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-s16437" xml:space="preserve">
              <pb o="245" file="0261" n="261" rhead="LIBER SECVNDVS."/>
            parallela agatur F K, communis videlicet ſectio Verticalis circuli, & </s>
            <s xml:id="echoid-s16438" xml:space="preserve">plani horologij, ſecans latera
              <lb/>
            triangulorum per axẽ in G, H, I, K, &</s>
            <s xml:id="echoid-s16439" xml:space="preserve">c. </s>
            <s xml:id="echoid-s16440" xml:space="preserve">vt ſint diametri conicarũ ſectionum G K, H K, I K, &</s>
            <s xml:id="echoid-s16441" xml:space="preserve">c.
              <lb/>
            </s>
            <s xml:id="echoid-s16442" xml:space="preserve">Si igitur puncta G, H, I, K, in lineam Verticalem A D, horologij transferantur ex A, infra hori-
              <lb/>
            zontalem lineam, & </s>
            <s xml:id="echoid-s16443" xml:space="preserve">circa Verticalem lineam deſcribantur, per propoſ. </s>
            <s xml:id="echoid-s16444" xml:space="preserve">8. </s>
            <s xml:id="echoid-s16445" xml:space="preserve">ſuperioris lib. </s>
            <s xml:id="echoid-s16446" xml:space="preserve">dictæ ſe-
              <lb/>
            ctiones conicæ tranſeuntes per puncta G, H, I, K, (quæ quidem conicæ ſectiones hyperbolæ ſunt,
              <lb/>
            ex propoſ. </s>
            <s xml:id="echoid-s16447" xml:space="preserve">6. </s>
            <s xml:id="echoid-s16448" xml:space="preserve">antecedentis lib. </s>
            <s xml:id="echoid-s16449" xml:space="preserve">cum Meridianus, cui planum horologij æquidiſtat, per polos paral-
              <lb/>
            lelorum Horizontis deſcriptus ipſos omnes ſecet.) </s>
            <s xml:id="echoid-s16450" xml:space="preserve">& </s>
            <s xml:id="echoid-s16451" xml:space="preserve">ſemper à linea horizontali eo magis recedẽ
              <lb/>
            tes, quo longius productæ fuerint ex vtraque parte Verticalis lineæ A D, deſcripti erunt paralleli
              <lb/>
            Horizontis. </s>
            <s xml:id="echoid-s16452" xml:space="preserve">quod eſt propoſitum.</s>
            <s xml:id="echoid-s16453" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">10</note>
          <p>
            <s xml:id="echoid-s16454" xml:space="preserve">ALITER Deſcripto quadrante A B C, cuiuſcunque magnitudinis, diuiſoq́ue in 90. </s>
            <s xml:id="echoid-s16455" xml:space="preserve">grad.
              <lb/>
            </s>
            <s xml:id="echoid-s16456" xml:space="preserve">
              <note position="right" xlink:label="note-0261-02" xlink:href="note-0261-02a" xml:space="preserve">A@ia deſcriptio
                <lb/>
              pa@allelorũ Ho
                <lb/>
              rizontis i
                <unsure/>
              n eo-
                <lb/>
              dem horologi
                <unsure/>
              o
                <lb/>
              Meridi
                <unsure/>
              ano.</note>
            vel in pauciores partes pro numero parallelorum deſcribendorum, emittantur ex centro A, per
              <lb/>
            puncta diuiſionum rectæ lineæ, quæ reſpon-
              <lb/>
              <figure xlink:label="fig-0261-01" xlink:href="fig-0261-01a" number="184">
                <image file="0261-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0261-01"/>
              </figure>
            debunt radiis parallelorũ Horizontis in qua
              <lb/>
            drante E C D, præcedentis figuræ contentis;
              <lb/>
            </s>
            <s xml:id="echoid-s16457" xml:space="preserve">initio ſumpto à recta A B, ita vt radius proxi
              <lb/>
            mus rectæ A B, ſit paralleli Horizontis grad. </s>
            <s xml:id="echoid-s16458" xml:space="preserve">
              <lb/>
            15. </s>
            <s xml:id="echoid-s16459" xml:space="preserve">ſequens, 30, &</s>
            <s xml:id="echoid-s16460" xml:space="preserve">c. </s>
            <s xml:id="echoid-s16461" xml:space="preserve">vt numeri appoſiti indi-
              <lb/>
            cant. </s>
            <s xml:id="echoid-s16462" xml:space="preserve">Deinde ex figura præcedentis propoſi-
              <lb/>
            ſitionis ſumantur interualla inter centrum
              <lb/>
              <note position="left" xlink:label="note-0261-03" xlink:href="note-0261-03a" xml:space="preserve">20</note>
