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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            ſtructum, cum horizontalis linea indicat horam 6. </s>
            <s xml:id="echoid-s28980" xml:space="preserve">à mer. </s>
            <s xml:id="echoid-s28981" xml:space="preserve">vel med. </s>
            <s xml:id="echoid-s28982" xml:space="preserve">noc. </s>
            <s xml:id="echoid-s28983" xml:space="preserve">Quod ſi horizontalis li-
              <lb/>
            nea non adſit, ſint autem lineæ horariæ parallelæ, erit propoſitum horologium in ſphæra recta ho
              <lb/>
            rizontale. </s>
            <s xml:id="echoid-s28984" xml:space="preserve">Quamobrem, dato horologio, vna cum ſtylo, eiusq́ue loco; </s>
            <s xml:id="echoid-s28985" xml:space="preserve">ad quam poli altitudinẽ
              <lb/>
            fabricatum ſit, &</s>
            <s xml:id="echoid-s28986" xml:space="preserve">c. </s>
            <s xml:id="echoid-s28987" xml:space="preserve">inueſtigauimus. </s>
            <s xml:id="echoid-s28988" xml:space="preserve">Quod faciendum erat.</s>
            <s xml:id="echoid-s28989" xml:space="preserve"/>
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        <div xml:id="echoid-div1493" type="section" level="1" n="357">
          <head xml:id="echoid-head370" xml:space="preserve">PROBLEMA 14. PROPOSITIO 14.</head>
          <p>
            <s xml:id="echoid-s28990" xml:space="preserve">HOROLOGIVM quodcunque deſcriptum ad maiorem, mi-
              <lb/>
            noremve formam, pro data magnitudine ſtyli, reducere.</s>
            <s xml:id="echoid-s28991" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">10</note>
          <p>
            <s xml:id="echoid-s28992" xml:space="preserve">PROPONATVR doctrinæ cauſa horologium Babylonicum declinans ab Horizonte,
              <lb/>
            quod propoſ. </s>
            <s xml:id="echoid-s28993" xml:space="preserve">22. </s>
            <s xml:id="echoid-s28994" xml:space="preserve">ſuperioris libri deſcripſimus, cuiuſque ſtylus eſt A B, augendum vel diminuen-
              <lb/>
            dum ſecundum proportionem ſtyli cuiuſuis dati C D, ita vt, quam proportionem habet ſtylus
              <lb/>
            A B, ad ſtylum C D, eandem habeant omnia lineamenta, atque vmbræ à ſtylo A B, cadentes ad
              <lb/>
            lineamenta reſpondentia, ac vmbras à ſtylo C D, proiectas: </s>
            <s xml:id="echoid-s28995" xml:space="preserve">permutandoq́ue, vt ſe habet ſtylus
              <lb/>
            A B, ad lineamenta, & </s>
            <s xml:id="echoid-s28996" xml:space="preserve">vmbras ſui horologii, ita ſe habeat ſtylus C D, ad reſpondentia lineamen
              <lb/>
            ta, atque vmbras in horologio, quod fabricandum eſt.</s>
            <s xml:id="echoid-s28997" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s28998" xml:space="preserve">PRIMVM omnium ducantur ſeorſum in plano quopiam duæ rectæ E F, E G, facientes in
              <lb/>
              <note position="left" xlink:label="note-0458-02" xlink:href="note-0458-02a" xml:space="preserve">Quo pacto ho-
                <lb/>
              rologium pro-
                <lb/>
              poſitum ad ma
                <lb/>
              iorem mino
                <lb/>
              re@@ ve formã
                <lb/>
              redigatur, pro
                <lb/>
              data magnitu-
                <lb/>
              dine ſtyli.</note>
            E, angulum quemcunque, & </s>
            <s xml:id="echoid-s28999" xml:space="preserve">ipſi E F, parallela vtcunque agatur H I: </s>
            <s xml:id="echoid-s29000" xml:space="preserve">In E F, autem ſ@matur recta
