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-s21843" xml:space="preserve">
              <pb o="327" file="0343" n="343" rhead="LIBER TERTIVS."/>
            diationes cœli, angulosq́ue terræ, ac puncta, quæ orientibus ſignis in circulo horæ 6 exiſtunt, com
              <lb/>
            modius omnia deſcribentur, vt patet. </s>
            <s xml:id="echoid-s21844" xml:space="preserve">Tranſibunt autem ſigna aſcendentia per ea puncta horizon
              <lb/>
            talis lineæ, vbi à parallelis ſignorum ſecatur, licet in noſtro exemplo vix ab arcubus ſignorum bo.
              <lb/>
            </s>
            <s xml:id="echoid-s21845" xml:space="preserve">
              <note position="right" xlink:label="note-0343-01" xlink:href="note-0343-01a" xml:space="preserve">Inuentio pun-
                <lb/>
              cto@ũ in linea
                <lb/>
              horizon@@@, er
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              quæ a cus ſi
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              gnorum, & aſ@é
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              dentia ſigna @u
                <lb/>
              @i debeant.</note>
            realium ſecetur. </s>
            <s xml:id="echoid-s21846" xml:space="preserve">Quæ quidem puncta, quamuis arcus ſignorum non ſint delineati in horologio,
              <lb/>
            inueniemus vel ex tabella quinta propol. </s>
            <s xml:id="echoid-s21847" xml:space="preserve">9. </s>
            <s xml:id="echoid-s21848" xml:space="preserve">ſuperioris lib. </s>
            <s xml:id="echoid-s21849" xml:space="preserve">vt in præcedentibus dictum eſt; </s>
            <s xml:id="echoid-s21850" xml:space="preserve">(Nam
              <lb/>
            ſi lineas horarias ducamus, quæ indicent horas arcus ſemidiurnos terminantes, ſecabunt hæ lineã
              <lb/>
            horizontalem in dictis punctis) vel certè ex vltima figura propoſ. </s>
            <s xml:id="echoid-s21851" xml:space="preserve">21. </s>
            <s xml:id="echoid-s21852" xml:space="preserve">ſuperioris lib. </s>
            <s xml:id="echoid-s21853" xml:space="preserve">quam hic re-
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            petiuimus, quoad radios latitudinum ſignorum, hoc modo. </s>
            <s xml:id="echoid-s21854" xml:space="preserve">Sit vt ibi, Horizon A B C D, cuius
              <lb/>
            centrum E; </s>
            <s xml:id="echoid-s21855" xml:space="preserve">communis eius ſectio cum Meridiano B D; </s>
            <s xml:id="echoid-s21856" xml:space="preserve">eiuſdem cum Verticali primario ſectio
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            communis A C; </s>
            <s xml:id="echoid-s21857" xml:space="preserve">ſintq́ue radij latitudinum ortiuarum, & </s>
            <s xml:id="echoid-s21858" xml:space="preserve">occiduarum, vt ibidem. </s>
            <s xml:id="echoid-s21859" xml:space="preserve">Pro horologio
              <lb/>
              <note position="left" xlink:label="note-0343-02" xlink:href="note-0343-02a" xml:space="preserve">10</note>
              <note position="right" xlink:label="note-0343-03" xlink:href="note-0343-03a" xml:space="preserve">Alia inuentio
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              eorundem pun
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              @@orum.</note>
              <figure xlink:label="fig-0343-01" xlink:href="fig-0343-01a" number="230">
                <image file="0343-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0343-01"/>
              </figure>
              <note position="left" xlink:label="note-0343-04" xlink:href="note-0343-04a" xml:space="preserve">20</note>
              <note position="left" xlink:label="note-0343-05" xlink:href="note-0343-05a" xml:space="preserve">30</note>
            ergo declinante à meridie in ortum conſtituatur in E, ad E D, angulus declinationis propoſiti plæ
              <unsure/>
              <lb/>
            ni D E K, ad partes ſeptentrionis verſus occaſum, id eſt, verſus punctum A: </s>
            <s xml:id="echoid-s21860" xml:space="preserve">In declinante verò
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            à meridie in occaſum, ex parte quoque ſeptẽtrionis verſus ortum, id eſt, verſus punctum C. </s>
            <s xml:id="echoid-s21861" xml:space="preserve">Quòd
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            ſi planum à borea declinet in ortum, conſticuendus erit dictus angulus declinationis in E, ad E B,
              <lb/>
            ad partes meridiei verſus occaſum, punctumve A: </s>
            <s xml:id="echoid-s21862" xml:space="preserve">at verò ex parte quoque meridiei verſus ortum,
              <lb/>
              <note position="left" xlink:label="note-0343-06" xlink:href="note-0343-06a" xml:space="preserve">40</note>
