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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            <s xml:id="echoid-s34239" xml:space="preserve">
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            ctus, & </s>
            <s xml:id="echoid-s34240" xml:space="preserve">ad orientem vergens, (poſito Meridiano in proprio ſitu) erit is omnino æqualis ſemicir-
              <lb/>
            culo F H G, propter eandem diametrum F G, in vtroque ſemicirculo. </s>
            <s xml:id="echoid-s34241" xml:space="preserve">Quare recte poterit hic
              <lb/>
            pro illo accipi, ita vt F H G, fungatur officio ſemicirculi Aequatoris orientalis, quem videlicet
              <lb/>
            Meridianus ab occidentali reliquo ſeparat: </s>
            <s xml:id="echoid-s34242" xml:space="preserve">Eritq́ue F H, quadrans Aequatoris orientalis ſupra
              <lb/>
              <figure xlink:label="fig-0548-01" xlink:href="fig-0548-01a" number="334">
                <image file="0548-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0548-01"/>
              </figure>
            terram, alter vero H G, quadrans
              <lb/>
            orientalis infra terram, ita vt re-
              <lb/>
            cta E H, communis ſectio ſit Ho-
              <lb/>
            rizontis, & </s>
            <s xml:id="echoid-s34243" xml:space="preserve">ſemicirculi Acquato-
              <lb/>
            ris orientalis. </s>
            <s xml:id="echoid-s34244" xml:space="preserve">Quod facile perci-
              <lb/>
            pietur, ſi ſemicirculus Aequato-
              <lb/>
              <note position="left" xlink:label="note-0548-01" xlink:href="note-0548-01a" xml:space="preserve">10</note>
            ris F H G, concipiatur conuerti
              <lb/>
            circa diametrum F G, donec re-
              <lb/>
            ctus inſiſtat plano Meridiani; </s>
            <s xml:id="echoid-s34245" xml:space="preserve">ſi-
              <lb/>
            militer & </s>
            <s xml:id="echoid-s34246" xml:space="preserve">ſemicirculus Horizon
              <lb/>
            tis ſupra diametrum B D, poſitus
              <lb/>
            ad idem planum Meridiani re-
              <lb/>
            ctus. </s>
            <s xml:id="echoid-s34247" xml:space="preserve">Erit enim tunc communis
              <lb/>
            horum ſemicirculorum ſectio ad
              <lb/>
            idem planum Meridiani perpen-
              <lb/>
            dicularis; </s>
            <s xml:id="echoid-s34248" xml:space="preserve">atque adeo, per defin.
              <lb/>
            </s>
            <s xml:id="echoid-s34249" xml:space="preserve">
              <note position="left" xlink:label="note-0548-02" xlink:href="note-0548-02a" xml:space="preserve">19. vndec.</note>
              <note position="left" xlink:label="note-0548-03" xlink:href="note-0548-03a" xml:space="preserve">20</note>
            3. </s>
            <s xml:id="echoid-s34250" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s34251" xml:space="preserve">11. </s>
            <s xml:id="echoid-s34252" xml:space="preserve">Eucl. </s>
            <s xml:id="echoid-s34253" xml:space="preserve">& </s>
            <s xml:id="echoid-s34254" xml:space="preserve">ad rectam F G.
