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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          <p>
            <s xml:id="echoid-s16130" xml:space="preserve">
              <pb o="238" file="0256" n="256" rhead="GNOMONICES"/>
            per E, & </s>
            <s xml:id="echoid-s16131" xml:space="preserve">puncta diuiſionum ductæ communes ſectiones circulorum horariorum à meridie, vel
              <lb/>
            media nocte, ac Æquatoris; </s>
            <s xml:id="echoid-s16132" xml:space="preserve">cum Æquator, & </s>
            <s xml:id="echoid-s16133" xml:space="preserve">circulus F G H I, circa idem centrum E, deſcripti
              <lb/>
            in arcus ſimiles ſecentur à dictis rectis, vt conſtat ex iis, quæ ad finem cap. </s>
            <s xml:id="echoid-s16134" xml:space="preserve">1. </s>
            <s xml:id="echoid-s16135" xml:space="preserve">in ſphæram ſcripſi-
              <lb/>
              <figure xlink:label="fig-0256-01" xlink:href="fig-0256-01a" number="179">
                <image file="0256-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0256-01"/>
              </figure>
            mus: </s>
            <s xml:id="echoid-s16136" xml:space="preserve">Nempe G I,
              <lb/>
            pſi A C, parallela,
              <lb/>
            cõmunis ſectio Æ-
              <lb/>
            quatoris, & </s>
            <s xml:id="echoid-s16137" xml:space="preserve">circuli
              <lb/>
            horæ 12. </s>
            <s xml:id="echoid-s16138" xml:space="preserve">ſeu Meri-
              <lb/>
            diani. </s>
            <s xml:id="echoid-s16139" xml:space="preserve">Nam com-
              <lb/>
            munes ſectiones Me
              <lb/>
              <note position="left" xlink:label="note-0256-01" xlink:href="note-0256-01a" xml:space="preserve">10</note>
            ridiani, hoc eſt cir-
              <lb/>
            culi horæ 12. </s>
            <s xml:id="echoid-s16140" xml:space="preserve">& </s>
            <s xml:id="echoid-s16141" xml:space="preserve">pla-
              <lb/>
            ni horologii factæ
              <lb/>
            ab Aequatore paral-
              <lb/>
            lelę ſunt, atque adeo
              <lb/>
            cum A C, ſit cõmu-
              <lb/>
            nis ſectio Æquato-
              <lb/>
            ris, ac plani horolo-
              <lb/>
            gii, vt oſtendimus,
              <lb/>
            erit G I, communis
              <lb/>
              <note position="left" xlink:label="note-0256-02" xlink:href="note-0256-02a" xml:space="preserve">20</note>
            ſectio Æquatoris, & </s>
            <s xml:id="echoid-s16142" xml:space="preserve">
              <lb/>
            Meridiani, ſeu circu
              <lb/>
            li horæ 12. </s>
            <s xml:id="echoid-s16143" xml:space="preserve">K L, cõ-
              <lb/>
            munis ſectio Æqua-
              <lb/>
            toris, & </s>
            <s xml:id="echoid-s16144" xml:space="preserve">circuli horę
              <lb/>
            11. </s>
            <s xml:id="echoid-s16145" xml:space="preserve">in horologio ad
              <lb/>
            ortum ſpectante; </s>
            <s xml:id="echoid-s16146" xml:space="preserve">at
              <lb/>
            in eo quod in occa-
              <lb/>
            ſum vergit, commu-
              <lb/>
            nis ſectio Æquatoris, & </s>
            <s xml:id="echoid-s16147" xml:space="preserve">circuli horæ primæ, & </s>
            <s xml:id="echoid-s16148" xml:space="preserve">ſic deinceps; </s>
            <s xml:id="echoid-s16149" xml:space="preserve">vt cõſtat, ſi diligenter circuli F G H I,
              <lb/>
              <note position="left" xlink:label="note-0256-03" xlink:href="note-0256-03a" xml:space="preserve">30</note>
            vel Æquatoris propria poſitio conſideretur in vtriuſque horologii Meridiani plano. </s>
            <s xml:id="echoid-s16150" xml:space="preserve">Quamobrem
              <lb/>
            circuli horarii à meridie, vel media nocte ſecabunt æquinoctialem lineam A C, in plano horolo-
              <lb/>
            gii in punctis, in quæ cadunt rectæ per centrum E, & </s>