            punctumve C, ſi à borea in occaſum deflectat. </s>
            <s xml:id="echoid-s21863" xml:space="preserve">Sumpta autem recta E K, ſtylo ęquali, in hac linea,
              <lb/>
            quæ dictum angulum declinationis cum B D, in E, conſtituit, ducatur per K, ad E K, perpendicu
              <lb/>
            laris ſecans B D, productam in M, & </s>
            <s xml:id="echoid-s21864" xml:space="preserve">radios latitudinum ortiuarum, occiduarumve productos in
              <lb/>
            aliis punctis. </s>
            <s xml:id="echoid-s21865" xml:space="preserve">Dico hæc puncta circino accepta ex puncto M, & </s>
            <s xml:id="echoid-s21866" xml:space="preserve">translata in horizontalem lineam
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            ex E, vbi à meridiana linea ſecatur, vel ſumpta ex puncto K, & </s>
            <s xml:id="echoid-s21867" xml:space="preserve">translata in lineam horizontalem
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            ex k, loco ſtyli, dare puncta, per quæ arcus ſignorum, & </s>
            <s xml:id="echoid-s21868" xml:space="preserve">ſigna aſcendentia duci debent. </s>
            <s xml:id="echoid-s21869" xml:space="preserve">Ducta
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            enim in horologio ex K, loco ſtyli ad horizontalem lineam perpendiculari K N, quæ ſtylo. </s>
            <s xml:id="echoid-s21870" xml:space="preserve">æqua-
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            lis ſit, coniunctaq́ue recta N E; </s>
            <s xml:id="echoid-s21871" xml:space="preserve">ſi intelligatur triangulum E K N, conuerti circa E K, donec re-
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            ctum ſit ad planum horologii, ac proinde in plano Horizontis ſit conſtitutum, & </s>
            <s xml:id="echoid-s21872" xml:space="preserve">vertex ſtyli N,
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            idem, quod centrum mundi; </s>
            <s xml:id="echoid-s21873" xml:space="preserve">erit recta N E, communis ſectio Horizontis, ac Meridiani, propte
              <lb/>
              <note position="left" xlink:label="note-0343-07" xlink:href="note-0343-07a" xml:space="preserve">50</note>
            rea quòd vterque circulus per centrum mundi, & </s>
            <s xml:id="echoid-s21874" xml:space="preserve">per punctum E, in quo communes corum cum
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            plano horologii ſectiones conueniunt, ductus ſit: </s>
            <s xml:id="echoid-s21875" xml:space="preserve">ac propterea angulus N E K, quem Meridianus
              <lb/>
            cum plano horologij in Horizontis plano efficit, æqualis erit complem ento declinationis plani à
              <lb/>
            Verticali, & </s>
            <s xml:id="echoid-s21876" xml:space="preserve">proinde E N K, angulus declinaticnis erit, & </s>
            <s xml:id="echoid-s21877" xml:space="preserve">ipſi D E K, angulo declinationis in figu-
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            ra latitudinum ortiuarum æqualis. </s>
            <s xml:id="echoid-s21878" xml:space="preserve">Quoniam igitur anguli K, E, trianguli E K M, in figura lati-
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            tudinum, angulis K, N, trianguli E N K, in horologio æquales ſunt, & </s>
            <s xml:id="echoid-s21879" xml:space="preserve">latera E K, N K, quibus
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            in vtroque triangulo adiacent, æqualia inter ſe; </s>
            <s xml:id="echoid-s21880" xml:space="preserve">erunt quoque latera M E, M K, prioris trianguli
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              <note position="right" xlink:label="note-0343-08" xlink:href="note-0343-08a" xml:space="preserve">26. primi.</note>
            lateribus E N, E K, trianguli poſterioris æqualia, & </s>
            <s xml:id="echoid-s21881" xml:space="preserve">angulus M, angulo E, æqualis. </s>
            <s xml:id="echoid-s21882" xml:space="preserve">Quare ſi re-
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            cta E M, rectæ N E, ſuperponatur, neutra alteram excedet, & </s>
            <s xml:id="echoid-s21883" xml:space="preserve">ſtylus E K, ſtylo N K, & </s>
            <s xml:id="echoid-s21884" xml:space="preserve">recta M K,
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            rectæ E K, congruet, ob æqualitatem angulorum; </s>
            <s xml:id="echoid-s21885" xml:space="preserve">ac proinde radij latitudinum ortiuarum, & </s>
            <s xml:id="echoid-s21886" xml:space="preserve">
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            occiduarum horizontali lineæ occurrent in dictis punctis arcuum ſignorum, in quæ nimirum </s>
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