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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            <s xml:id="echoid-s2444" xml:space="preserve">
              <pb o="36" file="0056" n="56" rhead="GNOMONICES"/>
            lineæ curuæ per puncta A, C, D, B, deſcriptæ æquales ſunt maiori axi AB, vt vult illa ꝓpoſitio Apollonij.</s>
            <s xml:id="echoid-s2445" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s2446" xml:space="preserve">INVENIEMVS quoque puncta F, G, pro clauiculorum locis hac ratione, & </s>
            <s xml:id="echoid-s2447" xml:space="preserve">fortaſſe certius,
              <lb/>
              <note position="left" xlink:label="note-0056-01" xlink:href="note-0056-01a" xml:space="preserve">Loca claniculo-
                <lb/>
              rũ ad Ellipſim
                <lb/>
              deſcribendam
                <lb/>
              alia ratione in-
                <lb/>
              ueniuntur.</note>
            propterea quod, cum minor axis fermè æqualis eſt maiori, arcus cir culorum ex C, vel D, deſcripti ualdè
              <lb/>
              <figure xlink:label="fig-0056-01" xlink:href="fig-0056-01a" number="40">
                <image file="0056-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0056-01"/>
              </figure>
            obliquè ſecant rectam A B.
              <lb/>
            </s>
            <s xml:id="echoid-s2448" xml:space="preserve">Diuiſa recta B E, quæ dimi-
              <lb/>
            dium eſt axis maioris, bifa-
              <lb/>
            riã in H, deſcribatur ex H,
              <lb/>
            ad interuallũ H B, vel H E,
              <lb/>
            ſemicir culus B I E, & </s>
            <s xml:id="echoid-s2449" xml:space="preserve">in eo
              <lb/>
            accõmodetur recta B I, dimi-
              <lb/>
              <note position="left" xlink:label="note-0056-02" xlink:href="note-0056-02a" xml:space="preserve">1. quarti.</note>
              <note position="left" xlink:label="note-0056-03" xlink:href="note-0056-03a" xml:space="preserve">10</note>
            dio minoris axis D E, æqua-
              <lb/>
            lis, ducatur{q́ue} recta E I. </s>
            <s xml:id="echoid-s2450" xml:space="preserve">Dico
              <lb/>
            rectã E I, æqualem eſſe tam
              <lb/>
            rectæ E F, quàm rectæ E G,
              <lb/>
            atque adeò, ſi abſcindantur
              <lb/>
            rectæ E F, E G, ipſi E I,
              <lb/>
            æquales, inuenta eſſe eadem
              <lb/>
            puncta F, G, pro locis claui-
              <lb/>
            culorum. </s>
            <s xml:id="echoid-s2451" xml:space="preserve">Quoniã enim qua-
              <lb/>
              <note position="left" xlink:label="note-0056-04" xlink:href="note-0056-04a" xml:space="preserve">47. primi.</note>
            dratum ex B E, æquale eſt
              <lb/>
              <note position="left" xlink:label="note-0056-05" xlink:href="note-0056-05a" xml:space="preserve">20</note>
            quadratis ex E I, I B; </s>
            <s xml:id="echoid-s2452" xml:space="preserve">Et tã
              <lb/>
            quadratum ex D G, quadra-
              <lb/>
            tis ex D E, E G, quàm qua-
              <lb/>
            dratum ex D F, quadratis ex
              <lb/>
            D E, E F, æquale: </s>
            <s xml:id="echoid-s2453" xml:space="preserve">Eſt aũt qua-
              <lb/>
            dratũ ex BE, tã quadrato ex
              <lb/>
            D G, quàm quadrato ex D F,
              <lb/>
            æquale, quod hæ lineæ æqua-
              <lb/>
            les ſint ex conſtructione; </s>
            <s xml:id="echoid-s2454" xml:space="preserve">& </s>
            <s xml:id="echoid-s2455" xml:space="preserve">
              <lb/>
            quadratũ ex B I, æquale qua-
              <lb/>
              <note position="left" xlink:label="note-0056-06" xlink:href="note-0056-06a" xml:space="preserve">30</note>
