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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        <div xml:id="echoid-div1317" type="section" level="1" n="318">
          <p>
            <s xml:id="echoid-s26218" xml:space="preserve">
              <pb o="399" file="0415" n="415" rhead="LIBER TERTIVS."/>
            inuerti, & </s>
            <s xml:id="echoid-s26219" xml:space="preserve">horas, quę prius à media nocte computabãtur, à meridie numerãdas eſſe, ut in propoſ.
              <lb/>
            </s>
            <s xml:id="echoid-s26220" xml:space="preserve">13. </s>
            <s xml:id="echoid-s26221" xml:space="preserve">& </s>
            <s xml:id="echoid-s26222" xml:space="preserve">14. </s>
            <s xml:id="echoid-s26223" xml:space="preserve">pręcedentis libri oſtendimus. </s>
            <s xml:id="echoid-s26224" xml:space="preserve">Item eadem horizontalis linea dirimit totum horologiũ
              <lb/>
            in diurnum, atque nocturnum, ut ex eadem propoſ. </s>
            <s xml:id="echoid-s26225" xml:space="preserve">14. </s>
            <s xml:id="echoid-s26226" xml:space="preserve">præcedentis lib perſpicuum eſt. </s>
            <s xml:id="echoid-s26227" xml:space="preserve">Itaque
              <lb/>
            parallelos, ſiue arcus ſignorum Zodiaci, & </s>
            <s xml:id="echoid-s26228" xml:space="preserve">c. </s>
            <s xml:id="echoid-s26229" xml:space="preserve">depinximus. </s>
            <s xml:id="echoid-s26230" xml:space="preserve">Quod erat faciendum.</s>
            <s xml:id="echoid-s26231" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1327" type="section" level="1" n="319">
          <head xml:id="echoid-head330" style="it" xml:space="preserve">SCHOLIVM.</head>
          <p style="it">
            <s xml:id="echoid-s26232" xml:space="preserve">QVI arcus in horol gio ad ſigna borealia pertineant, & </s>
            <s xml:id="echoid-s26233" xml:space="preserve">qui ad auſtralia, non difficile erit iudicare,
              <lb/>
              <note position="right" xlink:label="note-0415-01" xlink:href="note-0415-01a" xml:space="preserve">Qui arcus ad
                <lb/>
              ſigna borealia,
                <lb/>
              & qui ad au-
                <lb/>
              ſtralia peru-
                <lb/>
              neant.</note>
            ſi quatuor illa Analemmata, quæ in propoſ. </s>
            <s xml:id="echoid-s26234" xml:space="preserve">25. </s>
            <s xml:id="echoid-s26235" xml:space="preserve">hui{us} libri deſcripſim{us}, attentè conſiderentur. </s>
            <s xml:id="echoid-s26236" xml:space="preserve">Nam
              <lb/>
            in horologijs, quæ ad meridiem, & </s>
            <s xml:id="echoid-s26237" xml:space="preserve">ad verticem, ſeu polum Horizontis ſpectant, ſi quidem centrum ho-
              <lb/>
              <note position="left" xlink:label="note-0415-02" xlink:href="note-0415-02a" xml:space="preserve">10</note>
            rologij fuerit infra lineam æquinoctialem, continentur arcus ſignorum borealium inter centrũ, & </s>
            <s xml:id="echoid-s26238" xml:space="preserve">æqui-
              <lb/>
            noctialem lineam, vt ex primo Analemmate dictæ propoſ. </s>
            <s xml:id="echoid-s26239" xml:space="preserve">conſtat; </s>
            <s xml:id="echoid-s26240" xml:space="preserve">quia puncta quadrantis borealis
              <lb/>
            H F, proij ciunt in meridie vmbras in portionem meridianæ lineæ M N, inter centrum M, & </s>
            <s xml:id="echoid-s26241" xml:space="preserve">punctum
              <lb/>
            N, per quod æquinoctialis linea ducitur: </s>
            <s xml:id="echoid-s26242" xml:space="preserve">Si verò horologij centrum ſupra lineam æquinoctialem exti-
              <lb/>
