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

Table of figures

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          <p style="it">
            <s xml:id="echoid-s2390" xml:space="preserve">
              <pb o="35" file="0055" n="55" rhead="LIBER PRIMVS."/>
            in ſecunda, triplam intertia, & </s>
            <s xml:id="echoid-s2391" xml:space="preserve">quadruplam in quarta, &</s>
            <s xml:id="echoid-s2392" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2393" xml:space="preserve">Per extremitates enim harum linearum
              <lb/>
            parabole deſcribenda erit.</s>
            <s xml:id="echoid-s2394" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s2395" xml:space="preserve">PRO Hyperbolis verò ſumemus axem quemcunque F I, vt in antecedentibus hyperbolis, cui ex
              <lb/>
              <note position="right" xlink:label="note-0055-01" xlink:href="note-0055-01a" xml:space="preserve">Qua ratione
                <lb/>
              duæ hyperbolæ
                <lb/>
              oppoſitæ qua-
                <lb/>
              leſcunque de-
                <lb/>
              ſcribantur in
                <lb/>
              plano.</note>
            vtraque parte addemus rectas vtcunque F R, I Q, inter ſe æquales, & </s>
            <s xml:id="echoid-s2396" xml:space="preserve">intelligemus ad axem F I, ap-
              <lb/>
            plicatum eſſe rectangulum ſub F Q, Q I, æquale quartæ parti rectanguli ſub axe F I, & </s>
            <s xml:id="echoid-s2397" xml:space="preserve">recto latere
              <lb/>
            comprehenſi, excedens{q́ue}, quadrato ex Q I, &</s>
            <s xml:id="echoid-s2398" xml:space="preserve">c.</s>
            <s xml:id="echoid-s2399" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s2400" xml:space="preserve">PRO Ellipſi denique accipiemus axem E F, ad libitum, vt in proxima ellipſi, ex quo abſcindemus
              <lb/>
              <note position="right" xlink:label="note-0055-02" xlink:href="note-0055-02a" xml:space="preserve">Qua ratione El
                <lb/>
              lipſis qualiſcun
                <lb/>
              que in plano de
                <lb/>
              ſcribatur.</note>
            æquales hinc inde vtcunque E O, F N, intelligem{us}{q́ue} ad axem E F, applicatum eſſe rectangulum ſub
              <lb/>
            F O, O E, æquale quartæ parti rectanguli ſub axe E F, & </s>
            <s xml:id="echoid-s2401" xml:space="preserve">latere recto contenti, deficiens{q́ue} quadrato ex
              <lb/>
            E O; </s>
            <s xml:id="echoid-s2402" xml:space="preserve">&</s>
            <s xml:id="echoid-s2403" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2404" xml:space="preserve">Reliqua autem perficiemus vt prius.</s>
            <s xml:id="echoid-s2405" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">10</note>
          <p style="it">
            <s xml:id="echoid-s2406" xml:space="preserve">IMMO verò ſi in recta aliqua quantumuis protracta E F, nempe in eodem axe ellipſis, in duobus
              <lb/>
              <note position="right" xlink:label="note-0055-04" xlink:href="note-0055-04a" xml:space="preserve">Quo pacto El-
                <lb/>
              lipſis qualiſcun
                <lb/>
              que filo aliquo
                <lb/>
              deſctibatur in
                <lb/>
              plano.</note>
            punctis, vt in N, & </s>
            <s xml:id="echoid-s2407" xml:space="preserve">O, duo clauiculi infigantur, quibus filum circumponatur, ita vt duplicatum exce-
              <lb/>
            dat rectam N O, & </s>
            <s xml:id="echoid-s2408" xml:space="preserve">liberè poſſit circumuolui, deſcribetur Ellipſis facilè, & </s>
            <s xml:id="echoid-s2409" xml:space="preserve">expedite, ſi ſtylum aliquem
              <lb/>
            huic filo imponamus, eum{q́ue} circunducamus vnà cumfilo, extendentes ſemper filum, quantum fieri poteſt.