            F, & </s>
            <s xml:id="echoid-s16463" xml:space="preserve">puncta, quibus Verticales lineæ horizon
              <lb/>
            talem lineam interſecant, eaque ex A, hu-
              <lb/>
            ius figuræ in rectam A B, tranferantur, aſcri-
              <lb/>
            ptis numeris Verticalium linearum prope
              <lb/>
            puncta, quæ translata interualla in recta A B,
              <lb/>
            terminant, atq; </s>
            <s xml:id="echoid-s16464" xml:space="preserve">per hæc puncta agantur ipſi
              <lb/>
            A C, parallelæ.</s>
            <s xml:id="echoid-s16465" xml:space="preserve">
              <unsure/>
            Quod facile fiet, ſi ipſi A B, pa
              <lb/>
            rallela ducatur G H, & </s>
            <s xml:id="echoid-s16466" xml:space="preserve">in hanc puncta lineæ
              <lb/>
            A B, transferantur, &</s>
            <s xml:id="echoid-s16467" xml:space="preserve">c. </s>
            <s xml:id="echoid-s16468" xml:space="preserve">Exempli gratia, ex fi-
              <lb/>
            gura pręcedentis propoſ. </s>
            <s xml:id="echoid-s16469" xml:space="preserve">interuallum E L,
              <lb/>
            transferatur in rectam A B, huius figuræ
              <lb/>
              <note position="left" xlink:label="note-0261-04" xlink:href="note-0261-04a" xml:space="preserve">30</note>
            vſquead punctũ D, apponendo numerũ 60.
              <lb/>
            </s>
            <s xml:id="echoid-s16470" xml:space="preserve">& </s>
            <s xml:id="echoid-s16471" xml:space="preserve">per D, ipſi A C, parallella agatur D E, &</s>
            <s xml:id="echoid-s16472" xml:space="preserve">c.</s>
            <s xml:id="echoid-s16473" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s16474" xml:space="preserve">HAC antem figura ita conſtructa, deſcri
              <lb/>
            bentur paralleli Horizontis hoc modo. </s>
            <s xml:id="echoid-s16475" xml:space="preserve">Interualla rectarum ipſi A C, æquidiſtantium comprehẽ-
              <lb/>
            ſa inter rectam A B, radium v. </s>
            <s xml:id="echoid-s16476" xml:space="preserve">g. </s>
            <s xml:id="echoid-s16477" xml:space="preserve">paralleli Horizontis grad. </s>
            <s xml:id="echoid-s16478" xml:space="preserve">15. </s>
            <s xml:id="echoid-s16479" xml:space="preserve">transferantur ex punctis, quibus li-
              <lb/>
            nea horizontalis in figura præcedẽtis propoſ. </s>
            <s xml:id="echoid-s16480" xml:space="preserve">ſecatur à lineis Verticalibus, in lineas Verticales cor
              <lb/>
            reſpondentes numeris in recta A B, notatis, ſignando puncta in Verticalibus lineis: </s>
            <s xml:id="echoid-s16481" xml:space="preserve">vt v. </s>
            <s xml:id="echoid-s16482" xml:space="preserve">g. </s>
            <s xml:id="echoid-s16483" xml:space="preserve">rectæ
              <lb/>
            D E, accipiatur æqualis L M, in Verticali linea grad. </s>
            <s xml:id="echoid-s16484" xml:space="preserve">60 & </s>
            <s xml:id="echoid-s16485" xml:space="preserve">ſic de cæteris. </s>
            <s xml:id="echoid-s16486" xml:space="preserve">Si enim hæc puncta ap-
              <lb/>
            poſite iungantur linea quadã inflexa, deſcriptus erit parallelus Horizontis gr. </s>
            <s xml:id="echoid-s16487" xml:space="preserve">15. </s>
            <s xml:id="echoid-s16488" xml:space="preserve">Eodem modo
              <lb/>
            reliqui paralleli Horizontis deſcribentur, ſi rectæ inter lineam A B, & </s>
            <s xml:id="echoid-s16489" xml:space="preserve">radios parallelorũ Horizon-
              <lb/>
              <note position="left" xlink:label="note-0261-05" xlink:href="note-0261-05a" xml:space="preserve">40</note>
            tis interiectæ transferantur in lineas Verticales correſpondentes, ex linea horizontali, &</s>
            <s xml:id="echoid-s16490" xml:space="preserve">c. </s>
            <s xml:id="echoid-s16491" xml:space="preserve">Quod
              <lb/>
            hac ratione demonſtrabimus.</s>
            <s xml:id="echoid-s16492" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s16493" xml:space="preserve">IN figura antecedentis propoſ. </s>
            <s xml:id="echoid-s16494" xml:space="preserve">intelligatur recta A F, quæ ſtylo ſumpta eſt æqualis, ad rectos
