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-s26972" xml:space="preserve">
              <pb o="410" file="0426" n="426" rhead="GNOMONICES"/>
            triangulum A B K, concipiatur animo conuerti circa B K, donec rectum ſit ad horologii planũ,
              <lb/>
            ac proinde in plano Verticalis circuli inclinationem plani ad Horizontem metientis, & </s>
            <s xml:id="echoid-s26973" xml:space="preserve">per B K,
              <lb/>
            ducti, erit recta A B, communis ſectio Horizontis, & </s>
            <s xml:id="echoid-s26974" xml:space="preserve">dicti Verticalis, & </s>
            <s xml:id="echoid-s26975" xml:space="preserve">iuncta recta A F, cõmu-
              <lb/>
            nis ſectio Horizontis, ac Meridiani, propterea quod tam Horizon, quàm Meridianus per cen-
              <lb/>
            trum Mundi A, & </s>
            <s xml:id="echoid-s26976" xml:space="preserve">per pũctum F, ducitur, Quare angulus A F B, quem linea meridiana A F, Ho-
              <lb/>
            rizontis cum linea horizontali F B, plani horologij conſtituit, æqualis erit complemento decli-
              <lb/>
            nationis horologij à Verticali proprie dicto; </s>
            <s xml:id="echoid-s26977" xml:space="preserve">ac proinde cum angulus A B F, rectus ſit (quoniá
              <lb/>
            enim triangulum A B K, rectum eſt, & </s>
            <s xml:id="echoid-s26978" xml:space="preserve">ad planum horologij, & </s>
            <s xml:id="echoid-s26979" xml:space="preserve">ad Horizontem, erunt quoque
              <lb/>
            duo hæc plana ad triangulum recta. </s>
            <s xml:id="echoid-s26980" xml:space="preserve">Igitur & </s>
            <s xml:id="echoid-s26981" xml:space="preserve">cõmunis eorũ ſectio F B, ad idẽ perpendicularis erit
              <lb/>
              <note position="left" xlink:label="note-0426-01" xlink:href="note-0426-01a" xml:space="preserve">19. vndec.</note>
              <note position="left" xlink:label="note-0426-02" xlink:href="note-0426-02a" xml:space="preserve">10</note>
            ac propterea & </s>
            <s xml:id="echoid-s26982" xml:space="preserve">ad rectam B A, perpendicularis erit, ex defin. </s>
            <s xml:id="echoid-s26983" xml:space="preserve">3. </s>
            <s xml:id="echoid-s26984" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s26985" xml:space="preserve">11. </s>
            <s xml:id="echoid-s26986" xml:space="preserve">Eucl.) </s>
            <s xml:id="echoid-s26987" xml:space="preserve">erit reliquus an-
              <lb/>
            gulus B A F, declinationi horologii à Verticali proprie dicto æqualis, hoc eſt, angulo B E G, in
              <lb/>
            figura latitudinum ortiuarum propoſ. </s>
            <s xml:id="echoid-s26988" xml:space="preserve">9. </s>
            <s xml:id="echoid-s26989" xml:space="preserve">huius lib. </s>
            <s xml:id="echoid-s26990" xml:space="preserve">Quoniá igitur anguli E, G, trianguli G E H,
              <lb/>
            in figura latitudinum ortiuarum æquales ſunt angulis A, B, trianguli B A F, in ſigura huius pro-
              <lb/>
            poſ. </s>
            <s xml:id="echoid-s26991" xml:space="preserve">& </s>
            <s xml:id="echoid-s26992" xml:space="preserve">latera E G, A B, quibus dicti anguli adiacent, æqualia quoque ex conſtructione, erũt quo-
              <lb/>
            que latera E H, H G, lateribus A F, F B, æqualia, & </s>
            <s xml:id="echoid-s26993" xml:space="preserve">angulus H, angulo A F B. </s>