            drato ex D E, quòd per con-
              <lb/>
            ſtructionẽ æquales quoque ſint poſitæ rectæ B I, D E; </s>
            <s xml:id="echoid-s2456" xml:space="preserve">crit reliquũ quadratũ ex E I, reliquo quadrato tam ex
              <lb/>
            E G, quàm ex E F, deſcripto æquale, ac proinde recta E I, rectis E G, E F, æqualis erit, quod eſt propoſitũ.</s>
            <s xml:id="echoid-s2457" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s2458" xml:space="preserve">DEINDE ſi datus ſit maior duntaxat axis Ellipſis A B, & </s>
            <s xml:id="echoid-s2459" xml:space="preserve">aliquod punctum K, per quod tranſi-
              <lb/>
              <note position="left" xlink:label="note-0056-07" xlink:href="note-0056-07a" xml:space="preserve">Quomodo El-
                <lb/>
              lipſis circa datũ
                <lb/>
              axem maiorem,
                <lb/>
              & per datũ pun
                <lb/>
              ctum deſcriba-
                <lb/>
              tur.</note>
            re debeat Ellipſis circa axem A B, deſcripta, reperiemus minorem axem, hoc eſt, latitudinem Ellipſis,
              <lb/>
            & </s>
            <s xml:id="echoid-s2460" xml:space="preserve">puncta F, G, in quibus affigendi ſunt clauiculi, hac ratione. </s>
            <s xml:id="echoid-s2461" xml:space="preserve">Diuiſa A B, bifariam in E, ducatur per
              <lb/>
            E, ad A B, perpendicularis C D, & </s>
            <s xml:id="echoid-s2462" xml:space="preserve">ex dato puncto K, ad eandem A B, alia perpendicularis K L, vel ip-
              <lb/>
            ſi C D, parallela. </s>
            <s xml:id="echoid-s2463" xml:space="preserve">Deinde per ea, quæ in problemate tertio ſcholij propoſ. </s>
            <s xml:id="echoid-s2464" xml:space="preserve">vltimæ lib. </s>
            <s xml:id="echoid-s2465" xml:space="preserve">6. </s>
            <s xml:id="echoid-s2466" xml:space="preserve">Euclidis demon-
              <lb/>
            ſtr ata ſunt à nobis, fiat, vt rectangulum ſub A L, L B, contentum ad rectangulum contentum ſub A E,
              <lb/>
            E B, hoc eſt, ad quadratum ex A E, vel E B, (Hoc enim rectangulum quadratum eſt, ob æqualitatem re-
              <lb/>
              <note position="left" xlink:label="note-0056-08" xlink:href="note-0056-08a" xml:space="preserve">40</note>
            ctarum A E, E B) ita quadratum ex K L, ad aliud quadratũ, cuius latus ſit E D, vel E C. </s>
            <s xml:id="echoid-s2467" xml:space="preserve">Erit{q́ue} ex de-
              <lb/>
            monſtratis ab Apollonio propoſ. </s>
            <s xml:id="echoid-s2468" xml:space="preserve">21. </s>
            <s xml:id="echoid-s2469" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s2470" xml:space="preserve">1. </s>
            <s xml:id="echoid-s2471" xml:space="preserve">E D, vel E C, dimidium axis minoris; </s>
            <s xml:id="echoid-s2472" xml:space="preserve">per quam, vt paulo an-
              <lb/>
            te docuimus, inueniemus puncta F, & </s>
            <s xml:id="echoid-s2473" xml:space="preserve">G, quorum beneficio Ellipſim deſcribemus.</s>
            <s xml:id="echoid-s2474" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s2475" xml:space="preserve">ITA autem expedite quadratum lateris E D, vel E C, quæſiti comperiemus. </s>
            <s xml:id="echoid-s2476" xml:space="preserve">Ex E, ad interuallum
              <lb/>
            E A, vel E B, ſemicir culus deſcribatur A M B, quem recta L K, producta ſecet in M; </s>
            <s xml:id="echoid-s2477" xml:space="preserve">Eritq́, ex ſcholio
              <lb/>
            propoſ. </s>
            <s xml:id="echoid-s2478" xml:space="preserve">13. </s>
            <s xml:id="echoid-s2479" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s2480" xml:space="preserve">6. </s>