              <lb/>
            </s>
            <s xml:id="echoid-s2410" xml:space="preserve">Vt ſi filum circa clauiculos N, O, extendatur vſque ad I, quantum poteſt, ſi ſtylus aliquis ferreus in I,
              <lb/>
            ponatur, & </s>
            <s xml:id="echoid-s2411" xml:space="preserve">manentefilo ſemper ita extenſo circunducatur, donec eo reuertatur, vnde moueri incepit, de-
              <lb/>
            ſc
              <unsure/>
            ripta erit Ellipſis E G F; </s>
            <s xml:id="echoid-s2412" xml:space="preserve">Nam hac ratione erunt ſemper duæ rectæ ex N, & </s>
            <s xml:id="echoid-s2413" xml:space="preserve">O, vſque ad ſtylum cir-
              <lb/>
            cumductum ęquales axi E F, quem idem ſtylus circumductus ſecat in E, & </s>
            <s xml:id="echoid-s2414" xml:space="preserve">F. </s>
            <s xml:id="echoid-s2415" xml:space="preserve">Id quod longè facilius re
              <lb/>
            ipſa, & </s>
            <s xml:id="echoid-s2416" xml:space="preserve">vſu percipi poteſt, quàm multis verbis doceri.</s>
            <s xml:id="echoid-s2417" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s2418" xml:space="preserve">SED quoniam deſcriptio hæc Ellipſis per filum circa clauiculos accommodatum & </s>
            <s xml:id="echoid-s2419" xml:space="preserve">per ſe ipſa iucun-
              <lb/>
              <note position="left" xlink:label="note-0055-05" xlink:href="note-0055-05a" xml:space="preserve">20</note>
            daeſt, & </s>
            <s xml:id="echoid-s2420" xml:space="preserve">ad multa vtilis, li-
              <lb/>
              <figure xlink:label="fig-0055-01" xlink:href="fig-0055-01a" number="39">
                <image file="0055-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0055-01"/>
              </figure>
            bet paulo vberius eam hoc
              <lb/>
              <note position="right" xlink:label="note-0055-06" xlink:href="note-0055-06a" xml:space="preserve">Qua ratione
                <lb/>
              Ellipſis deſcri-
                <lb/>
              batur per filũ,
                <lb/>
              ſecundum lon-
                <lb/>
              gitudinem & la
                <lb/>
              titudinem da-
                <lb/>
              tam.</note>
            loco explicare. </s>
            <s xml:id="echoid-s2421" xml:space="preserve">Primum igi-
              <lb/>
            tur, ſi datus ſit vterque axis
              <lb/>
            Ellipſis, nempe A B, maior,
              <lb/>
            et C D, minor, ita vt Ellipſis
              <lb/>
            deſcribenda longitudinẽ ha-
              <lb/>
            beat A B, latitudinem ve-
              <lb/>
            rò C D, inueniemus puncta
              <lb/>
            in maiore axe, in quibus fi-
              <lb/>
              <note position="left" xlink:label="note-0055-07" xlink:href="note-0055-07a" xml:space="preserve">30</note>
            gendi ſunt clauiculi, & </s>
            <s xml:id="echoid-s2422" xml:space="preserve">lon
              <lb/>
            gitudinem fili circa clauicu-
              <lb/>
            los circumducendi, hac ra-
              <lb/>
            tione. </s>
            <s xml:id="echoid-s2423" xml:space="preserve">Diuiſo maiore axe
              <lb/>
            A B, bifariam in E, duca-
              <lb/>
            tur per E, ad A B, perpen-
              <lb/>
            dicularis C D, ſit{q́ue} tam E C,
              <lb/>
            quàm E D, dimidio minoris
              <lb/>
            axis æqualis, ita vt C D, to-
              <lb/>
            ti axi minori ſit æqualis.
