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-s22859" xml:space="preserve">
              <pb o="343" file="0359" n="359" rhead="LIBER TERTIVS."/>
            horæ 6. </s>
            <s xml:id="echoid-s22860" xml:space="preserve">& </s>
            <s xml:id="echoid-s22861" xml:space="preserve">æquinoctialis; </s>
            <s xml:id="echoid-s22862" xml:space="preserve">alias non caderet radius Solis in omnes tres ſectiones, quas planum ho-
              <lb/>
            rologij cum illis tribus circulis facit. </s>
            <s xml:id="echoid-s22863" xml:space="preserve">quod eſt abſurdum. </s>
            <s xml:id="echoid-s22864" xml:space="preserve">Quòd autem eadem parallela eſſe de-
              <lb/>
            beat lineæ meridianæ, perſpicuè colligitur ex propoſ. </s>
            <s xml:id="echoid-s22865" xml:space="preserve">18. </s>
            <s xml:id="echoid-s22866" xml:space="preserve">primi libri. </s>
            <s xml:id="echoid-s22867" xml:space="preserve">Quia enim Meridianus, Ho-
              <lb/>
            rizon, & </s>
            <s xml:id="echoid-s22868" xml:space="preserve">circulus maximus, cui horologium æquidiſtat, communem ſectionem habent axem Ver
              <lb/>
            ticalis circuli, erunt communes ſectiones, quas Meridianus, & </s>
            <s xml:id="echoid-s22869" xml:space="preserve">Horizon cum plano horologij fa-
              <lb/>
            ciunt, parallelæ inter ſeſe, vt in dicta propoſ. </s>
            <s xml:id="echoid-s22870" xml:space="preserve">18. </s>
            <s xml:id="echoid-s22871" xml:space="preserve">demonſtratum eſt.</s>
            <s xml:id="echoid-s22872" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s22873" xml:space="preserve">HANC eandem lineam horizontalem ducemus hac ratione. </s>
            <s xml:id="echoid-s22874" xml:space="preserve">Per K, locum ſtyli agatur re-
              <lb/>
              <note position="right" xlink:label="note-0359-01" xlink:href="note-0359-01a" xml:space="preserve">Alia deſcriptio
                <lb/>
              lineæ horizon-
                <lb/>
              talis.</note>
            cta K A, meridianæ lineæ parallela, ad quam ex quolibet puncto B, excitetur perpendicularis B D,
              <lb/>
            verſus illam partem horologii, vbi æquinoctialis linea, & </s>
            <s xml:id="echoid-s22875" xml:space="preserve">linea horæ 6. </s>
            <s xml:id="echoid-s22876" xml:space="preserve">ſe interſecant. </s>
            <s xml:id="echoid-s22877" xml:space="preserve">Deinde
              <lb/>
            ſumpta recta A B, quæ ſtylo I K, æqualis ſit, conſtituatur in A, angulus B A D, complemento de-
              <lb/>
              <note position="left" xlink:label="note-0359-02" xlink:href="note-0359-02a" xml:space="preserve">10</note>
            clinationis plani ab Horizonte æqualis, ſecetq́ue recta A D, rectam B D, in D. </s>
            <s xml:id="echoid-s22878" xml:space="preserve">Nam per punctum
              <lb/>
            D, acta ipſi meridianæ lineæ
              <unsure/>
            parallela dabit horizontalem lineam, vt prius, quæ neceſſario per ho-
              <lb/>
            ram 6. </s>
            <s xml:id="echoid-s22879" xml:space="preserve">in line@ æquinoctiali tranſibit, ſi erratum non eſt. </s>
            <s xml:id="echoid-s22880" xml:space="preserve">Atque hoc modo ducendo lineam ho-
              <lb/>
            rizontalem facile examinabimus, an hora 6. </s>
            <s xml:id="echoid-s22881" xml:space="preserve">ſit rectè deſcripta, necne. </s>
            <s xml:id="echoid-s22882" xml:space="preserve">Quòd autem linea hori-
              <lb/>
            zontalis ducenda ſit per punctum D, hac arte inuentum, (Ipſam enim duci per horam 6. </s>