            <s xml:id="echoid-s2481" xml:space="preserve">Euclidis, recta L M, media proportionalis inter A L, L B, atq; </s>
            <s xml:id="echoid-s2482" xml:space="preserve">adeo eius quadratũ re-
              <lb/>
              <note position="left" xlink:label="note-0056-09" xlink:href="note-0056-09a" xml:space="preserve">17. ſexti.</note>
            ctangulo ſub A L, L B, cõtento æquale. </s>
            <s xml:id="echoid-s2483" xml:space="preserve">Vnde facili negotio reperiemus quadratũ, ad quod eandẽ propor-
              <lb/>
            tionẽ habeat quadratũ ex L K, quã habet quadratũ ex L M, hoc eſt, rectangulũ ſub A L, L B, comprehen-
              <lb/>
            ſum, ad quadratum ex E A, vel E B, hoc eſt, ad rectangulum ſub A E, E B, contentum, ſi tribus rectis
              <lb/>
              <note position="left" xlink:label="note-0056-10" xlink:href="note-0056-10a" xml:space="preserve">12. ſexti.</note>
            L M, E A, L K, quartam proportionalem inueniamus E D; </s>
            <s xml:id="echoid-s2484" xml:space="preserve">propterea quod eandem proportionẽ habent
              <lb/>
              <note position="left" xlink:label="note-0056-11" xlink:href="note-0056-11a" xml:space="preserve">50</note>
            quadrata ſupra rectas L M, E A, L K, E D, deſcripta, quam ipſęmet rectæ. </s>
            <s xml:id="echoid-s2485" xml:space="preserve">Hoc autem artificio dictam
              <lb/>
              <note position="left" xlink:label="note-0056-12" xlink:href="note-0056-12a" xml:space="preserve">22. ſexti.</note>
            quartam proportionalem E D, reperiemus. </s>
            <s xml:id="echoid-s2486" xml:space="preserve">Ductis rectis duabus N O, N P, facientibus angulum in N,
              <lb/>
            quemcunque, ſumatur N Q, ipſi L M, & </s>
            <s xml:id="echoid-s2487" xml:space="preserve">Q O, ipſi E A, & </s>
            <s xml:id="echoid-s2488" xml:space="preserve">N R, ipſi L K, æqualis. </s>
            <s xml:id="echoid-s2489" xml:space="preserve">Deinde ducta Q R,
              <lb/>
            agatur per O, ipſi Q R, parallela O P. </s>
            <s xml:id="echoid-s2490" xml:space="preserve">Erit R P, dicta quarta proportionalis; </s>
            <s xml:id="echoid-s2491" xml:space="preserve">cum ſit, vt N Q, hoc eſt,
              <lb/>
              <note position="left" xlink:label="note-0056-13" xlink:href="note-0056-13a" xml:space="preserve">2. ſexti.</note>
            L M, ad Q O, hoc eſt, ad E A, ita N R, hoc eſt, L K, ad R P. </s>
            <s xml:id="echoid-s2492" xml:space="preserve">Quare ſi ſumamus E D, ipſi R P, æqualem,
              <lb/>
            habebimus minoris axis dimidium E D, & </s>
            <s xml:id="echoid-s2493" xml:space="preserve">c.</s>
            <s xml:id="echoid-s2494" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s2495" xml:space="preserve">CAETERVM loco clauiculorum vti poterimus inſtrumento quodam ad ſimilitudinẽ circini fabri-
              <lb/>
              <note position="left" xlink:label="note-0056-14" xlink:href="note-0056-14a" xml:space="preserve">Inſtrumentum
                <lb/>
              pro Ellipſi per
                <lb/>
              filum deſcriben
                <lb/>
              da.</note>
            cato, cuius crura in extremitatibus ſint reſecta, & </s>
            <s xml:id="echoid-s2496" xml:space="preserve">frusta abſciſſa ita adaptata, vt hinc inde poſſint di-
              <lb/>
            moueri, & </s>
            <s xml:id="echoid-s2497" xml:space="preserve">cochleolis aſtringi, vt quãtumuis dilatentur circini crura, ſemper fruſta illa cochleolis aſtricta
              <lb/>
            recta ſint ad planũ, in quo Ellipſis deſcribenda eſt. </s>
            <s xml:id="echoid-s2498" xml:space="preserve">Hæc autẽ fruſta habeant etiã in extremis partibus ca-
              <lb/>
            naliculos quoſdam per circuitum inciſos, ita vt filum in ijs circumuolutum neque ſurſum aſcendat, </s>
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