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 Notes

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          <p>
            <s xml:id="echoid-s25151" xml:space="preserve">
              <pb o="383" file="0399" n="399" rhead="LIBER TERTIVS."/>
            nã ſecet. </s>
            <s xml:id="echoid-s25152" xml:space="preserve">Ex quo etiã fit, ſi portio axis E M, ſumatur æqualis portioni axis ρ I, in ſuperioribus ho-
              <lb/>
            rologiis inter centrũ mundi I, & </s>
            <s xml:id="echoid-s25153" xml:space="preserve">centrum horologii ρ, ubi lineam meridianam ſecat axis mundi,
              <lb/>
            & </s>
            <s xml:id="echoid-s25154" xml:space="preserve">per M, ducatur ipſi K L, parallela M N, (dũmodo arcus D K, uel B K, æqualis ſit arcui Meridiani
              <lb/>
            inter planum, & </s>
            <s xml:id="echoid-s25155" xml:space="preserve">Horizontẽ inuento) ſecans Æquatoris diametrum in N, rectã M N, æqualẽ eſſe
              <lb/>
            rectæ ρ M, hoc eſt, portioni lineæ meridianæ inter centrum horologii ρ, & </s>
            <s xml:id="echoid-s25156" xml:space="preserve">punctum M, lineæ æ-
              <lb/>
            quinoctialis; </s>
            <s xml:id="echoid-s25157" xml:space="preserve">rectam autẽ EN, æqualem rectæ illi in horologio, quæ ex vertice ſtyli, ſeu centro mũ-
              <lb/>
            di I, in ſublimi poſito cadit in punctum M. </s>
            <s xml:id="echoid-s25158" xml:space="preserve">Sicut enim triangulum E M N, conſtituitur in Ana-
              <lb/>
            lemmate ex axe E M, communi ſectione Meridiani, & </s>
            <s xml:id="echoid-s25159" xml:space="preserve">plani horologii inclinati M N, & </s>
            <s xml:id="echoid-s25160" xml:space="preserve">commu-
              <lb/>
            ni ſectione Meridiani, & </s>
            <s xml:id="echoid-s25161" xml:space="preserve">Æquatoris E N, ita quoque in horologio triangulum ρ I M, in plano
              <lb/>
            Meridiani exiſtens, ſi axis ρ I, in proprio ſitu eſle intelligatur, (tranſit enim Meridianus per axem
              <lb/>
              <note position="left" xlink:label="note-0399-01" xlink:href="note-0399-01a" xml:space="preserve">10</note>
            ρ I, & </s>
            <s xml:id="echoid-s25162" xml:space="preserve">per punctum M,) ex eiſdem lineis conſtat, atque illi omnino æquale eſt. </s>
            <s xml:id="echoid-s25163" xml:space="preserve">Quoniam enim
              <lb/>
            angulus E M N, in Analemmate, quem axis cum linea meridiana horologii facit, æqualis eſt an-
              <lb/>
            gulo I ρ M, in horologio, quem axis, ſi in proprio ſitu collocetur, cum linea meridiana conſtituit,
              <lb/>
            & </s>
            <s xml:id="echoid-s25164" xml:space="preserve">angulus M E N, rectus angulo recto ρ I M; </s>
            <s xml:id="echoid-s25165" xml:space="preserve">(Nam Aequator ſecat axem in I, ad rectos angulos,
              <lb/>
            ac proinde per defin. </s>
            <s xml:id="echoid-s25166" xml:space="preserve">3. </s>
            <s xml:id="echoid-s25167" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s25168" xml:space="preserve">11. </s>
            <s xml:id="echoid-s25169" xml:space="preserve">Eucl. </s>
            <s xml:id="echoid-s25170" xml:space="preserve">axis cum recta I M, in Aequatore exiſtente rectos angulos fa-
              <lb/>
            cit) ponitur autem & </s>
            <s xml:id="echoid-s25171" xml:space="preserve">recta E M, rectę I ρ, æqualis; </s>
            <s xml:id="echoid-s25172" xml:space="preserve">erit quoque recta M N, rectę ρ M, & </s>
            <s xml:id="echoid-s25173" xml:space="preserve">recta E N,
              <lb/>
              <note position="right" xlink:label="note-0399-02" xlink:href="note-0399-02a" xml:space="preserve">26. primi.</note>
            rectæ I M, æqualis. </s>
            <s xml:id="echoid-s25174" xml:space="preserve">Iam uerò ipſamet Analemmata perſpicuè indicãt, an centrum horologii ſit in-
              <lb/>
            fra lineam æquinoctialem, an uero ſupra eãdem. </s>
            <s xml:id="echoid-s25175" xml:space="preserve">Quoniam enim in Analemmate primo & </s>
            <s xml:id="echoid-s25176" xml:space="preserve">quar-
              <lb/>
            to centrum M, in linea meridiana M N, horologii ſuperioris infra punctum N, per quod linea æ-
              <lb/>
            quinoctialis ducenda eſt, in aliis autem duobus intermediis ſupra idem punctum N, exiſtit, fit ut
