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 Notes

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          <pb o="221" file="0241" n="241" rhead="LIBER SECVNDVS."/>
          <p style="it">
            <s xml:id="echoid-s15136" xml:space="preserve">HIS ita demonstratis, facile oſtendemus, rectas E G, L M, M P, & </s>
            <s xml:id="echoid-s15137" xml:space="preserve">quaſcunque alias, in horolo-
              <lb/>
            gio boreali, vel inferiori, eſſe eorundem circulorum maximorum, & </s>
            <s xml:id="echoid-s15138" xml:space="preserve">plani horologij ſectiones communes,
              <lb/>
            quorum ſunt ſectiones in auſtrali, ſuperiorive horologio; </s>
            <s xml:id="echoid-s15139" xml:space="preserve">ſi auſt rale, vel ſuperius horologium in facie bo-
              <lb/>
            reali, vel inferiori plani horologij ita collocetur, vt pars eius ſuperior mutetur in inferiorẽ, & </s>
            <s xml:id="echoid-s15140" xml:space="preserve">pars, quæ
              <lb/>
            in eo ſitu poſt hanc permutationem nobis ad horologium conuerſis dextra eſt, fiat ſinistra, & </s>
            <s xml:id="echoid-s15141" xml:space="preserve">contra.
              <lb/>
            </s>
            <s xml:id="echoid-s15142" xml:space="preserve">Nam ſi horologium auſtrale, ſiue ſuperius intelligatur poni ſupra boreale, ſeu inferius, vt stylus ſtylo
              <lb/>
            congruat, & </s>
            <s xml:id="echoid-s15143" xml:space="preserve">dextra pars ad G, dextræ parti ad H, punctum{q́ue}, A, puncto C, et linea A G, lineæ C H; </s>
            <s xml:id="echoid-s15144" xml:space="preserve">ca-
              <lb/>
            dent puncta G, P, in puncta H, Q, propterea quòd rectæ A G, A P, rectis C H, C Q, oſtenſæ ſunt
              <lb/>
            æquales. </s>
            <s xml:id="echoid-s15145" xml:space="preserve">Quòd ſi in hoc ſitu auſtrale horologium, ſiue ſuperius, circa rectam G P, vel (quod idem eſt)
              <lb/>
            circa H Q, quia hę duæ lineæ in hoc ſitu vnam & </s>
            <s xml:id="echoid-s15146" xml:space="preserve">eandem conſtituunt, conuerti animo concipiamus, vt
              <lb/>
              <note position="left" xlink:label="note-0241-01" xlink:href="note-0241-01a" xml:space="preserve">10</note>
            pars ſuperior fiat inferior, & </s>
            <s xml:id="echoid-s15147" xml:space="preserve">contra, cadent puncta E, L, in puncta F, N, eo quòd rectæ A E, A L,
              <lb/>
            rectis C F, C N, demonſtratæ ſint æquales. </s>
            <s xml:id="echoid-s15148" xml:space="preserve">Quare linea E G, lineæ F H, congruet, quòd puncta E, G,
              <lb/>
            punctis F, H, congruere oſtenderimus; </s>
            <s xml:id="echoid-s15149" xml:space="preserve">& </s>
            <s xml:id="echoid-s15150" xml:space="preserve">linea L M, lineæ N O, & </s>
            <s xml:id="echoid-s15151" xml:space="preserve">linea M P, lineæ O Q, congruet,
              <lb/>
            propterea quòd puncta L, P, in punctis N, Q, existunt, & </s>
            <s xml:id="echoid-s15152" xml:space="preserve">anguli ad L, P, N, Q, oſtenſi ſunt recti.