            <s xml:id="echoid-s22883" xml:space="preserve">in linea
              <lb/>
            æquinoctiali, & </s>
            <s xml:id="echoid-s22884" xml:space="preserve">parallelam eſſe lineæ meridianæ, proximè iam demonſtratum eſt) hoc modo ma-
              <lb/>
            nifeſtabimus. </s>
            <s xml:id="echoid-s22885" xml:space="preserve">Intelligatur triangulum A B D, circa rectam B D, moueri, vſque dum ad horologij
              <lb/>
            planum ſit rectam, & </s>
            <s xml:id="echoid-s22886" xml:space="preserve">ſtylus I K, in K, rectus cogitetur eſſe ad horologium. </s>
            <s xml:id="echoid-s22887" xml:space="preserve">Erunt hac ratione re-
              <lb/>
            ctæ I K, A B inter ſe parallelæ, quòd vtraque ad planum horologij recta ſit; </s>
            <s xml:id="echoid-s22888" xml:space="preserve">ipſa quidem I k, ex
              <lb/>
              <note position="right" xlink:label="note-0359-03" xlink:href="note-0359-03a" xml:space="preserve">6. vndec.</note>
            poſitione, at verò A B, ex defin. </s>
            <s xml:id="echoid-s22889" xml:space="preserve">4. </s>
            <s xml:id="echoid-s22890" xml:space="preserve">lib 11. </s>
            <s xml:id="echoid-s22891" xml:space="preserve">Euclidis. </s>
            <s xml:id="echoid-s22892" xml:space="preserve">Cum ergo & </s>
            <s xml:id="echoid-s22893" xml:space="preserve">æquales inter ſe ſint, erit & </s>
            <s xml:id="echoid-s22894" xml:space="preserve">re-
              <lb/>
              <note position="left" xlink:label="note-0359-04" xlink:href="note-0359-04a" xml:space="preserve">20</note>
            cta A I, ducta ex A, ad I, (poſita vtraque linea I K, A B, ad planum recta) parallela ipſi B K. </s>
            <s xml:id="echoid-s22895" xml:space="preserve">Ho-
              <lb/>
              <note position="right" xlink:label="note-0359-05" xlink:href="note-0359-05a" xml:space="preserve">33. primi.</note>
            rizon ergo tranſiens per I, verticem ſtyli, æquidiſtansq́ue meridianæ lineæ, ac proinde & </s>
            <s xml:id="echoid-s22896" xml:space="preserve">ipſi
              <lb/>
            B K, ducetur per rectam A I, atque adeo per punctum A. </s>
            <s xml:id="echoid-s22897" xml:space="preserve">Et quia angulus B A D, ex conſtructio-
              <lb/>
            ne, complemento declinationis plani ab Horizonte ęqualis eſt, erit reliquus A D B, ipſi declinatio-
              <lb/>
            niæqualis. </s>
            <s xml:id="echoid-s22898" xml:space="preserve">Quare Horizon per rectam A D, ducetur, cum hac ratione plano horologii occurrat
              <lb/>
            ſecua
              <unsure/>
            dum angulum declinationis A D B, ita vt A D, communis ſectio ſit Horizontis, & </s>
            <s xml:id="echoid-s22899" xml:space="preserve">trianguli
              <lb/>
            A B D. </s>
            <s xml:id="echoid-s22900" xml:space="preserve">Quocirca Horizon plano horologii occurret in D, puncto, ac propterea per D, ducenda
              <lb/>
            erit linea horizontalis.</s>
            <s xml:id="echoid-s22901" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s22902" xml:space="preserve">DENIQVE eadem horizontalis linea ducetur hac arte. </s>
            <s xml:id="echoid-s22903" xml:space="preserve">Ex figura radiorum, ſi horologium
              <lb/>
              <note position="right" xlink:label="note-0359-06" xlink:href="note-0359-06a" xml:space="preserve">Horizontalis li
                <lb/>
              neæ deſcriptio
                <lb/>
              alia.</note>
            Superius ad occaſum ſpecter, ſumantur interualla horæ ſeptimæ à meridie, inter C, & </s>
