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-s4739" xml:space="preserve">
              <pb o="86" file="0106" n="106" rhead="GNOMONICES"/>
            Sol in P, exiſtet, altitudo{q́ue} Solis erit arcus I P, vt ex ijs, quæ propoſ. </s>
            <s xml:id="echoid-s4740" xml:space="preserve">2. </s>
            <s xml:id="echoid-s4741" xml:space="preserve">hui{us} lib. </s>
            <s xml:id="echoid-s4742" xml:space="preserve">ſcripſimus, facile col-
              <lb/>
            ligi poteſt.</s>
            <s xml:id="echoid-s4743" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s4744" xml:space="preserve">QVOD ſi quando recta P Q, ceciderit in punctum N, hoc est, ſi altitudo Solis inuenta fuerit æqua
              <lb/>
            lis meridianæ altitudini Solis illius diei, exiſtet Sol in Meridiano circulo, ac propterea vmbra ipſa A B,
              <lb/>
            erit linea meridiana.</s>
            <s xml:id="echoid-s4745" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s4746" xml:space="preserve">PER idem Analemma eadem ferè ratione explorare nobis licebit declinationem cuiuſcunque plani
              <lb/>
            propoſiti, etiamſi in plano Horizonti parallelo lineam meridianam non inueniamus, quemadmodum
              <lb/>
            & </s>
            <s xml:id="echoid-s4747" xml:space="preserve">à Ioan. </s>
            <s xml:id="echoid-s4748" xml:space="preserve">Baptiſta Benedicto traditur in Gnomonica. </s>
            <s xml:id="echoid-s4749" xml:space="preserve">Quod vt fiat, ſit murus ad Horizontem rectus
              <lb/>
            A B, in quo ducta recta C D,
              <lb/>
              <note position="left" xlink:label="note-0106-01" xlink:href="note-0106-01a" xml:space="preserve">Declinatio pla-
                <lb/>
              ni propoſiti, per
                <lb/>
              Analẽma qua
                <lb/>
              arte ſit exqui-
                <lb/>
              renda.</note>
              <figure xlink:label="fig-0106-01" xlink:href="fig-0106-01a" number="69">
                <image file="0106-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0106-01"/>
              </figure>
            Horizonti parallela, figatur
              <lb/>
              <note position="left" xlink:label="note-0106-02" xlink:href="note-0106-02a" xml:space="preserve">10</note>
            in ea ſtylus C E, cuiusuis longi-
              <lb/>
            tudinis ad murum rectus in
              <lb/>
            puncto C, obſeruetur{q́ue} quo-
              <lb/>
            cunque tempore, cum Sol pla-
              <lb/>
            num muri illuminat, ſiue ante
              <lb/>
            meridiem, ſiue poſt, extremitas
              <lb/>
            vmbræ E F, quam ſtylus proij-
              <lb/>
            cit, nempe punctũ F, per quod
              <lb/>
            ad rectam C D, perpendicula-
              <lb/>
            ris ducatur F D; </s>
            <s xml:id="echoid-s4750" xml:space="preserve">quæ dicto ci-
              <lb/>
              <note position="left" xlink:label="note-0106-03" xlink:href="note-0106-03a" xml:space="preserve">20</note>
            tius ducetur hoc modo. </s>
            <s xml:id="echoid-s4751" xml:space="preserve">Ap-
              <lb/>
            plicetur muro filum cum per-
              <lb/>
            pendiculo, ita vt per punctum
              <lb/>
            F, tranſeat, ſignetur in mu-
              <lb/>
            ro punctum quodcunque D.