              <lb/>
            </s>
            <s xml:id="echoid-s15153" xml:space="preserve">Eadem ratione concludemus, quamlibet aliam lineam in horologio australi, vel ſuperiori, ſiue ea ſecet
              <lb/>
            vtramque A E, A G, ſiue alter am tantum, & </s>
            <s xml:id="echoid-s15154" xml:space="preserve">alteri ſit parallela, congruere lineæ ſibi reſpondenti in ho-
              <lb/>
            rologio boreali, ſeu inferiori, ſi illa ſuperpoſitio, & </s>
            <s xml:id="echoid-s15155" xml:space="preserve">permutatio, vt proximè diximus, fiat. </s>
            <s xml:id="echoid-s15156" xml:space="preserve">Quocirca to-
              <lb/>
            tum horologium auſtrale, ſuperiusve toti boreali horologio, ſiue inferiori, ea ratione congruet. </s>
            <s xml:id="echoid-s15157" xml:space="preserve">Cum ergo
              <lb/>
            per illam ſuperpoſitionem, conuerſionem{q́ue}, ſuperior pars auſtralis horologij, ſuperiorisve, fiat inferior,
              <lb/>
            & </s>
            <s xml:id="echoid-s15158" xml:space="preserve">dextra ſiniſtra, vt patet: </s>
            <s xml:id="echoid-s15159" xml:space="preserve">(Nam ſi auſtrale horologium ſeorſum intelligatur conuerti, vt pars ſupe-
              <lb/>
              <note position="left" xlink:label="note-0241-02" xlink:href="note-0241-02a" xml:space="preserve">20</note>
            rior in inferiorem mutetur, remanebit nobis ad horologium conuerſis punctum G, ad ſiniſtram, & </s>
            <s xml:id="echoid-s15160" xml:space="preserve">P, ad
              <lb/>
            dextram. </s>
            <s xml:id="echoid-s15161" xml:space="preserve">Vnde vt recta E G, rectæ F H, congruat, & </s>
            <s xml:id="echoid-s15162" xml:space="preserve">reliquæ lineæ reliquis lineis, neceſſe eſt, partem
              <lb/>
            ſiniſtram G, mutari in dextram, & </s>
            <s xml:id="echoid-s15163" xml:space="preserve">dextram P, in ſiniſtram. </s>
            <s xml:id="echoid-s15164" xml:space="preserve">Ita enim fiet, vt ſingulæ lineæ congruant
              <lb/>
            ſingulis. </s>
            <s xml:id="echoid-s15165" xml:space="preserve">Quod etiam hac ratione fiet perſpicuum. </s>
            <s xml:id="echoid-s15166" xml:space="preserve">Poſtquam recta G P, rectæ H Q, ſuperpoſita eſt,
              <lb/>
            manet quidem punctum G, nobis ad horologium conuerſis ad dexteram, quemadmodum & </s>
            <s xml:id="echoid-s15167" xml:space="preserve">punctum H,
              <lb/>
            borealis, vel inferioris horologij: </s>
            <s xml:id="echoid-s15168" xml:space="preserve">Sed poſt conuerſionem horologij auſtralis, ſuperiorisve, circa rectam
              <lb/>
            G P, vel H Q, vt ſuperiora fiant inferiora, poſitum erit nobis punctum G, ad ſiniſtram, vt dictum eſt,
              <lb/>
            ſi conuertamus faciem ad horologium ipſum: </s>
            <s xml:id="echoid-s15169" xml:space="preserve">quia verò tunc horologium conuerſum est ad meridiem,
              <lb/>
            fit vt eius lineamenta deſcribenda ſint in facie oppoſita, quæ boream reſpicit, atque ita exiſtet n@bis co@
              <lb/>
            uerſis ad faciem borealem horologij idem punctum G, ad dextram) liquido conſtat, ex horologio auſtra-
              <lb/>
              <note position="left" xlink:label="note-0241-03" xlink:href="note-0241-03a" xml:space="preserve">30</note>
            li, vel ſuperiori, ſi fiat omnium partium permutatio, vt ſuperior in inferiorem mutetur, & </s>
            <s xml:id="echoid-s15170" xml:space="preserve">quæ poſt
              <lb/>
            hanc mutationem nobis ad horologium conuerſis dextra eſt, fiat ſiniſtra, & </s>
            <s xml:id="echoid-s15171" xml:space="preserve">contra, fieri horologium bo-
              <lb/>
            reale, ſiue inferius.</s>
            <s xml:id="echoid-s15172" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s15173" xml:space="preserve">QVONIAM verò in prædicta ſuperpoſitione, conuerſione{q́ue} horologij auſtralis, ſuperiorisve, li-
              <lb/>
            nea eius horizontalis horizontali lineæ horologij borealis, ſeu inferioris, cõgruit, (quia inhorologiijs, quo-
              <lb/>
            rum plana ad Horizontem recta ſunt, cuiuſmodi ſunt Verticale, Declinans à
              <unsure/>
            Verticali, & </s>
            <s xml:id="echoid-s15174" xml:space="preserve">Meridia-
              <lb/>
            num, linea horizontalis ducitur per locum ſtyli, at que ita horizontales lineæ erunt A G, C H, quæ ex
