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-s17850" xml:space="preserve">ALITER. </s>
            <s xml:id="echoid-s17851" xml:space="preserve">Deſcripto quadrante A B C, cuiuſuis magnitudinis, eoq́ue diuiſo in grad. </s>
            <s xml:id="echoid-s17852" xml:space="preserve">90.
              <lb/>
            </s>
            <s xml:id="echoid-s17853" xml:space="preserve">
              <note position="right" xlink:label="note-0279-01" xlink:href="note-0279-01a" xml:space="preserve">Alia deſctiptio
                <lb/>
              parallelorum
                <lb/>
              Horizon@is in
                <lb/>
              c
                <unsure/>
              odem horolo-
                <lb/>
              gio polati.</note>
            vel in pauciores partes pro numero parallelorum Horizontis delineandorum, ducantu
              <unsure/>
            r ex A, cen-
              <lb/>
            tro per puncta diuiſionum lineæ rectæ, quæ reſpondebunt radiis parallelorum Horizontis in qua-
              <lb/>
            drante D C 90. </s>
            <s xml:id="echoid-s17854" xml:space="preserve">figuræ præcedentis contenti, initio ſumpto à recta A B, vt figura indicat. </s>
            <s xml:id="echoid-s17855" xml:space="preserve">Deinde
              <lb/>
            ex figura antecedentis propoſ. </s>
            <s xml:id="echoid-s17856" xml:space="preserve">rectæ B C, ſumatur æqualis A D, in linea A C, huius figuræ; </s>
            <s xml:id="echoid-s17857" xml:space="preserve">& </s>
            <s xml:id="echoid-s17858" xml:space="preserve">re-
              <lb/>
            ctæ D B, vel D E, in recta A B, acci-
              <lb/>
            piatur æqualis A E, ducaturq́ue recta
              <lb/>
              <figure xlink:label="fig-0279-01" xlink:href="fig-0279-01a" number="194">
                <image file="0279-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0279-01"/>
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            D E. </s>
            <s xml:id="echoid-s17859" xml:space="preserve">Erit triangulum hoc A D E,
              <lb/>
            æquale omnino triangulo C B D, fi-
              <lb/>
              <note position="right" xlink:label="note-0279-02" xlink:href="note-0279-02a" xml:space="preserve">4. primi.</note>
            guræ præcedentis propoſ. </s>
            <s xml:id="echoid-s17860" xml:space="preserve">cum angu
              <lb/>
              <note position="left" xlink:label="note-0279-03" xlink:href="note-0279-03a" xml:space="preserve">10</note>
            li ad A, & </s>
            <s xml:id="echoid-s17861" xml:space="preserve">B, recti ſint, continean-
              <lb/>
            turq́; </s>
            <s xml:id="echoid-s17862" xml:space="preserve">lateribus æqualibus, ex conſtru
              <lb/>
            ctione; </s>
            <s xml:id="echoid-s17863" xml:space="preserve">ita vt D E, meridianæ lineæ
              <lb/>
            C D, ſit æqualis. </s>
            <s xml:id="echoid-s17864" xml:space="preserve">Idẽ quoque triangu-
              <lb/>
            lum A D E, æquale erit triangulo
              <lb/>
            D V T, proximè antecedentis figu-
              <lb/>
            ræ, cum hoc æquale ſit prædicto triã
              <lb/>
            gulo C B D. </s>
            <s xml:id="echoid-s17865" xml:space="preserve">Cum enim angulus
              <lb/>
            I D V, angulo A B C, ſit æqualis, cũ
              <lb/>
            vterque ſit altitudinis poli, & </s>
            <s xml:id="echoid-s17866" xml:space="preserve">angu-
              <lb/>
              <note position="left" xlink:label="note-0279-04" xlink:href="note-0279-04a" xml:space="preserve">20</note>
            lus rectus D I V, recto angulo B A C,
              <lb/>
            ſintq́ue latera D I, A B, inter ſe æqua
              <lb/>
            lia, quòd vtrumque ſumptũ ſit æqua-
              <lb/>
            le ſtylo; </s>
            <s xml:id="echoid-s17867" xml:space="preserve">erunt & </s>
            <s xml:id="echoid-s17868" xml:space="preserve">latera D V, V I, late-
              <lb/>
              <note position="right" xlink:label="note-0279-05" xlink:href="note-0279-05a" xml:space="preserve">26. primi.</note>
            ribus B A, C A, æqualia. </s>
            <s xml:id="echoid-s17869" xml:space="preserve">Eademq́ue
              <lb/>
            ratione latera D T, T I, lateribus
              <lb/>
            B D, D A, æqualia erũt, &</s>
            <s xml:id="echoid-s17870" xml:space="preserve">c. </s>
            <s xml:id="echoid-s17871" xml:space="preserve">Poſt hęc
              <lb/>
            ex figura præcedentis propoſ. </s>
            <s xml:id="echoid-s17872" xml:space="preserve">inter-
              <lb/>
            ualla omnia inter centrum E, & </s>
            <s xml:id="echoid-s17873" xml:space="preserve">pun-
              <lb/>
            cta, in quibus Verticales lineæ horizontalem lineam interſecant, in hanc figuram transferantur ex
              <lb/>
              <note position="left" xlink:label="note-0279-06" xlink:href="note-0279-06a" xml:space="preserve">30</note>
            A, in rectam A B, notatis punctis in recta A B, aſcriptisq́ue numeris linearum Verticalium, vt 90.