              <lb/>
            </s>
            <s xml:id="echoid-s4752" xml:space="preserve">Nam linea recta per F, & </s>
            <s xml:id="echoid-s4753" xml:space="preserve">D, ducta perpendicularis erit ad C D, cum filum ad Horizontẽ ſit rectũ. </s>
            <s xml:id="echoid-s4754" xml:space="preserve">Hinc
              <lb/>
            enim fit, vt & </s>
            <s xml:id="echoid-s4755" xml:space="preserve">recta F D, quæ à filo perpendiculi non differt, vel certe ei parallela eſt, ad Horizontem,
              <lb/>
            qui per rectam C D, ducitur, ſit perpendicularis; </s>
            <s xml:id="echoid-s4756" xml:space="preserve">atque adeo per definitionem 3. </s>
            <s xml:id="echoid-s4757" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s4758" xml:space="preserve">11. </s>
            <s xml:id="echoid-s4759" xml:space="preserve">Euclidis, cum
              <lb/>
            recta C D, in Horizonte rectos conſtituat angulos. </s>
            <s xml:id="echoid-s4760" xml:space="preserve">Ego loco ſtyli vtor hic quoque inſtrumento illo, quod
              <lb/>
            ad initium huius ſcholij deſcripſimus. </s>
            <s xml:id="echoid-s4761" xml:space="preserve">Si enim applicetur muro A B, ita vt punctum D, in punctum C,
              <lb/>
              <note position="left" xlink:label="note-0106-04" xlink:href="note-0106-04a" xml:space="preserve">30</note>
            cadat, & </s>
            <s xml:id="echoid-s4762" xml:space="preserve">latus D A, in rectam C D, recta D I, vergente deorſum verſus, fungetur latus D H, mune-
              <lb/>
            re ſtyli ad murum recti. </s>
            <s xml:id="echoid-s4763" xml:space="preserve">Quare obſeruata extremitate vmbræ illius in puncto F, amouendum erit instru
              <lb/>
            mentum, & </s>
            <s xml:id="echoid-s4764" xml:space="preserve">punctum C, diligenter notandum. </s>
            <s xml:id="echoid-s4765" xml:space="preserve">Itaque quoniam radius Solis E F, per E, verticem ſtyli,
              <lb/>
            qui in centro mundi eſt, per propoſ. </s>
            <s xml:id="echoid-s4766" xml:space="preserve">2. </s>
            <s xml:id="echoid-s4767" xml:space="preserve">huius libri, in plano illius Verticalis exiſtit, qui tempore obſerua-
              <lb/>
            tionis per centrum Solis ducitur, occurret hic Verticalis muro A B, in puncto F. </s>
            <s xml:id="echoid-s4768" xml:space="preserve">Quia verò tam planũ
              <lb/>
            muri, quàm huius Verticalis rectum eſt ad Horizontem, erit quoque communis eorum ſectio ad Horizon-
              <lb/>
              <note position="left" xlink:label="note-0106-05" xlink:href="note-0106-05a" xml:space="preserve">19. vndec.</note>
            tem recta, atque adeo, per defin. </s>
            <s xml:id="echoid-s4769" xml:space="preserve">3. </s>
            <s xml:id="echoid-s4770" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s4771" xml:space="preserve">11. </s>
            <s xml:id="echoid-s4772" xml:space="preserve">Euclidis, perpendicularis ad rectam C D, in Horizonte exiſten
              <lb/>
            tem. </s>
            <s xml:id="echoid-s4773" xml:space="preserve">Cum ergo F D, ſit ad C D, perpendicularis, erit F D, communis ſectio muri A B, & </s>
            <s xml:id="echoid-s4774" xml:space="preserve">Verticalis
              <lb/>
            tunc temporis per centrum Solis ducti, atque adeo idem Verticalis per punctum D, tranſibit. </s>
            <s xml:id="echoid-s4775" xml:space="preserve">Ducta igi-
              <lb/>
            tur recta E D, erit communis ſectio Horizontis, & </s>
            <s xml:id="echoid-s4776" xml:space="preserve">eiuſdem Verticalis, cum vterque circulus per pun-
              <lb/>
              <note position="left" xlink:label="note-0106-06" xlink:href="note-0106-06a" xml:space="preserve">40</note>
            cta E, D, tranſeat; </s>
            <s xml:id="echoid-s4777" xml:space="preserve">atque adeo linea F D, ad Horizontem recta, perpendicularis erit, per defin. </s>
            <s xml:id="echoid-s4778" xml:space="preserve">3. </s>
            <s xml:id="echoid-s4779" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s4780" xml:space="preserve">11.