            <s xml:id="echoid-s22904" xml:space="preserve">radium ho
              <lb/>
              <note position="left" xlink:label="note-0359-07" xlink:href="note-0359-07a" xml:space="preserve">30</note>
            rarum 14. </s>
            <s xml:id="echoid-s22905" xml:space="preserve">& </s>
            <s xml:id="echoid-s22906" xml:space="preserve">horæ 5. </s>
            <s xml:id="echoid-s22907" xml:space="preserve">à meridie inter C, & </s>
            <s xml:id="echoid-s22908" xml:space="preserve">radium horarum 10. </s>
            <s xml:id="echoid-s22909" xml:space="preserve">vel ſi ad ortum vergat, horæ 5. </s>
            <s xml:id="echoid-s22910" xml:space="preserve">à
              <lb/>
            media nocte inter C, & </s>
            <s xml:id="echoid-s22911" xml:space="preserve">radium horarum 14. </s>
            <s xml:id="echoid-s22912" xml:space="preserve">& </s>
            <s xml:id="echoid-s22913" xml:space="preserve">horæ 7. </s>
            <s xml:id="echoid-s22914" xml:space="preserve">à media nocte inter C, & </s>
            <s xml:id="echoid-s22915" xml:space="preserve">radium horarũ
              <lb/>
            10 & </s>
            <s xml:id="echoid-s22916" xml:space="preserve">transferantur ex C, centro horologii in reſpondentes lineas, imprimendo puncta in ipſis.
              <lb/>
            </s>
            <s xml:id="echoid-s22917" xml:space="preserve">Per hæc enim puncta erit horizontalis linea ducenda: </s>
            <s xml:id="echoid-s22918" xml:space="preserve">quoniam Sol in eo parallelo exiſtens, cuius
              <lb/>
            arcus diurnus continet horas 14. </s>
            <s xml:id="echoid-s22919" xml:space="preserve">qui quidem, per ea, quæ demonſtrata ſunt, tranſit in horologio
              <lb/>
            per inuenta puncta in hora 7. </s>
            <s xml:id="echoid-s22920" xml:space="preserve">à meridie, & </s>
            <s xml:id="echoid-s22921" xml:space="preserve">hora 5. </s>
            <s xml:id="echoid-s22922" xml:space="preserve">à media nocte, occidit hora 7. </s>
            <s xml:id="echoid-s22923" xml:space="preserve">à meridie, & </s>
            <s xml:id="echoid-s22924" xml:space="preserve">
              <lb/>
            oritur hora 5. </s>
            <s xml:id="echoid-s22925" xml:space="preserve">à media nocte. </s>
            <s xml:id="echoid-s22926" xml:space="preserve">Exiſtens verò in illo parallelo, cuius arcus diurnus complectitur
              <lb/>
            horas 10. </s>
            <s xml:id="echoid-s22927" xml:space="preserve">qui ex demonſtratis quoque tranſit in horologio per puncta inuenta in hora 5. </s>
            <s xml:id="echoid-s22928" xml:space="preserve">à meri-
              <lb/>
            die
              <unsure/>
            , & </s>
            <s xml:id="echoid-s22929" xml:space="preserve">hora 7. </s>
            <s xml:id="echoid-s22930" xml:space="preserve">à media nocte, occidit hora 5. </s>
            <s xml:id="echoid-s22931" xml:space="preserve">à meridie, & </s>
            <s xml:id="echoid-s22932" xml:space="preserve">oritur hora 7. </s>
            <s xml:id="echoid-s22933" xml:space="preserve">à media nocte; </s>
            <s xml:id="echoid-s22934" xml:space="preserve">ac proin
              <lb/>
            de per dictas horas in nominatis arcubus diurnis horizontalis linea ducenda erit, quæ vt ante de-
              <lb/>
              <note position="left" xlink:label="note-0359-08" xlink:href="note-0359-08a" xml:space="preserve">40</note>
            monſtrauimu
              <unsure/>
            s, neceſſario per horam 6. </s>
            <s xml:id="echoid-s22935" xml:space="preserve">in linea æquinoctiali tranſibit, & </s>
            <s xml:id="echoid-s22936" xml:space="preserve">lineæ meridianæ paral-