            terit, arcus auſtralium ſignorum inter centrum, & </s>
            <s xml:id="echoid-s26243" xml:space="preserve">æquinoctialem lineam comprehenduntur, vt ex ſe-
              <lb/>
            cundo Analemmate manifeſtum eſt; </s>
            <s xml:id="echoid-s26244" xml:space="preserve">quoniam puncta quadrantis auſtralis G H, proijciunt in meridie
              <lb/>
            vmbras in portionem lineæ meridianæ M N, inter centrum M, & </s>
            <s xml:id="echoid-s26245" xml:space="preserve">lineam æquinoctialem, quæ per N, du
              <lb/>
            citur. </s>
            <s xml:id="echoid-s26246" xml:space="preserve">Quòd ſi horologium centro careat, pertinebunt arcus infr a æquinoctialom lineam ad ſigna borea-
              <lb/>
            lia, vt perſpicuum eſt ex primo Analemmate, ſi duceretur infra E, linea parallela axi F G, quæ commu
              <lb/>
            nis ſectio eſſet Meridiani, ac plani horologij. </s>
            <s xml:id="echoid-s26247" xml:space="preserve">Nam tunc puncta quadrantis borealis H F, proijcerent
              <lb/>
              <note position="left" xlink:label="note-0415-03" xlink:href="note-0415-03a" xml:space="preserve">20</note>
            vmbras in meridie in portionem lineæ meridianæ infra punctum, per quod linea æquinoctialis eſſet ducẽ-
              <lb/>
            da. </s>
            <s xml:id="echoid-s26248" xml:space="preserve">At verò in horologijs, quæ ad ſeptentrionem, & </s>
            <s xml:id="echoid-s26249" xml:space="preserve">ad verticem pertinent, vbicunque centrum horolo-
              <lb/>
            gij exiſtat, perpetuo arcus ſignorum borealium inter centrum, & </s>
            <s xml:id="echoid-s26250" xml:space="preserve">æquinoctialem lineam continentur. </s>
            <s xml:id="echoid-s26251" xml:space="preserve">Id
              <lb/>
            quod ex poſteriorib{us} duob{us} Analemmatib{us} liquido conſtat. </s>
            <s xml:id="echoid-s26252" xml:space="preserve">In tertio enim puncta quadrantis borea
              <lb/>
            lis H F, vmbr{as} ſu{as} proijciunt in portionem meridianæ lineæ M N, inter cẽtrum M, & </s>
            <s xml:id="echoid-s26253" xml:space="preserve">punctum N,
              <lb/>
            lineæ æquinoctialis: </s>
            <s xml:id="echoid-s26254" xml:space="preserve">Idem{q́ue} cernitur in quadrante boreali F I, quarti Analemmatis, vbi in media no-
              <lb/>
            cte proijciuntur vmbræ in portionem lineæ meridianæ M N, inter centrum & </s>
            <s xml:id="echoid-s26255" xml:space="preserve">lineam æquinoctialem:
              <lb/>
            </s>
            <s xml:id="echoid-s26256" xml:space="preserve">Neque obſtat, quòd aliquando puncta quædam ſemicirculi borealis H F I, in vtroque Analemmate po-
              <lb/>
            ſteriori proijciant quoque vmbr{as} ſu{as} vltra centrum M, vt in quadrante F H, quarti Analemmatis
              <lb/>
            contingit, quia tunc arc{us} ſignorum ſunt Ellipſes, ita vt ſinguli in duob{us} punctis meridianam lineam ſe
              <lb/>
              <note position="left" xlink:label="note-0415-04" xlink:href="note-0415-04a" xml:space="preserve">30</note>
            cent, quorum vnum neceſſario inter centrum, & </s>
            <s xml:id="echoid-s26257" xml:space="preserve">æquinoctialem lineam exiſtit; </s>
            <s xml:id="echoid-s26258" xml:space="preserve">adeò vt verum ſemper
              <lb/>
            ſit, arc{us} contentos inter centrum, & </s>
            <s xml:id="echoid-s26259" xml:space="preserve">æquinoctialem lineam pertinere ad ſigna borealia. </s>
            <s xml:id="echoid-s26260" xml:space="preserve">Quòd ſi horolo
              <lb/>
            gium it a ex parte auſtrali eleuatum ſit, vt arc{us} Meridiani inter ipſum, & </s>