            <s xml:id="echoid-s26994" xml:space="preserve">Quamcbrem ſi
              <lb/>
              <note position="left" xlink:label="note-0426-03" xlink:href="note-0426-03a" xml:space="preserve">26. primi.</note>
            recta E G, figuræ latitudinum ortiuarum rectę A B, in horologio congruat, congruet quoque re-
              <lb/>
            cta E H, rectæ A F, & </s>
            <s xml:id="echoid-s26995" xml:space="preserve">recta H G, rectæ F B, ob æqualitaté angulorum, & </s>
            <s xml:id="echoid-s26996" xml:space="preserve">denique tota H G, pro
              <lb/>
            ducta in utramque partem toti horizontali lineæ congruet; </s>
            <s xml:id="echoid-s26997" xml:space="preserve">atque idcirco radii latitudinum orti-
              <lb/>
            uarum, occiduarumve lineę horizontali occurrent in punctis tanto ſpatio à pũcto B, vel F, diſtá-
              <lb/>
            tibus, quanto ſpatio à puncto G, vel H, abſunt puncta, vbi radii latitudinum rectam G H, ſecát,
              <lb/>
              <note position="left" xlink:label="note-0426-04" xlink:href="note-0426-04a" xml:space="preserve">20</note>
            & </s>
            <s xml:id="echoid-s26998" xml:space="preserve">c. </s>
            <s xml:id="echoid-s26999" xml:space="preserve">Signa igitur aſcendentia Zodiaci in eodem horologio declinante ſimul & </s>
            <s xml:id="echoid-s27000" xml:space="preserve">inclinato repoſui-
              <lb/>
            mus. </s>
            <s xml:id="echoid-s27001" xml:space="preserve">Quod faciendum erat.</s>
            <s xml:id="echoid-s27002" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1367" type="section" level="1" n="330">
          <head xml:id="echoid-head341" style="it" xml:space="preserve">SCHOLIVM.</head>
          <p style="it">
            <s xml:id="echoid-s27003" xml:space="preserve">SI eadem aſcendentia ſigna deſcribere velim{us} ſecundum doctrinam Andreæ Schoneri, vtemur
              <lb/>
              <note position="left" xlink:label="note-0426-05" xlink:href="note-0426-05a" xml:space="preserve">Aſcendentis
                <lb/>
              figna, quo pa-
                <lb/>
              cto ex doctina
                <lb/>
              Andreæ Scho-
                <lb/>
              neri deſcriban
                <lb/>
              tur.</note>
            hac arte. </s>
            <s xml:id="echoid-s27004" xml:space="preserve">Inpriori figura ſcholij propoſ. </s>
            <s xml:id="echoid-s27005" xml:space="preserve">9. </s>
            <s xml:id="echoid-s27006" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s27007" xml:space="preserve">2. </s>
            <s xml:id="echoid-s27008" xml:space="preserve">ex recta E D, vel E B, abſcindatur recta E H, æqualis
              <lb/>
            rectæ L M, quæ in horologio intercipitur inter centrum L, & </s>
            <s xml:id="echoid-s27009" xml:space="preserve">punctum M, vbi æquinoctialis linea, & </s>
            <s xml:id="echoid-s27010" xml:space="preserve">
              <lb/>
            meridiana ſe interſecant, & </s>
            <s xml:id="echoid-s27011" xml:space="preserve">in H, conſtituatur cum recta B D, angul{us} æqualis ei, quem in horologio li-
              <lb/>
            nea æquinoctialis cum recta L M, efficit, hac tamen lege, vt poſito centro E, in centro L, & </s>
            <s xml:id="echoid-s27012" xml:space="preserve">recta E D,
              <lb/>
              <note position="left" xlink:label="note-0426-06" xlink:href="note-0426-06a" xml:space="preserve">30</note>
            ſupra rectam L M, recta per punctum H, ducta, & </s>