              <lb/>
              <note position="left" xlink:label="note-0399-03" xlink:href="note-0399-03a" xml:space="preserve">20</note>
            idem centrum in prioribus duobus infra æquinoctialem lineã, in duobus uerò poſterioribus infra
              <lb/>
            eãdem exiſtat. </s>
            <s xml:id="echoid-s25177" xml:space="preserve">Quãdo enim centrũ horologii in linea meridiana exiſtit infra, uel ſupra punctum
              <lb/>
            N, æquinoctialis lineæ, idem centrum neceſſario exiſtit quoque infra lineam æquinoctialem uel
              <lb/>
            ſupra in linea ſtyli G N. </s>
            <s xml:id="echoid-s25178" xml:space="preserve">Nam quia æquinoctialis linea ſecat lineam ſtyli G N, ad angulos rectos
              <lb/>
            liquido conſtat, ſi æquinoctialis linca ſecet meridianam lineam ſupra, uel infra centrum, eandem
              <lb/>
            ſecare quoque lineam ſtyli G N, ſupra centrum uel infra, ut ex ſuprapoſitis fig uris manifeſtum eſt.</s>
            <s xml:id="echoid-s25179" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s25180" xml:space="preserve">QVOD ſi arcus Meridiani inter planum, & </s>
            <s xml:id="echoid-s25181" xml:space="preserve">Horizontẽ æqualis fuerit cõplemento altitudinis
              <lb/>
            poli ex parte auſtrali, ita ut cõmunis ſectio ipſius plani, & </s>
            <s xml:id="echoid-s25182" xml:space="preserve">Meridiani eadem ſit in Analemmate,
              <lb/>
            quæ ſectio cõmunis Meridiani & </s>
            <s xml:id="echoid-s25183" xml:space="preserve">Aequatoris H I, ſecabit axis F G, meridianam lineam horologii,
              <lb/>
            quæ in Analemmate parallela ducitur ipſi H I, ad angulos rectos: </s>
            <s xml:id="echoid-s25184" xml:space="preserve">atque adeo & </s>
            <s xml:id="echoid-s25185" xml:space="preserve">linea ſtyli G N, ad
              <lb/>
              <note position="left" xlink:label="note-0399-04" xlink:href="note-0399-04a" xml:space="preserve">30</note>
              <note position="right" xlink:label="note-0399-05" xlink:href="note-0399-05a" xml:space="preserve">29. primi.</note>
            eandem lineam meridianam in horologio perpendicularis erit; </s>
            <s xml:id="echoid-s25186" xml:space="preserve">& </s>
            <s xml:id="echoid-s25187" xml:space="preserve">Æquatoris diameter in eodem
              <lb/>
            Anlemmate meridianam lineam horologii, hoc eſt, communem ſectionem Meridiani, & </s>
            <s xml:id="echoid-s25188" xml:space="preserve">plani
              <lb/>
              <note position="right" xlink:label="note-0399-06" xlink:href="note-0399-06a" xml:space="preserve">In quonam ho
                <lb/>
              rologio linea
                <lb/>
              æquinoctialis,
                <lb/>
              & li
                <unsure/>
              nea meri-
                <lb/>
              diana inter ſe
                <lb/>
              parallelę ſint.</note>
            horologii non ſecabit. </s>
            <s xml:id="echoid-s25189" xml:space="preserve">Vnde in horologio parallelæ erunt inter ſelinea meridiana, & </s>
            <s xml:id="echoid-s25190" xml:space="preserve">æquinoctia-
              <lb/>
            lis. </s>
            <s xml:id="echoid-s25191" xml:space="preserve">Quæ omnia ita confirmabimus. </s>
            <s xml:id="echoid-s25192" xml:space="preserve">Quoniam tres circuli Æquator, Meridianus, & </s>
            <s xml:id="echoid-s25193" xml:space="preserve">circulus ma-
              <lb/>
            ximus, cui horologium æquidiſtat, habent unam eandemq́; </s>
            <s xml:id="echoid-s25194" xml:space="preserve">cõmunem ſectionem H I, in Analem-
              <lb/>
            mate, planum autem horologii uni illorum, atque adeo communi huic ſectioni æquidiſtat, erunt
              <lb/>
            communes ſectiones, quas reliqu
              <unsure/>
            @uo circuli, nempe Æquator, & </s>
            <s xml:id="echoid-s25195" xml:space="preserve">Meridianus in plano horolo-
              <lb/>
            gij faciunt, parallelæ, ex propoſ. </s>
            <s xml:id="echoid-s25196" xml:space="preserve">18. </s>
            <s xml:id="echoid-s25197" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s25198" xml:space="preserve">1. </s>
            <s xml:id="echoid-s25199" xml:space="preserve">quales ſunt linea æquinoctialis, & </s>
            <s xml:id="echoid-s25200" xml:space="preserve">linea meridiana.