            <s xml:id="echoid-s26261" xml:space="preserve">Horizontem ęqualis ſit al-
              <lb/>
            titudini Aequatoris, ſeu complemento altitudinis poli, ac proinde linea meridiana M N, diametro Ae-
              <lb/>
            quatoris H I, ęquidiſtet, perſpicuum quoque eſt, tunc arc{us} ſignorum prope centrum pertinere ad bo-
              <lb/>
            realia ſigna, propterea quòd vmbræ punctorum ſemicirculi borealis H F I, cadunt in meridianam lineã,
              <lb/>
            in cui{us} medio centrum M, existit, vt patet.</s>
            <s xml:id="echoid-s26262" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s26263" xml:space="preserve">IN horologijs, quæ ad Nadir ſpectant, hoc eſt, in Inferiorib{us}, contrarium prorſ{us} intelligendum
              <lb/>
            eſt, vt eadem quatuor Analemmata demonſtrant.</s>
            <s xml:id="echoid-s26264" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s26265" xml:space="preserve">RVRSVS arcus ſignorum in illis horologijs, in quib{us} horariæ lineæ parallelæ ſunt, cuiuſmodi est
              <lb/>
              <note position="left" xlink:label="note-0415-05" xlink:href="note-0415-05a" xml:space="preserve">40</note>
              <note position="right" xlink:label="note-0415-06" xlink:href="note-0415-06a" xml:space="preserve">Qui arcus R-
                <lb/>
              gnorũ ſint hy-
                <lb/>
              perbolæ, & qui
                <lb/>
              parabolæ, vel
                <lb/>
              Ellipſes.</note>
            horologium tertium præcedenti propoſ. </s>
            <s xml:id="echoid-s26266" xml:space="preserve">deſcriptum, omnes ſunt hyperbolæ, quemadmodum in Polari ho
              <lb/>
            rologio, vt ad propoſ. </s>
            <s xml:id="echoid-s26267" xml:space="preserve">38. </s>
            <s xml:id="echoid-s26268" xml:space="preserve">præcedentis libri dictum est. </s>
            <s xml:id="echoid-s26269" xml:space="preserve">Eadem enim hic eſt ratio. </s>
            <s xml:id="echoid-s26270" xml:space="preserve">In alijs autem iudica
              <lb/>
            bim{us}, vt in propoſ. </s>
            <s xml:id="echoid-s26271" xml:space="preserve">2. </s>
            <s xml:id="echoid-s26272" xml:space="preserve">eiuſdem libri tradidim{us}, quinam arc{us} ſint hyperbolæ, qui parabolæ, & </s>
            <s xml:id="echoid-s26273" xml:space="preserve">qui El-
              <lb/>
            lipſes. </s>
            <s xml:id="echoid-s26274" xml:space="preserve">Vel certè idem ex propoſ. </s>
            <s xml:id="echoid-s26275" xml:space="preserve">4. </s>
            <s xml:id="echoid-s26276" xml:space="preserve">5. </s>
            <s xml:id="echoid-s26277" xml:space="preserve">6. </s>
            <s xml:id="echoid-s26278" xml:space="preserve">& </s>
            <s xml:id="echoid-s26279" xml:space="preserve">7. </s>
            <s xml:id="echoid-s26280" xml:space="preserve">primi libri petatur.</s>
            <s xml:id="echoid-s26281" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s26282" xml:space="preserve">QVOD ſi ex figura radiorum Zodiaci maius, aut minus horologium deſcribendum ſit, pro datalon
              <lb/>
              <note position="right" xlink:label="note-0415-07" xlink:href="note-0415-07a" xml:space="preserve">Qua ratione ex
                <lb/>
              figura radiorũ
                <lb/>
              ad datam ſtyli
                <lb/>
              longitudinem
                <lb/>
              maius au mi-
                <lb/>
              nus horologiũ
                <lb/>
              deſcribatur.</note>
            gitudine gnomonis, fiet id hoc modo. </s>
            <s xml:id="echoid-s26283" xml:space="preserve">Deſcribatur ſeorſum, veluti iuxta figuram radiorum huius propoſ.