            <s xml:id="echoid-s27013" xml:space="preserve">dictum angulum conſtituens congruat lineæ æqui-
              <lb/>
            noctiali. </s>
            <s xml:id="echoid-s27014" xml:space="preserve">Deinde interualla prædictæ rectæ per H, ductæinter H, & </s>
            <s xml:id="echoid-s27015" xml:space="preserve">lineas ſignorum interiecta transfe-
              <lb/>
            rantur in lineam æquinoctialem ex puncto M, imprimendo puncta in ipſa æquinoctiali linea. </s>
            <s xml:id="echoid-s27016" xml:space="preserve">Si enim ex
              <lb/>
            puncto, vbi meridiana linea, & </s>
            <s xml:id="echoid-s27017" xml:space="preserve">horizontalis ſe interſecant, per hæc puncta æquinoctialis lineæ ducantur
              <lb/>
            rectæ occultæ, ſecabuntur ambo tropici in punctis, per quæ ſigna aſcendẽtia erunt ducenda, hoc ordine ſer
              <lb/>
              <note position="left" xlink:label="note-0426-07" xlink:href="note-0426-07a" xml:space="preserve">Ordo ſignorũ
                <lb/>
              aſcendentium
                <lb/>
              in tropicis.</note>
            uato. </s>
            <s xml:id="echoid-s27018" xml:space="preserve">Si horologium vergat in ortum, pertinebit punctũ, vbi tropic{us} ♑, lineam horizontalẽ interſecat,
              <lb/>
            ad ♑, punctum verò, in quo ſe interſecant tropic{us} ♋, & </s>
            <s xml:id="echoid-s27019" xml:space="preserve">horizontalis linea, ad ♋. </s>
            <s xml:id="echoid-s27020" xml:space="preserve">Proximum deinde
              <lb/>
            punctum in tropico infra horizontalem lineam debetur illi ſigno, quod proximè oritur post ♑, vel ♋,
              <lb/>
            vt ſigno ♒, vel ♌, & </s>
            <s xml:id="echoid-s27021" xml:space="preserve">ita deinceps ſecundum ſucceſſionem ſignorum. </s>
            <s xml:id="echoid-s27022" xml:space="preserve">Si autem in occaſum deflectat ho-
              <lb/>
            rologium, tribuendum erit punctum, vbitropicus ♑, & </s>
            <s xml:id="echoid-s27023" xml:space="preserve">linea horizontalis ſe mutuo ſecant, ſigno ♋;
              <lb/>
            </s>
            <s xml:id="echoid-s27024" xml:space="preserve">punctum vero, vbi tropicus ♋, eandem horizontalem lineam ſecat, conueniet ſigno ♑. </s>
            <s xml:id="echoid-s27025" xml:space="preserve">Deinde proxi-
              <lb/>
              <note position="left" xlink:label="note-0426-08" xlink:href="note-0426-08a" xml:space="preserve">40</note>
            mum punctum infra lineam horizontalem illi ſigno reſpondebit, quod ante ♑, vel ♋, oritur, vt ſigno
              <lb/>
            ♐, vel ♊, & </s>
            <s xml:id="echoid-s27026" xml:space="preserve">ſic deinceps contra ſignorum ſucceſſionem. </s>
            <s xml:id="echoid-s27027" xml:space="preserve">Exhis facili negotio intelligem{us}, quib{us} ſi-
              <lb/>
            gnis reſpondeant puncta tropicorum ſupra horizontalem lineam inuenta. </s>
            <s xml:id="echoid-s27028" xml:space="preserve">Nam ſi infra ſeruant ordinẽ
              <lb/>
            ſecundum ſucceſſionem ſignorum, ſeruabunt ſupra horizontalem lineam ordinem contra ſucceſſionem ſi-
              <lb/>
            gnorum, & </s>
            <s xml:id="echoid-s27029" xml:space="preserve">contra, vt ex figuris aſcendentium ſignorum, qu{as} hactenus in varijs planis conſtruxim{us},
              <lb/>
            perſpicuum eſt. </s>
            <s xml:id="echoid-s27030" xml:space="preserve">Semper autem quælibet recta occulta ex puncto, vbi ſe interſecant meridiana linea, at-