              <lb/>
            </s>
            <s xml:id="echoid-s17874" xml:space="preserve">iuxta punctum E, & </s>
            <s xml:id="echoid-s17875" xml:space="preserve">75. </s>
            <s xml:id="echoid-s17876" xml:space="preserve">prope proximum, &</s>
            <s xml:id="echoid-s17877" xml:space="preserve">c. </s>
            <s xml:id="echoid-s17878" xml:space="preserve">Poſtremo ex D, per puncta in A B, ſignata educan-
              <lb/>
            tur rectæ lineæ. </s>
            <s xml:id="echoid-s17879" xml:space="preserve">Pro Verticali autem linea proprie dicta, à qua principium aliarum ſumitur, du-
              <lb/>
            cenda eſt per D, ipſi A B, parallela D F, & </s>
            <s xml:id="echoid-s17880" xml:space="preserve">in alteram partem transferendæ ſunt quoque lineæ iam
              <lb/>
            ductæ ex puncto D, per puncta rectæ A B, vt habeantur lineæ Verticales trans, & </s>
            <s xml:id="echoid-s17881" xml:space="preserve">citra lineam Ver
              <lb/>
            ticalem propriè dictam, quemadmodum in horologio horizontali factum eſt de lineis ante 6. </s>
            <s xml:id="echoid-s17882" xml:space="preserve">ho-
              <lb/>
            ram, & </s>
            <s xml:id="echoid-s17883" xml:space="preserve">poſt, in propoſ. </s>
            <s xml:id="echoid-s17884" xml:space="preserve">2. </s>
            <s xml:id="echoid-s17885" xml:space="preserve">huius libri. </s>
            <s xml:id="echoid-s17886" xml:space="preserve">Nam lineæ ex D, per puncta rectæ A B, ductæ, ſunt Vertica-
              <lb/>
            les lineæ vltra Verticalem lineam propriè dictam, in quas videlicet vmbra ſtyli proiicitur, Sole
              <lb/>
            exiſtente in Verticalibus auſtralibus; </s>
            <s xml:id="echoid-s17887" xml:space="preserve">aliæ verò, Verticales lineæ citra Verticalem lineam pro-
              <lb/>
            prie dictam, &</s>
            <s xml:id="echoid-s17888" xml:space="preserve">c.</s>
            <s xml:id="echoid-s17889" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">40</note>
          <p>
            <s xml:id="echoid-s17890" xml:space="preserve">IAM verò ſi interualla ſingula rectarum ex D, prodeuntium inter D, & </s>
            <s xml:id="echoid-s17891" xml:space="preserve">radium v. </s>
            <s xml:id="echoid-s17892" xml:space="preserve">g. </s>
            <s xml:id="echoid-s17893" xml:space="preserve">paralleli
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            Horizontis grad. </s>
            <s xml:id="echoid-s17894" xml:space="preserve">15. </s>
            <s xml:id="echoid-s17895" xml:space="preserve">comprehenſa transferantur ex puncto C, figuræ præcedentis propoſ. </s>
            <s xml:id="echoid-s17896" xml:space="preserve">in lineas
              <lb/>
            binas Verticales æqualiter à meridiana linea diſtantes, reſpondentesq́ue numeris in recta A B, hu-
              <lb/>
            ius figuræ ſignatis, notando puncta in ipſis lineis Verticalibus, (ita tamen, vt interualla rectarum
              <lb/>
            ex D, in A B, cadentium tranſportentur ex Zenith C, in lineas Verticales horologii ſupra lineam
              <lb/>
            Verticalem propriè dictã, interualla vero rectarum ex D, cadentium ad dextram rectæ D F, tranſ-
              <lb/>
            ferantur in Verticales lineas infra lineam propriè dictam Verticalem) & </s>
            <s xml:id="echoid-s17897" xml:space="preserve">hæc puncta appoſitè
              <unsure/>
            , & </s>
            <s xml:id="echoid-s17898" xml:space="preserve">