              <lb/>
              <note position="left" xlink:label="note-0458-03" xlink:href="note-0458-03a" xml:space="preserve">20</note>
            E K, ſtylo A B, & </s>
            <s xml:id="echoid-s29001" xml:space="preserve">in E G, recta E L, ſtylo C D, æqualis, iungaturq́ue recta K L, ſecans H I, in M; </s>
            <s xml:id="echoid-s29002" xml:space="preserve">ac
              <lb/>
            poſtremo per E, ipſi K L, parallela agatur E H, ſecans H I, in H. </s>
            <s xml:id="echoid-s29003" xml:space="preserve">Ita enim parata erit figura, per quã
              <lb/>
            horologium propoſitum ſine magno labore ad maiorem minoremve figuram redigetur.</s>
            <s xml:id="echoid-s29004" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s29005" xml:space="preserve">DEINDE in propoſito horologio per A, locum ſtyli ducantur duæ rectæ occultæ A P, A a,
              <lb/>
            ſeſe ad rectos angulos in A, ſecantes, quarum altera in horologiis ad Horizontem rectis eadem
              <lb/>
            ſit, quæ linea horizontalis per locum ſtyli ducta, & </s>
            <s xml:id="echoid-s29006" xml:space="preserve">altera ad Horizontem perpendicularis. </s>
            <s xml:id="echoid-s29007" xml:space="preserve">In ho-
              <lb/>
            rologijs autem inclinatis vna ſit horizontali lineæ æquidiſtans, & </s>
            <s xml:id="echoid-s29008" xml:space="preserve">altera idcirco communis ſectio
              <lb/>
            plani horologij, & </s>
            <s xml:id="echoid-s29009" xml:space="preserve">Verticalis circuli inclinationem ipſius ad Horizontem metientis. </s>
            <s xml:id="echoid-s29010" xml:space="preserve">Pari ratione
              <lb/>
            in muro, vel in plano aliquo, in quo horologium amplificandum eſt, aut diminuendum, eligatur
              <lb/>
            C, locus ſtyli C D, & </s>
            <s xml:id="echoid-s29011" xml:space="preserve">per C, duæ quoque rectæ occultæ ducantur ſeſe ad angulos rectos ſecantes
              <lb/>
            in C, quarum vna reſpondeat horizontali lineæ propoſiti horologij, vel certè ei, quæ lineæ hori-
              <lb/>
              <note position="left" xlink:label="note-0458-04" xlink:href="note-0458-04a" xml:space="preserve">30</note>
            zontali parallela eſt, altera verò alteri: </s>
            <s xml:id="echoid-s29012" xml:space="preserve">hoc eſt, ſi hoiologium propoſitum rectum eſt ad Horizon
              <lb/>
            tem, & </s>
            <s xml:id="echoid-s29013" xml:space="preserve">offeratur murus, ſeu planum aliquod ſtabile, ac firmum, in quo horologium eſt delinean-
              <lb/>
            dum maius, aut minus, vna ex dictis lineis per locum ſtyli C, ducta Horizonti æquidiſter, @ſitq́ue
              <lb/>
            horizontalis linea, altera verò ad Horizontem ſit perpendicularis: </s>
            <s xml:id="echoid-s29014" xml:space="preserve">at verò, ſi horologium oblatum
              <lb/>
            non eſt rectum ad Horizontem, vna dictarum linearum in muro, vel plano firmo, ac ſtabili æqui-
              <lb/>
            diſtet quidem Horizonti, ſed altera ſit ſectio communis ipſius, & </s>
            <s xml:id="echoid-s29015" xml:space="preserve">Verticalis circuli, qui inclina-
              <lb/>
            tionem plani ad Horizontem metitur. </s>
            <s xml:id="echoid-s29016" xml:space="preserve">Harum autem linearum in horologijs horizontalibus, vbi
              <lb/>
            linea horizontalis duci non poteſt, vna ſit linea meridiana, & </s>
            <s xml:id="echoid-s29017" xml:space="preserve">altera lineæ ęquinoctiali æquidiſtãs.