            <s xml:id="echoid-s16151" xml:space="preserve">puncta diuiſionum circuli F G H I, eductæ;
              <lb/>
            </s>
            <s xml:id="echoid-s16152" xml:space="preserve">ac proinde per hæc puncta ducentur communes ſectiones eorundem circulorum horariorum, & </s>
            <s xml:id="echoid-s16153" xml:space="preserve">
              <lb/>
            plani horologii, quæ quidem ſunt horariæ lineæ à meridie, vel media nocte. </s>
            <s xml:id="echoid-s16154" xml:space="preserve">Cum ergo ex coroll. </s>
            <s xml:id="echoid-s16155" xml:space="preserve">
              <lb/>
            propoſ. </s>
            <s xml:id="echoid-s16156" xml:space="preserve">22. </s>
            <s xml:id="echoid-s16157" xml:space="preserve">ſuperioris lib. </s>
            <s xml:id="echoid-s16158" xml:space="preserve">hæ lineæ horariæ parallelæ ſint in Meridiano horologio, perſpicuum eſt
              <lb/>
            rectas, quæ per puncta lineæ A C, ipſi D E, parallelæ aguntur, lineas horarias eſſe à meridie, vel me
              <lb/>
            dia nocte. </s>
            <s xml:id="echoid-s16159" xml:space="preserve">Sed dubitabit fortaſſe quiſpiam, an lineæ horarum à mer. </s>
            <s xml:id="echoid-s16160" xml:space="preserve">vel med. </s>
            <s xml:id="echoid-s16161" xml:space="preserve">noc. </s>
            <s xml:id="echoid-s16162" xml:space="preserve">ſint perpendi-
              <lb/>
            culares ad lineam æquinoctialem A C; </s>
            <s xml:id="echoid-s16163" xml:space="preserve">atqueadeo parallelæ ipſi D E, quæ perpendicularis du-
              <lb/>
            cta eſt ad A C, quemadmodum eas nos duximus: </s>
            <s xml:id="echoid-s16164" xml:space="preserve">demonſtrabimus & </s>
            <s xml:id="echoid-s16165" xml:space="preserve">hoc hac ratione. </s>
            <s xml:id="echoid-s16166" xml:space="preserve">Quo-
              <lb/>
              <note position="left" xlink:label="note-0256-04" xlink:href="note-0256-04a" xml:space="preserve">40</note>
            niam tam planum horologii, quàm planum cuiuſuis circuli horarii à mer. </s>
            <s xml:id="echoid-s16167" xml:space="preserve">vel med. </s>
            <s xml:id="echoid-s16168" xml:space="preserve">noc. </s>
            <s xml:id="echoid-s16169" xml:space="preserve">rectum
              <lb/>
            eſtad Æquatorem, erit quoque communis illorum ſectio ad eundem Æquatorem perpendicula-
              <lb/>
              <note position="left" xlink:label="note-0256-05" xlink:href="note-0256-05a" xml:space="preserve">19. vndec.</note>
            ris, atque adeo, per defin. </s>
            <s xml:id="echoid-s16170" xml:space="preserve">3. </s>
            <s xml:id="echoid-s16171" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s16172" xml:space="preserve">11. </s>
            <s xml:id="echoid-s16173" xml:space="preserve">Eucl. </s>
            <s xml:id="echoid-s16174" xml:space="preserve">& </s>
            <s xml:id="echoid-s16175" xml:space="preserve">ad rectam A C, in Æquatore exiſtentem. </s>
            <s xml:id="echoid-s16176" xml:space="preserve">Igitur omnes
              <lb/>
            lineæ horariæ à mer. </s>
            <s xml:id="echoid-s16177" xml:space="preserve">vel med. </s>
            <s xml:id="echoid-s16178" xml:space="preserve">noc. </s>
            <s xml:id="echoid-s16179" xml:space="preserve">nempe communes ſectiones circulorum horariorum & </s>
            <s xml:id="echoid-s16180" xml:space="preserve">plani
              <lb/>
            horologii ad rectam A C, perpendiculares ſunt: </s>
            <s xml:id="echoid-s16181" xml:space="preserve">Ac proinde cum per puncta inuenta in recta A C,
              <lb/>
              <note position="left" xlink:label="note-0256-06" xlink:href="note-0256-06a" xml:space="preserve">29. primi.</note>
            ducendæ ſint, recte eas per illa puncta parallelas ipſi D E, quæ ad A C, perpẽdicularis eſt, duximus:
              <lb/>
            </s>
            <s xml:id="echoid-s16182" xml:space="preserve">quia hac ratione omnes ad A C, perpendiculares erunt. </s>
            <s xml:id="echoid-s16183" xml:space="preserve">Quod idem hac ratione demonſtrabitur. </s>