              <lb/>
            </s>
            <s xml:id="echoid-s2424" xml:space="preserve">
              <note position="left" xlink:label="note-0055-08" xlink:href="note-0055-08a" xml:space="preserve">40</note>
            Deinde centro C, vel D, & </s>
            <s xml:id="echoid-s2425" xml:space="preserve">
              <lb/>
            interuallo E A, vel E B, duo
              <lb/>
            arcus circuli deſcribantur
              <lb/>
            ſecantes rectam A B, in F,
              <lb/>
            & </s>
            <s xml:id="echoid-s2426" xml:space="preserve">G, punctis, quæomnino
              <lb/>
              <note position="left" xlink:label="note-0055-09" xlink:href="note-0055-09a" xml:space="preserve">50</note>
            citra puncta A, & </s>
            <s xml:id="echoid-s2427" xml:space="preserve">B, erunt.
              <lb/>
            </s>
            <s xml:id="echoid-s2428" xml:space="preserve">Quoniam enim recta C A,
              <lb/>
              <note position="right" xlink:label="note-0055-10" xlink:href="note-0055-10a" xml:space="preserve">19. primi.</note>
            maior eſt, quàm A E, ob
              <lb/>
            angulum rectum A E C, fit, vt arcus ex C, ad interuallum A E, deſcriptus ſecet ipſam C A, atque adeò
              <lb/>
              <note position="right" xlink:label="note-0055-11" xlink:href="note-0055-11a" xml:space="preserve">Loca clauiculo-
                <lb/>
              rum, & longitu
                <lb/>
              do fili pro Elli-
                <lb/>
              pſi deſctibẽda.</note>
            & </s>
            <s xml:id="echoid-s2429" xml:space="preserve">ipſam A E, citra punctum A, &</s>
            <s xml:id="echoid-s2430" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2431" xml:space="preserve">Dico in punctis F, G, clauiculos eſſe figendos, vt propoſita Elli-
              <lb/>
            pſis deſcribatur, filum autem circa F, G, poſitum duplicandũ eſſe, ita vt extenſum pertingat præcisè ad
              <lb/>
            punctũ A, vel ad punctũ D, aut B, totum{q́ue} filum ſit D F G D, hac lege clauiculis in F, & </s>
            <s xml:id="echoid-s2432" xml:space="preserve">G, affixis cir-
              <lb/>
            cũpoſitum, vt liberè circa ipſos poſſit circũduci vnà cum ſtylo, adeò vt neque à clauiculis, neque à filo ſty-
              <lb/>
            lus impediatur, quo minus circumduci queat, vt integram ellipſim deſcribat. </s>
            <s xml:id="echoid-s2433" xml:space="preserve">Cum enim portiones G A,
              <lb/>
            F A, fili duplicati (relicta portione F G, inter clauiculos poſita) æquales ſint maiori axi A B, quòd A F,
              <lb/>
            ipſi B G, æqualis ſit, atq; </s>
            <s xml:id="echoid-s2434" xml:space="preserve">eodẽ modo reliquæ portiones, circũducto filo circa pũcta F, G, eidẽ aximaiori ſint
              <lb/>
            æquales, propterea quòd filum neq; </s>
            <s xml:id="echoid-s2435" xml:space="preserve">augetur, neque diminuitur in illa circũductione, manet{q́ue} eadẽ ſemper
              <lb/>
            portio communis F G, (Ita enim vides, exempli gratia, cum extremũ duplicati fili in D, collocatũ fuerit,
              <lb/>
            portiones D F, D G, toti axi A B, æquales eſſe, propterea quod ipſis A E, B E, ſumptæ ſunt æquales, &</s>
            <s xml:id="echoid-s2436" xml:space="preserve">c.)
              <lb/>
            </s>
            <s xml:id="echoid-s2437" xml:space="preserve">perſpicuum eſt, ex propoſ. </s>
            <s xml:id="echoid-s2438" xml:space="preserve">52. </s>
            <s xml:id="echoid-s2439" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s2440" xml:space="preserve">3. </s>
            <s xml:id="echoid-s2441" xml:space="preserve">Apollonij, beneficio illius fili deſcribi Ellipſim, cuius maior axis
              <lb/>
            A B, & </s>
            <s xml:id="echoid-s2442" xml:space="preserve">minor C D: </s>
            <s xml:id="echoid-s2443" xml:space="preserve">quandoquidem lineæ rectæ ex punctis F, & </s>
            <s xml:id="echoid-s2444" xml:space="preserve">G, inclinatæ ad quodcunque </s>
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