              <lb/>
            </s>
            <s xml:id="echoid-s25201" xml:space="preserve">Cum ergo linea ſtyli ρ G, æquinoctialem lineam ſecet ad angulos rectos, ſecabit eadem & </s>
            <s xml:id="echoid-s25202" xml:space="preserve">meri-
              <lb/>
            dianam lineam ad rectos angulos. </s>
            <s xml:id="echoid-s25203" xml:space="preserve">Erit nihilominus adhuc centrum horologii infra lineam æqui
              <lb/>
              <note position="left" xlink:label="note-0399-07" xlink:href="note-0399-07a" xml:space="preserve">40</note>
              <note position="right" xlink:label="note-0399-08" xlink:href="note-0399-08a" xml:space="preserve">29. primi.</note>
            noctialem, vt in ſexta figura apparet.</s>
            <s xml:id="echoid-s25204" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">Quodnam ho-
            <lb/>
          rologium @@-
            <lb/>
          tro careat.</note>
          <p>
            <s xml:id="echoid-s25205" xml:space="preserve">SI denique arcus Meridiani inter planum inclinatum, & </s>
            <s xml:id="echoid-s25206" xml:space="preserve">Horizontem æqualis fuerit ex par-
              <lb/>
            te boreali altitudini poli, ita vt communis ſectio plani, & </s>
            <s xml:id="echoid-s25207" xml:space="preserve">Meridiani non differatab axe F G, per-
              <lb/>
            ſpicuum eſt, horologium centro carere, quia axis lineam meridianam ſecare non poteſt, immo
              <lb/>
            nec ipſum planum horologii, cum parallelum ſit circulo maximo per axem ducto. </s>
            <s xml:id="echoid-s25208" xml:space="preserve">Rectè igitur
              <lb/>
            præſcripſimus, rectam H I, ex portione Analemmatis in rectam G N, quæ eſt linea ſtyli in horolo
              <lb/>
            gio, modo infra punctum G, modo ſupra idem eſſe transferendam vſque ad punctum ρ, & </s>
            <s xml:id="echoid-s25209" xml:space="preserve">c.</s>
            <s xml:id="echoid-s25210" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s25211" xml:space="preserve">INVENTO hac ratione horologij centro ρ, quod modo infra æquinoctialem lineam eſt,
              <lb/>
            modo ſupra eandem, vt tradidimus, progrediemur vlterius in conſtructione horologij hoc mo-
              <lb/>
            do. </s>
            <s xml:id="echoid-s25212" xml:space="preserve">Ex portione Analemmatis ſumatur recta D I, nempe portio ſectionis Meridiani, & </s>
            <s xml:id="echoid-s25213" xml:space="preserve">Aequato-
              <lb/>
              <note position="left" xlink:label="note-0399-10" xlink:href="note-0399-10a" xml:space="preserve">50</note>
            ris intercepta inter D, centrum Mundi, & </s>
            <s xml:id="echoid-s25214" xml:space="preserve">rectam H I, transferaturq́ue in rectam G N, ex puncto
              <lb/>
            G, ſiue ſurſum, ſiue deorſum verſus vſque ad punctum L, ex quo circulus cuiuſuis magnitudinis
              <lb/>
            deſcribatur, qui ſecetur in 24. </s>
            <s xml:id="echoid-s25215" xml:space="preserve">partes æquales. </s>
            <s xml:id="echoid-s25216" xml:space="preserve">Verum diuiſio inchoanda hic non eſt à recta G N,
              <lb/>
            vt in horologio horizontali à linea H E, incipit, quia linea G N, non eſt hic meridiana, vt ibi H E,
              <lb/>
            ſed communis ſectio plani horologii, & </s>
            <s xml:id="echoid-s25217" xml:space="preserve">circuli maximi per polos ipſius plani, & </s>
            <s xml:id="echoid-s25218" xml:space="preserve">polos mundi trã
              <lb/>
            ſeuntis, inſtar proprii Meridiani ipſius plani, qui non eſt Meridianus Horizontis. </s>
            <s xml:id="echoid-s25219" xml:space="preserve">Hinc enim fit,
              <lb/>
            rectam G N, in circulo ex L, deſcripto non poſſe eſſe ſectionem communem Aequatoris, & </s>
            <s xml:id="echoid-s25220" xml:space="preserve">Meri-
              <lb/>
            diani ipſius Horizontis, ſi circulus ex L, deſcriptus in propria poſitione intelligatur eſſe conſtitu
              <lb/>
            tus, quemadmodum in horizontali horologio recta I E, in circulo ex E, deſcripto eſt communis
              <lb/>
            ſectio Meridiani, & </s>
            <s xml:id="echoid-s25221" xml:space="preserve">Aequatoris, ſi dictus circulus proprium ſitum habeat, vt ibi oſtendimus.
              <lb/>
            </s>
            <s xml:id="echoid-s25222" xml:space="preserve">Vnde cum à communi ſectione dicta Meridiani, & </s>
            <s xml:id="echoid-s25223" xml:space="preserve">Aequatoris, nempe ab hora 12. </s>
            <s xml:id="echoid-s25224" xml:space="preserve"/>
          </p>
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