              <lb/>
              <note position="right" xlink:label="note-0261-06" xlink:href="note-0261-06a" xml:space="preserve">Demonſtratio
                <lb/>
              poſterioris de-
                <lb/>
              ſcriptionis pa-
                <lb/>
              rallelorum Ho
                <unsure/>
                <lb/>
              rizontis.</note>
            angulos inſiſtere plano horologij in puncto A, & </s>
            <s xml:id="echoid-s16495" xml:space="preserve">figura proxime cõſtructa circa punctũ F, quod
              <lb/>
            eſt in centro mundi, circumduci verſus horologiũ, ita vt punctum A, coniungatur cũ centro mũ-
              <lb/>
            di, ſeu puncto E, & </s>
            <s xml:id="echoid-s16496" xml:space="preserve">recta A C, perpetuo lineæ Verticali A D, æquidiſter, hoc eſt, coniuncta ſit cũ
              <lb/>
            axe Horizontis, eiuſque parallelorum, & </s>
            <s xml:id="echoid-s16497" xml:space="preserve">idcirco recta A B, à plano Horizontis non recedens oc-
              <lb/>
            currat ſemper illo motu horizontali lineæ. </s>
            <s xml:id="echoid-s16498" xml:space="preserve">Nam in hac circumductione cadet punctum D, v. </s>
            <s xml:id="echoid-s16499" xml:space="preserve">g. </s>
            <s xml:id="echoid-s16500" xml:space="preserve">in
              <lb/>
            punctum L, horizontalis lineæ, propterea quòd rectæ F L, in præcedenti propoſ. </s>
            <s xml:id="echoid-s16501" xml:space="preserve">ſumpta eſt hic
              <lb/>
              <note position="left" xlink:label="note-0261-07" xlink:href="note-0261-07a" xml:space="preserve">50</note>
            æqualis, A D. </s>
            <s xml:id="echoid-s16502" xml:space="preserve">Eſt enim recta F L, cadens ex puncto F, in ſublimi, nempe à Vertice ſtyli, rectæ
              <lb/>
            F L, in plano horologii æqualis; </s>
            <s xml:id="echoid-s16503" xml:space="preserve">vt conſtat, ſi triangulum F A L, in ſublimi conferatur cum trian-
              <lb/>
              <note position="right" xlink:label="note-0261-08" xlink:href="note-0261-08a" xml:space="preserve">4. primi.</note>
            gulo F A L, in plano horologij, quemadmodũ propoſ. </s>
            <s xml:id="echoid-s16504" xml:space="preserve">26. </s>
            <s xml:id="echoid-s16505" xml:space="preserve">huius libri de trangulis E A N, E A N,
              <lb/>
            dictum eſt. </s>
            <s xml:id="echoid-s16506" xml:space="preserve">Cum igitur tam recta L M, quàm D E, axi Horizontis æquidiſtet, erunt etiam L M,
              <lb/>
              <note position="right" xlink:label="note-0261-09" xlink:href="note-0261-09a" xml:space="preserve">9. vndec.</note>
            D E, inter ſe parallelæ, & </s>
            <s xml:id="echoid-s16507" xml:space="preserve">ob id congruet recta D E, rectæ L M, aliàs nõ eſſent parallelæ L M, D E,
              <lb/>
            cum in illa circumductione in L, conueniant; </s>
            <s xml:id="echoid-s16508" xml:space="preserve">ac proinde cum L M, ſumpta ſit æqualis rectæ D E,
              <lb/>
            cadet punctum E, in punctum M, atque adeo radius paralleli Horizontis grad. </s>
            <s xml:id="echoid-s16509" xml:space="preserve">15. </s>
            <s xml:id="echoid-s16510" xml:space="preserve">occurret plano
              <lb/>
            horologii in puncto M. </s>
            <s xml:id="echoid-s16511" xml:space="preserve">Per punctum ergo M, tranſibit arcus paralleli Horizontis grad. </s>
            <s xml:id="echoid-s16512" xml:space="preserve">15. </s>
            <s xml:id="echoid-s16513" xml:space="preserve">cum
              <lb/>
            in illud radius dicti paralleli in illa circumuolutione incidat, vt demonſtratum eſt. </s>
            <s xml:id="echoid-s16514" xml:space="preserve">Non aliter oſtẽ
              <lb/>
            demus punctum F, eiuſdem radii cadere in punctum N, & </s>
            <s xml:id="echoid-s16515" xml:space="preserve">ſic de cætetis. </s>
            <s xml:id="echoid-s16516" xml:space="preserve">Parallelos igitur Hori-
              <lb/>
            zontis in eodem horologio Meridiano deſcripſimus. </s>
            <s xml:id="echoid-s16517" xml:space="preserve">Quod faciendum erat.</s>
            <s xml:id="echoid-s16518" xml:space="preserve"/>
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