              <lb/>
            lela exiſtet. </s>
            <s xml:id="echoid-s22937" xml:space="preserve">Adducimus tot modos ducendæ lineæ horizontalis, quia & </s>
            <s xml:id="echoid-s22938" xml:space="preserve">iucundum eſt cernere,
              <lb/>
            tanta varietate ad eundem ſemper ſcopum nos poſſe peruenire, & </s>
            <s xml:id="echoid-s22939" xml:space="preserve">certi eſſe poſſumus, in horarum
              <lb/>
            deſcriptione nullum errorem fuiſſe commiſſum, ſi omnes modi concordes conſentientesq́ue in-
              <lb/>
            ter ſe fuerint.</s>
            <s xml:id="echoid-s22940" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s22941" xml:space="preserve">HÆC autem linea horizontalis totum horologium diuidit in duo, quorum maius eſt Supe-
              <lb/>
              <note position="right" xlink:label="note-0359-09" xlink:href="note-0359-09a" xml:space="preserve">Horizontalis Ii
                <unsure/>
                <lb/>
              nea dirimit to-
                <lb/>
              tum horologiũ
                <lb/>
              in Superius In-
                <lb/>
              feriusq́ue, & in
                <lb/>
              diurnum no-
                <lb/>
              cturnumque.</note>
            rius, & </s>
            <s xml:id="echoid-s22942" xml:space="preserve">minus Inferius, vt in præcedentibus oſtenſum eſt; </s>
            <s xml:id="echoid-s22943" xml:space="preserve">dummodo partes Inferioris immuten-
              <lb/>
            tur, vt in præcedenti propoſ. </s>
            <s xml:id="echoid-s22944" xml:space="preserve">diximus.</s>
            <s xml:id="echoid-s22945" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s22946" xml:space="preserve">SECATVR horologium quoque totum ab eadem horizontali linea in diurnum, & </s>
            <s xml:id="echoid-s22947" xml:space="preserve">noctur
              <lb/>
            num, veluti in ſuperioribus dictum eſt. </s>
            <s xml:id="echoid-s22948" xml:space="preserve">Parallelos igitur, ſiue arcus, &</s>
            <s xml:id="echoid-s22949" xml:space="preserve">c. </s>
            <s xml:id="echoid-s22950" xml:space="preserve">figurauimus. </s>
            <s xml:id="echoid-s22951" xml:space="preserve">quod
              <lb/>
              <note position="left" xlink:label="note-0359-10" xlink:href="note-0359-10a" xml:space="preserve">50</note>
            faciendum erat.</s>
            <s xml:id="echoid-s22952" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1165" type="section" level="1" n="276">
          <head xml:id="echoid-head286" xml:space="preserve">PROBLEMA 15. PROPOSITIO 15.</head>
          <p>
            <s xml:id="echoid-s22953" xml:space="preserve">PARALLELOS arcuum diurnorum in eodem horologio, quod
              <lb/>
            ab Horizonte declinat, deſcribere.</s>
            <s xml:id="echoid-s22954" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">Areuum diu@-
            <lb/>
          n
            <unsure/>
          orum deſcri-
            <lb/>
          ptio in eodem
            <unsure/>
            <lb/>
          horologio dec
            <unsure/>
          li
            <lb/>
          nanteab Hori-
            <lb/>
          zon
            <unsure/>
          te.</note>
          <p>
            <s xml:id="echoid-s22955" xml:space="preserve">IN his parallelis deſcribendis nihil difficultatis eſt, cum eodem modo deſcribantur, quo pa-
              <lb/>
            ralleli ſignorum Zodiaci in præcedenti propoſ. </s>
            <s xml:id="echoid-s22956" xml:space="preserve">delineati ſunt, vt patet, ſi pro ſignorum </s>
          </p>
        </div>
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