              <lb/>
            </s>
            <s xml:id="echoid-s29018" xml:space="preserve">Deſcripto quoque ex A, circulo P O, cuiuſque magnitudinis, ei æqualis Q R, ex centro C,
              <lb/>
            deſcribatur.</s>
            <s xml:id="echoid-s29019" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">40</note>
          <p>
            <s xml:id="echoid-s29020" xml:space="preserve">QVIBVS confectis, ita amplificationem diminutionemve horologij abſoluemus. </s>
            <s xml:id="echoid-s29021" xml:space="preserve">Ex cen-
              <lb/>
            tro A, per N, punctum horæ 6. </s>
            <s xml:id="echoid-s29022" xml:space="preserve">ab ortu, in tropico ♋, verbi gratia, ducatur recta occulta A N, ſe-
              <lb/>
            cans circumferentiam circuli in O, & </s>
            <s xml:id="echoid-s29023" xml:space="preserve">arcui P O, ſumatur æqualis arcus Q R, in altero circulo, du-
              <lb/>
            caturq́ue recta C R. </s>
            <s xml:id="echoid-s29024" xml:space="preserve">Sumptis deinde in E F, H G, rectis E S, H T, ipſi A N, ęqualibus, iungatur
              <lb/>
            recta S T, ſecans E G, in V, & </s>
            <s xml:id="echoid-s29025" xml:space="preserve">ex C R, rectæ E V, æqualis abſcindatur C X. </s>
            <s xml:id="echoid-s29026" xml:space="preserve">Dico, Sole exiſtente in
              <lb/>
            principio ♋, & </s>
            <s xml:id="echoid-s29027" xml:space="preserve">in circulo horæ 6. </s>
            <s xml:id="echoid-s29028" xml:space="preserve">ab ortu, vmbram ſtyli C D, cadere in punctum X, quemadmo
              <lb/>
            dum eodem illo tempore vmbra ſtyli A B, in punctum N, cadit. </s>
            <s xml:id="echoid-s29029" xml:space="preserve">Si enim circulus maximus, cui
              <lb/>
            horologium vtrumque æquidiſtat, concipiatur eſſe Horizon aliquis, ita vt tam ſtylus A B, quàm
              <lb/>
            C D, ſit axis ipſius, per quem omnes ipſius Verticales circuli ducuntur, vt in horologio horizonta
              <lb/>
            li contingit; </s>
            <s xml:id="echoid-s29030" xml:space="preserve">erit recta A N, communis ſectio plani horologii, & </s>
            <s xml:id="echoid-s29031" xml:space="preserve">circuli illius Verticalis reſpectu
              <lb/>
              <note position="left" xlink:label="note-0458-06" xlink:href="note-0458-06a" xml:space="preserve">50</note>
            dicti Horizontis, qui tunc per centrum Solis ducitur, atque adeò eadem A N, longitudo erit vm-
              <lb/>
            bræ in prædicta hora 6. </s>
            <s xml:id="echoid-s29032" xml:space="preserve">ab ortu. </s>
            <s xml:id="echoid-s29033" xml:space="preserve">Quoniam autem ille Verticalis eandem poſitionem habet in om
              <lb/>
            nibus planis parallelis, ita vt cum recta C Q, quæ rectæ A P, reſpondet, æqualem faciat angulum
              <lb/>
            angulo N A P, fit vt cum angulus R C Q, æqualis ſit angulo O A P, propterea quod & </s>
            <s xml:id="echoid-s29034" xml:space="preserve">arcus Q R,
              <lb/>
              <note position="left" xlink:label="note-0458-07" xlink:href="note-0458-07a" xml:space="preserve">27. tertij.</note>
            arcui P O, æqualis eſt, recta C R, ſit quoque communis ſectio dicti Verticalis circuli, & </s>
            <s xml:id="echoid-s29035" xml:space="preserve">plani ho-
              <lb/>
            rologii, in quo ſtylus C D. </s>
            <s xml:id="echoid-s29036" xml:space="preserve">Quare vmbra ſtyli C D, tunc temporis in rectam C R, cadet. </s>
            <s xml:id="echoid-s29037" xml:space="preserve">Quia
              <lb/>
            verò rectæ E S, H T, æquales inter ſe ſunt, (vtraque enim ſumpta eſt æqualis rectæ A N,) & </s>
            <s xml:id="echoid-s29038" xml:space="preserve">pa-
              <lb/>
            rallelæ, erunt quoque E H, S T, æquales, & </s>
            <s xml:id="echoid-s29039" xml:space="preserve">parallelæ. </s>
            <s xml:id="echoid-s29040" xml:space="preserve">Cum ergo & </s>
            <s xml:id="echoid-s29041" xml:space="preserve">K L, ipſi E H, ſit, ex conſtructio
              <lb/>
              <note position="left" xlink:label="note-0458-08" xlink:href="note-0458-08a" xml:space="preserve">33. primi.</note>
            ne, parallela, erunt & </s>
            <s xml:id="echoid-s29042" xml:space="preserve">K L, S T, inter ſe parallelæ. </s>
            <s xml:id="echoid-s29043" xml:space="preserve">Igitur erit, vt E K, hoc eſt, vt A B, ſtylus ad E S,
              <lb/>
              <note position="left" xlink:label="note-0458-09" xlink:href="note-0458-09a" xml:space="preserve">30. primi.</note>
            hoc eſt, ad A N, vmbram, ita E L, hoc eſt, ita C D, ſtylus, ad E V, hoc eſt, ad C X. </s>
            <s xml:id="echoid-s29044" xml:space="preserve">Quocirca cum
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              <note position="left" xlink:label="note-0458-10" xlink:href="note-0458-10a" xml:space="preserve">2. vel 4. ſexti</note>
            </s>
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