              <lb/>
            que horizontalis, ducta per puncta in linea æquinoctiali inuenta, pertinet ad duo ſigna oppoſita, quem-
              <lb/>
            admodum & </s>
            <s xml:id="echoid-s27031" xml:space="preserve">in priori figura radiorum ſignorum aſcendentium quælibet linea ad duo oppoſita ſigna per-
              <lb/>
            tinet: </s>
            <s xml:id="echoid-s27032" xml:space="preserve">ita vt ſi v. </s>
            <s xml:id="echoid-s27033" xml:space="preserve">g. </s>
            <s xml:id="echoid-s27034" xml:space="preserve">vnum punctum, per quod dicta linea occulta tranſit, pertinet ad ♊, alterum pun-
              <lb/>
            ctum, quod eadem recta monſtr at ſiue in oppoſito tropico, ſiue in eodem, pertineat ad ♐, & </s>
            <s xml:id="echoid-s27035" xml:space="preserve">c. </s>
            <s xml:id="echoid-s27036" xml:space="preserve">vt ex ſu-
              <lb/>
              <note position="left" xlink:label="note-0426-09" xlink:href="note-0426-09a" xml:space="preserve">50</note>
            periorib{us} figuris ſignorum aſcendentium, qu{as} in varijs planis depinximus, manifestum eſt.</s>
            <s xml:id="echoid-s27037" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s27038" xml:space="preserve">IN propoſito exemplo, vbi meridiana linea, atque æquinoctialis æquidiſtantes ſunt, recta L M,
              <lb/>
              <note position="left" xlink:label="note-0426-10" xlink:href="note-0426-10a" xml:space="preserve">Quuando æqui
                <lb/>
              noctialis linea,
                <lb/>
              & meridiana
                <lb/>
              parallelæ ſunt,
                <lb/>
              quid agendum
                <lb/>
              in aſcendenti-
                <lb/>
              bus ſignis deli-
                <lb/>
              meandis.</note>
            ęquinoctialem lineam non ſecat, ſed ei parallela eſt, vnde cum ea angulum conſtituere non poteſt. </s>
            <s xml:id="echoid-s27039" xml:space="preserve">In
              <lb/>
            priori ergo figura ſignorum ducenda erit ipſi E D, linea parallela reſpondens æquinoctiali lineæ in horolo
              <lb/>
            gio, hac ratione. </s>
            <s xml:id="echoid-s27040" xml:space="preserve">Ex E C, ſumatur E K, æqualis rectæ, quæ in horologio inter centrum L, & </s>
            <s xml:id="echoid-s27041" xml:space="preserve">punctum,
              <lb/>
            vbi linea horizontalis æquinoctialem diuidit, intercipitur, & </s>
            <s xml:id="echoid-s27042" xml:space="preserve">per K, excitetur ad E K, perpendicularis
              <lb/>
            ſecans lineas ſignorum in punctis, quæ accepta ex puncto K, & </s>
            <s xml:id="echoid-s27043" xml:space="preserve">translata in lineam æquinoctialem ex di-
              <lb/>
            cto puncto, vbi ſe ſecant linea æquinoctialis, & </s>
            <s xml:id="echoid-s27044" xml:space="preserve">horizontalis, dabunt in æquinoctiali linea pun-
              <lb/>
            cta, vt pri{us}.</s>
            <s xml:id="echoid-s27045" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s27046" xml:space="preserve">QVOD ſi in horologio primæ figuræ propoſ. </s>
            <s xml:id="echoid-s27047" xml:space="preserve">37. </s>
            <s xml:id="echoid-s27048" xml:space="preserve">hui{us} lib. </s>
            <s xml:id="echoid-s27049" xml:space="preserve">deſcribenda ſint aſcendentia ſigna, </s>
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