            cum recta A B, efficit angulum acutum, cui ſemper ſubtenditur recta I E, & </s>
            <s xml:id="echoid-s4425" xml:space="preserve">reliquum obtuſum;
              <lb/>
            </s>
            <s xml:id="echoid-s4426" xml:space="preserve">ex qua parte extiterit hic angulus obtuſus, in eam planũ declinabit, adeo vt ſi angulus obtuſus fue
              <lb/>
            rit verſus ortum, planũ à meridie vel Septẽtrione in ortũ, ſi vero in occaſum, in occaſum declinet.</s>
            <s xml:id="echoid-s4427" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4428" xml:space="preserve">CAETERVM tunc planum à meridie declinare in ortum vel occaſum, hoc eſt, ad meridiẽ
              <lb/>
              <note position="left" xlink:label="note-0100-08" xlink:href="note-0100-08a" xml:space="preserve">50</note>
            ſpectare ſciemus, cum nobis ad planum conuerſis Sol à dextris oritur, & </s>
            <s xml:id="echoid-s4429" xml:space="preserve">occidit à ſiniſtris; </s>
            <s xml:id="echoid-s4430" xml:space="preserve">à Se-
              <lb/>
              <note position="left" xlink:label="note-0100-09" xlink:href="note-0100-09a" xml:space="preserve">An planũ pro-
                <lb/>
              poſitum ad me-
                <lb/>
              ridiem ſpectet,
                <lb/>
              an ad Septen-
                <lb/>
              trionem.</note>
            ptentrione vero, cum ex parte ſiniſtra oritur, & </s>
            <s xml:id="echoid-s4431" xml:space="preserve">ex parte dextra occidit. </s>
            <s xml:id="echoid-s4432" xml:space="preserve">Quòd ſi planum tantam
              <lb/>
            habeat declinationem à Verticali, vt parum à Meridiano circulo differat, proptereaq́; </s>
            <s xml:id="echoid-s4433" xml:space="preserve">difficile ad-
              <lb/>
            modum ſit dignoſcere, an ad meridiem ſpecter, an vero ad Septentrionem, vtemur hac arte. </s>
            <s xml:id="echoid-s4434" xml:space="preserve">Ad
              <lb/>
            muri planum, vel certe ad rectam, quę in eo parallela ducta eſt Horizõti, ducemus in plano, quod
              <lb/>
            Horizonti ęquidiſter, perpendicularem, & </s>
            <s xml:id="echoid-s4435" xml:space="preserve">eius declinationem inueſtigabimus. </s>
            <s xml:id="echoid-s4436" xml:space="preserve">Si enim murus à
              <lb/>
            Meridiano circulo parum declinat, parum etiam declinabit dicta perpendicularis à Verticali cir-
              <lb/>
            culo proprie dicto, ac proinde ſacile intelligemus, num ea ad meridiem, vel ad Septentrionem
              <lb/>
            ſpectet, ſecundum regulam pręſcript@m: </s>
            <s xml:id="echoid-s4437" xml:space="preserve">quare & </s>
            <s xml:id="echoid-s4438" xml:space="preserve">eius declinationem cognoſcemus. </s>
            <s xml:id="echoid-s4439" xml:space="preserve">Itaque ſi hęc
              <lb/>
            perpendicularis declinet à meridie in ortũ, vel à Septentrione in occaſum, declinabit murus pro-
              <lb/>
            poſitus à Septentrione in ortum, ſi ad ortum ſpectat, vel à meridie in occaſum, ſi ad occaſum </s>
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