              <lb/>
            concinne coniungantur linea quadam flexa, deſcriptus erit parallelus Horizontis grad. </s>
            <s xml:id="echoid-s17899" xml:space="preserve">15. </s>
            <s xml:id="echoid-s17900" xml:space="preserve">Eo-
              <lb/>
            demq́ue modo reliqui paralleli Horizontis deſcribentur. </s>
            <s xml:id="echoid-s17901" xml:space="preserve">Demonſtratio huius rei non differt ab
              <lb/>
              <note position="right" xlink:label="note-0279-08" xlink:href="note-0279-08a" xml:space="preserve">Demonſtratio
                <lb/>
              poſterioris hu-
                <lb/>
              iuſce deſcriptio
                <lb/>
              nis parallelorũ
                <lb/>
              Horizontis.</note>
            ea, quam in horologio horizontali tradidimus in ſecundo modo deſcribendorum arcuum ſigno-
              <lb/>
              <note position="left" xlink:label="note-0279-09" xlink:href="note-0279-09a" xml:space="preserve">50</note>
            rum. </s>
            <s xml:id="echoid-s17902" xml:space="preserve">Nam hic linea horizontalis eſt veluti Aequatoris linea, & </s>
            <s xml:id="echoid-s17903" xml:space="preserve">lineæ Verticales tanquam lineæ
              <lb/>
            horariæ, quarum centrum eſt Zenith, nempe punctum C, &</s>
            <s xml:id="echoid-s17904" xml:space="preserve">c. </s>
            <s xml:id="echoid-s17905" xml:space="preserve">vt in præcedenti Analemmate di-
              <lb/>
            ximus. </s>
            <s xml:id="echoid-s17906" xml:space="preserve">Itaque linea A B, huius figuræ reſpondebit radio Aequatoris D C, poſtremæ figuræ pro-
              <lb/>
            poſ. </s>
            <s xml:id="echoid-s17907" xml:space="preserve">2. </s>
            <s xml:id="echoid-s17908" xml:space="preserve">huius libri, in qua radii ſignorum deſcripti ſunt, & </s>
            <s xml:id="echoid-s17909" xml:space="preserve">rectæ ex A, ductæ radiis aliorum ſigno-
              <lb/>
            rum ex D, emiſſis in dicta illa figura; </s>
            <s xml:id="echoid-s17910" xml:space="preserve">recta autem A D, axi D H, & </s>
            <s xml:id="echoid-s17911" xml:space="preserve">punctum D, puncto H; </s>
            <s xml:id="echoid-s17912" xml:space="preserve">lineæ
              <lb/>
            denique Verticales ex D, cadentes lineis horariis ex H, productis. </s>
            <s xml:id="echoid-s17913" xml:space="preserve">Idem fiet, ſi int
              <unsure/>
            erualla rectarũ
              <lb/>
            ex D, progredientium inter rectam A B, quæ eſt, (vt diximus) inſtar Æquatoris, & </s>
            <s xml:id="echoid-s17914" xml:space="preserve">rectas ex A,
              <lb/>
            emiſſas transferantur in reſpondentes lineas Verticales à linea horizontali horologii, &</s>
            <s xml:id="echoid-s17915" xml:space="preserve">c. </s>
            <s xml:id="echoid-s17916" xml:space="preserve">quemad
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            modum in horizontali horologio interualla inter radium Aequatoris, & </s>
            <s xml:id="echoid-s17917" xml:space="preserve">radios ſignorum transla
              <lb/>
            ta ſunt, vt arcus ſignorum deſcriberentur. </s>
            <s xml:id="echoid-s17918" xml:space="preserve">Pro horologio polari inferiori transferendi ſunt in hac
              <lb/>
            figura radii parallelorum Horizontis ex A, educti ad ſiniſtrã partem rectæ A B, ita vt </s>
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