              <lb/>
            </s>
            <s xml:id="echoid-s4781" xml:space="preserve">Euclidis, ad rectam E D, in Horizonte exiſtentem: </s>
            <s xml:id="echoid-s4782" xml:space="preserve">Eſt autem & </s>
            <s xml:id="echoid-s4783" xml:space="preserve">ad C D, perpendicularis oſtenſa. </s>
            <s xml:id="echoid-s4784" xml:space="preserve">Igi-
              <lb/>
            tur cum vtraque linea C D, E D, quarum illa in muro, hæc autem in Verticali per Solem tranſeunte exi-
              <lb/>
            ſtit, ad F D, communem ſectionem muri, & </s>
            <s xml:id="echoid-s4785" xml:space="preserve">dicti Verticalis ſit perpendicularis, erit per defin. </s>
            <s xml:id="echoid-s4786" xml:space="preserve">6. </s>
            <s xml:id="echoid-s4787" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s4788" xml:space="preserve">11. </s>
            <s xml:id="echoid-s4789" xml:space="preserve">
              <lb/>
            Euclidis, C D E, angulus inclinationis muri ad dictum Verticalem. </s>
            <s xml:id="echoid-s4790" xml:space="preserve">Cui in plano muri æqualem exhibe-
              <lb/>
            bimus hoc modo. </s>
            <s xml:id="echoid-s4791" xml:space="preserve">Ducta recta C G, ad C D, perpendiculari, fiat C G, ſtylo, vel lateri D H, inſtrumenti
              <lb/>
            ad initium huius ſcholij deſcripti, æqualis, iungatur{q́ue} recta G D. </s>
            <s xml:id="echoid-s4792" xml:space="preserve">Dico angulum C D G, angulo C D E,
              <lb/>
            æqualem eſſe. </s>
            <s xml:id="echoid-s4793" xml:space="preserve">Quoniam enim duo latera C E, C D, trianguli C D E, duobus lateribus C G, C D, trian-
              <lb/>
            guli C D G, æqualia ſunt, angulosq́, comprehendunt æquales, vtpote rectos, (Eſt enim angulus E C D,
              <lb/>
            rectus, per d@fin. </s>
            <s xml:id="echoid-s4794" xml:space="preserve">3. </s>
            <s xml:id="echoid-s4795" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s4796" xml:space="preserve">11. </s>
            <s xml:id="echoid-s4797" xml:space="preserve">Euclidis, angulus verò G C D, ex conſtructione) erit quoque baſis E D, baſi
              <lb/>
              <note position="left" xlink:label="note-0106-07" xlink:href="note-0106-07a" xml:space="preserve">50</note>
            G D, & </s>
            <s xml:id="echoid-s4798" xml:space="preserve">angulus C D E, angulo C D G, æqualis. </s>
            <s xml:id="echoid-s4799" xml:space="preserve">Ex hoc autem angulo C D G, cognito inuestigabimus de-
              <lb/>
              <note position="left" xlink:label="note-0106-08" xlink:href="note-0106-08a" xml:space="preserve">4. primi.</note>
            clinationem muri propoſiti à Verticali proprie dicto, hac ratione.</s>
            <s xml:id="echoid-s4800" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s4801" xml:space="preserve">POST QVAM vmbræ extremitas F, notata eſt, inquiratur ſtatim, antequã recta F D, ducatur,
              <lb/>
            (quoniã ſi mora aliqua interceſſerit, vmbra mutabitur, & </s>
            <s xml:id="echoid-s4802" xml:space="preserve">Sol alium Verticalẽ occupabit, propter motum
              <lb/>
            diurnũ) altitudo Solis, quæ in Analemmate ſuperiori, quod hic repetiuimus, ſupputetur ex punctis G, I,
              <lb/>
            vſq;</s>
            <s xml:id="echoid-s4803" xml:space="preserve">
              <unsure/>
            ad puncta Q, P. </s>
            <s xml:id="echoid-s4804" xml:space="preserve">Iuncta enim recta PQ, erit diameter paralleli Horizõtis per centrũ Solis tempore
              <lb/>
            obſeruationis ducti, vt ſupra demonſtrauimus, ſecans diametrum paralleli Solis in S, & </s>
            <s xml:id="echoid-s4805" xml:space="preserve">diametrum
              <lb/>
            Verticalis proprie dicti in R. </s>
            <s xml:id="echoid-s4806" xml:space="preserve">Deſcripto autem circa P Q, ex centro R, ſemicirculo P T Q, ducatur
              <lb/>
            ex S, ad P Q, perpendicularis S T, ſecans circunferentiam ſemicirculi P T Q, in T, iungatur{q́ue}
              <unsure/>
            re-
              <lb/>
            cta T R, quæ communis ſectio erit paralleli Horizontis, & </s>
            <s xml:id="echoid-s4807" xml:space="preserve">Verticalis circuli, quorum vterque tunc per
              <lb/>
            Solis centrum ducitur; </s>
            <s xml:id="echoid-s4808" xml:space="preserve">adeo vt angulus acutus Q R T, vel P R T, ſit angulus declinationis dicti </s>
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