              <lb/>
            ipſa ſuperpoſitione ſibi mutuo congruunt: </s>
            <s xml:id="echoid-s15175" xml:space="preserve">In alijs verò horologijs, quorum plana ad Horizontem non
              <lb/>
            ſunt recta, qualia ſunt Polare, Aequinoctiale, Declinans ab Horizonte, Inclinatum ad Horizontem, & </s>
            <s xml:id="echoid-s15176" xml:space="preserve">
              <lb/>
            Declinans à Verticali, quod ſimul ad Horizontem inclinatum eſt, quoniam linea horizontalis cadit in ſu-
              <lb/>
              <note position="left" xlink:label="note-0241-04" xlink:href="note-0241-04a" xml:space="preserve">40</note>
            perioribus quidem ſupra ſtylum, in inferioribus autem infra eundem, eſt{q́ue} ſemper parallela rectæ A G,
              <lb/>
            vt paulo ante demonſtrauimus, fit vt hac ratione horizontalis linea ſuperioris horologij lineæ horizonta-
              <lb/>
            li inferioris etiam congruat; </s>
            <s xml:id="echoid-s15177" xml:space="preserve">quod demonſtrabitur, vt demonſtratum est, rectam L M, congruere rectæ
              <lb/>
            N O,) est portio horologij ſupra lineam horizontalem existens ſuperuacanea in quouis horologio, cum
              <lb/>
            in illam vmbra styli nunquam cadere poſſit interdiu; </s>
            <s xml:id="echoid-s15178" xml:space="preserve">efficitur vniuersè verum eſſe, lineam horizonta-
              <lb/>
            lem in quocunque horologio ad partes ſuperiores portionem auferre, quæ in facie plani horologij oppoſita
              <lb/>
            idem horologium nobis exhibeat, ſi it a collocetur, vt linea horizontalis ſuperiorem locum occupet in fa-
              <lb/>
            cie oppoſita, & </s>
            <s xml:id="echoid-s15179" xml:space="preserve">pars, quę in eo ſitu nobis ad horologium conuerſis dextra est, fiat ſinistra, & </s>
            <s xml:id="echoid-s15180" xml:space="preserve">contra: </s>
            <s xml:id="echoid-s15181" xml:space="preserve">quia
              <lb/>
            facta illa partium permutatione, pars ſupra lineam horizontalem australis horologii collocatur in borea
              <lb/>
            li horologio infra eandem lineam horizontalem, vt manifestum est. </s>
            <s xml:id="echoid-s15182" xml:space="preserve">Quod erat demonstrandum.</s>
            <s xml:id="echoid-s15183" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">50</note>
          <p style="it">
            <s xml:id="echoid-s15184" xml:space="preserve">QVOD ſi quando contingat, lineas in horologio, quæ communes ſectiones ſunt plani horologij, & </s>
            <s xml:id="echoid-s15185" xml:space="preserve">
              <lb/>
            circulorum maximorum, per A, locum styli in australi, vel ſuperiori horologio, & </s>
            <s xml:id="echoid-s15186" xml:space="preserve">per C, locum styli
              <lb/>
            in boreali, inferiorive horologio tranſire, (vt accidit in domibus cœlestibus horologii Verticalis, & </s>
            <s xml:id="echoid-s15187" xml:space="preserve">ho-
              <lb/>
            ris à meridie, vel media nocte, atque Meridianis circulis horologii æquinoctialis, vt perſpicuum fiet ex
              <lb/>
            ſequentibus) nihilominus ſequetur, australe horologium, vel ſuperius congruere boreali, inferiorive, ſi il-
              <lb/>
            li@s partes omnes inuertantur, vt docuimus. </s>
            <s xml:id="echoid-s15188" xml:space="preserve">Circulus enim aliquis maximus in australi horologio, vel
              <lb/>
            ſuperiori, per stylum A B, ductus ſaciat ſectionem R S, per locum ſtyli A, tranſeuntem. </s>
            <s xml:id="echoid-s15189" xml:space="preserve">Secabit idem
              <lb/>
            ci@culus, cum per stylum tranſeat, boreale horologium, ſeu inferius, per rectam T V, per C, locum ſty-
              <lb/>
            li quoque tranſeuntem, in partihus tamen non oppoſitis, ſed correſpondentibus, hoc eſt, ſi ſectio R S, ſu-
              <lb/>
            pra ſiylum vergit ad ſiniſtram, & </s>
            <s xml:id="echoid-s15190" xml:space="preserve">infra ſtylum ad dextram, deflectet ſectio T V, ſupra ſtylum in par-
              <lb/>
            tem dextram, & </s>
            <s xml:id="echoid-s15191" xml:space="preserve">in ſiniſtram infra ſ@ylum, & </s>
            <s xml:id="echoid-s15192" xml:space="preserve">contra. </s>
            <s xml:id="echoid-s15193" xml:space="preserve">Hæ enim partes illis partibus reſpondent, vt </s>
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