            <s xml:id="echoid-s16184" xml:space="preserve">
              <lb/>
            Quoniam ſectiones factæ in Meridiano & </s>
            <s xml:id="echoid-s16185" xml:space="preserve">plano horologii ab Horizonte parallelæ ſunt; </s>
            <s xml:id="echoid-s16186" xml:space="preserve">Item ſe-
              <lb/>
              <note position="left" xlink:label="note-0256-07" xlink:href="note-0256-07a" xml:space="preserve">10. vndec.</note>
            ctiones factæ in eiſdẽ planis à circulo horæ 6. </s>
            <s xml:id="echoid-s16187" xml:space="preserve">erit angulus ſub illis contentus in Meridiano æqua
              <lb/>
              <note position="left" xlink:label="note-0256-08" xlink:href="note-0256-08a" xml:space="preserve">16. vndec.</note>
            lis angulo comprehenſo ſub his in plano horologii. </s>
            <s xml:id="echoid-s16188" xml:space="preserve">Cum ergo ille ſit angulus altitudinis poli,
              <lb/>
              <note position="left" xlink:label="note-0256-09" xlink:href="note-0256-09a" xml:space="preserve">50</note>
            vt conſtat, erit quoque hic angulus altitudinis poli. </s>
            <s xml:id="echoid-s16189" xml:space="preserve">Quocirca cum angulus B A D, ſit angulus al-
              <lb/>
            titudinis poli, propterea quòd, per conſtructionem, reliquus ex recto B A C, æqualis eſt comple-
              <lb/>
            mento altitudinis poli; </s>
            <s xml:id="echoid-s16190" xml:space="preserve">& </s>
            <s xml:id="echoid-s16191" xml:space="preserve">A B, ſit communis ſectio plani horologii & </s>
            <s xml:id="echoid-s16192" xml:space="preserve">Horizontis, erit A D, com-
              <lb/>
            munis ſectio eiuſdem plani horologii, & </s>
            <s xml:id="echoid-s16193" xml:space="preserve">circuli horæ 6. </s>
            <s xml:id="echoid-s16194" xml:space="preserve">à mer. </s>
            <s xml:id="echoid-s16195" xml:space="preserve">vel med. </s>
            <s xml:id="echoid-s16196" xml:space="preserve">noc. </s>
            <s xml:id="echoid-s16197" xml:space="preserve">Ac proinde cum om
              <lb/>
            nes lineæ horariæ ſint inter ſe parallelæ, ac idcirco & </s>
            <s xml:id="echoid-s16198" xml:space="preserve">ipſi A D, æquidiſtent, vt oſtendimus; </s>
            <s xml:id="echoid-s16199" xml:space="preserve">erunt
              <lb/>
            omnes ad A C, perpendiculares, quemadmodum & </s>
            <s xml:id="echoid-s16200" xml:space="preserve">ipſa A D, ad A C, perpendicularis eſt. </s>
            <s xml:id="echoid-s16201" xml:space="preserve">Sola li-
              <lb/>
              <note position="left" xlink:label="note-0256-10" xlink:href="note-0256-10a" xml:space="preserve">29. primi.</note>
            nea meridiana, vel horæ 12. </s>
            <s xml:id="echoid-s16202" xml:space="preserve">à mer. </s>
            <s xml:id="echoid-s16203" xml:space="preserve">vel med. </s>
            <s xml:id="echoid-s16204" xml:space="preserve">noc. </s>
            <s xml:id="echoid-s16205" xml:space="preserve">deſcribi in hoc horologio n
              <unsure/>
            on poteſt, ſed euane-
              <lb/>
              <note position="left" xlink:label="note-0256-11" xlink:href="note-0256-11a" xml:space="preserve">Linea meridia-
                <lb/>
              na, ſeu horæ 12.
                <lb/>
              deſcribi nequit
                <lb/>
              in Meridiano
                <lb/>
              horologio.</note>
            ſcit, vt liquido conſtat ex ſcholio propoſ. </s>
            <s xml:id="echoid-s16206" xml:space="preserve">11. </s>
            <s xml:id="echoid-s16207" xml:space="preserve">primi libri, cum Meridianus circulus planum ho-
              <lb/>
            rologii non ſecet, ſed ei æquidiſtet. </s>
            <s xml:id="echoid-s16208" xml:space="preserve">Itaque horologium Aſtronomicum Meridianum conſtitui-
              <lb/>
            mus, &</s>
            <s xml:id="echoid-s16209" xml:space="preserve">c. </s>
            <s xml:id="echoid-s16210" xml:space="preserve">Quod erat faciendum.</s>
            <s xml:id="echoid-s16211" xml:space="preserve"/>
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