              <lb/>
            </s>
            <s xml:id="echoid-s26284" xml:space="preserve">factum eſt, triangulum ρ I G, ex horologio, quod in propoſ. </s>
            <s xml:id="echoid-s26285" xml:space="preserve">præcedenti conſtruximus, vel ex ipſa figura
              <lb/>
            radiorum deſumptum, in quo axis mundi eſt ρ I; </s>
            <s xml:id="echoid-s26286" xml:space="preserve">Aequator I G; </s>
            <s xml:id="echoid-s26287" xml:space="preserve">linea styli, in quam gnomon I K, ad an-
              <lb/>
            gulos rectos cadit ρ G. </s>
            <s xml:id="echoid-s26288" xml:space="preserve">Deinde productis rectis I ρ, I G, I K, ſi ſumatur in I K, recta I A, dato gno-
              <lb/>
            moni æqualis, ſiue is maior existat ſtylo I K, ſiue minor, & </s>
            <s xml:id="echoid-s26289" xml:space="preserve">per A, ipſi ρ G, parallela agatur B D, erit
              <lb/>
            triangulum B I D, triangulo ρ I G, per coroll. </s>
            <s xml:id="echoid-s26290" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s26291" xml:space="preserve">4. </s>
            <s xml:id="echoid-s26292" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s26293" xml:space="preserve">6. </s>
            <s xml:id="echoid-s26294" xml:space="preserve">Eucl. </s>
            <s xml:id="echoid-s26295" xml:space="preserve">ſimile. </s>
            <s xml:id="echoid-s26296" xml:space="preserve">Itaque ſi axis I B, transſera-
              <lb/>
              <note position="left" xlink:label="note-0415-08" xlink:href="note-0415-08a" xml:space="preserve">50</note>
            tur in figuram radiorum ex ρ, vſque ad B, verſus I, & </s>
            <s xml:id="echoid-s26297" xml:space="preserve">reliqua fiant, vt in ſcholio propoſ. </s>
            <s xml:id="echoid-s26298" xml:space="preserve">2. </s>
            <s xml:id="echoid-s26299" xml:space="preserve">huius libri
              <lb/>
            præcepimus, mutando ſemper literam C, ibi poſitam in literam ρ, hic notatam, deſcribentur arcus ſigno
              <lb/>
            rum pro magnitudine ſtyli dati I A, & </s>
            <s xml:id="echoid-s26300" xml:space="preserve">c.</s>
            <s xml:id="echoid-s26301" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1331" type="section" level="1" n="320">
          <head xml:id="echoid-head331" xml:space="preserve">PROBLEMA 39. PROPOSITIQ 39.</head>
          <p>
            <s xml:id="echoid-s26302" xml:space="preserve">PARALLELOS arcuum diurnorum in eodem horologio de-
              <lb/>
            clinante ſimul & </s>
            <s xml:id="echoid-s26303" xml:space="preserve">inclinato delineare.</s>
            <s xml:id="echoid-s26304" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
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