              <lb/>
            </s>
            <s xml:id="echoid-s34255" xml:space="preserve">Quocirca recta E H, ad F G, per-
              <lb/>
            pendicularis cõmunis ſectio erit
              <lb/>
            Aequatoris, & </s>
            <s xml:id="echoid-s34256" xml:space="preserve">Horizontis. </s>
            <s xml:id="echoid-s34257" xml:space="preserve">Nulla
              <lb/>
            cnim alia recta in plano ſemicir-
              <lb/>
            culi Aequatoris F H G, ad F G, in
              <lb/>
            E, perpendicularis eſſe poteſt,
              <lb/>
            pręter E H; </s>
            <s xml:id="echoid-s34258" xml:space="preserve">quod tamen requiri-
              <lb/>
            tur ad communem ſectionem Horizontis, & </s>
            <s xml:id="echoid-s34259" xml:space="preserve">Aequatoris, vt diximus. </s>
            <s xml:id="echoid-s34260" xml:space="preserve">Itaque cum quadrans Ae-
              <lb/>
            quatoris F H, tendat ab ortu, qui in H, vbi Horizon Aequatorem interſecat, ponitur, ad meridiem
              <lb/>
              <note position="left" xlink:label="note-0548-04" xlink:href="note-0548-04a" xml:space="preserve">30</note>
            vſque, qui in F, ponitur, vbi Aequator Meridianum ſecat, poterit non incongrue idem quadrans
              <lb/>
            gerere vices alterius quadrantis, qui à meridie F, incipit, & </s>
            <s xml:id="echoid-s34261" xml:space="preserve">in occaſu finitur, ita vt H, ſit etiam pun
              <lb/>
            ctum occaſus. </s>
            <s xml:id="echoid-s34262" xml:space="preserve">Habet enim quadrans Aequatoris occidentalis eandem prorſus poſitionem in ſphę
              <lb/>
            ra, quam orientalis: </s>
            <s xml:id="echoid-s34263" xml:space="preserve">Atque hac ratione quadrans F H, repręſentabit nobis totum ſemicirculum
              <lb/>
            Aequatoris ſupra terram.</s>
            <s xml:id="echoid-s34264" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s34265" xml:space="preserve">STATVATVR igitur Sol in alterutro æquinoctiorum in puncto K, æquinoctialis circu-
              <lb/>
              <note position="left" xlink:label="note-0548-05" xlink:href="note-0548-05a" xml:space="preserve">Inuentio ſex di
                <lb/>
              ctarum circun-
                <lb/>
              ferentiarum ex
                <lb/>
              Analemmate,
                <lb/>
              Sole exiſten te
                <lb/>
              in Aequatore.</note>
            li, ſiue illud punctum terminet horam aliquam à mer. </s>
            <s xml:id="echoid-s34266" xml:space="preserve">vel med. </s>
            <s xml:id="echoid-s34267" xml:space="preserve">noc. </s>
            <s xml:id="echoid-s34268" xml:space="preserve">ſiue ab or. </s>
            <s xml:id="echoid-s34269" xml:space="preserve">vel occ. </s>
            <s xml:id="echoid-s34270" xml:space="preserve">aut certe
              <lb/>
            particulam aliquam horæ, ita vt H K, ſit arcus Aequatoris inter centrum Solis, atque Horizon-
              <lb/>
            tem ſiue ex parte orientis, ſiue occidentis interiectus; </s>
            <s xml:id="echoid-s34271" xml:space="preserve">arcus vero Aequatoris F K, poſitus ſit inter
              <lb/>
            Meridianum, & </s>
            <s xml:id="echoid-s34272" xml:space="preserve">centrum Solis ſiue ex parte orientis, ſiue occidentis: </s>
            <s xml:id="echoid-s34273" xml:space="preserve">inquirendumq́ue ſit Geo-
              <lb/>
              <note position="left" xlink:label="note-0548-06" xlink:href="note-0548-06a" xml:space="preserve">40</note>
            metrice ex Analem mate, quantæ ſint eo temp
              <unsure/>
            ore ſex expoſitæ circunferentiæ. </s>
            <s xml:id="echoid-s34274" xml:space="preserve">Ducatur ex K, pun
              <lb/>
            cto datæ horæ, vbi Sol ponitur, recta K L, ad F G, diametrum Aequatoris perpendicularis; </s>
            <s xml:id="echoid-s34275" xml:space="preserve">& </s>
            <s xml:id="echoid-s34276" xml:space="preserve">per
              <lb/>
            L, excitentur ad B E, A E, duæ perpendiculares N L M, O L P: </s>
            <s xml:id="echoid-s34277" xml:space="preserve">Ex quibus, quoniam maiores ſunt
              <lb/>
            recta k L, (Nam ductis rectis E K, E M, E P; </s>
            <s xml:id="echoid-s34278" xml:space="preserve">quoniam quadrata earum æqualia inter ſe ſunt, eſtq́;
              <lb/>
            </s>
            <s xml:id="echoid-s34279" xml:space="preserve">quadratum ex E K, æquale duobus quadratis ſimul ex E L, L K, & </s>
            <s xml:id="echoid-s34280" xml:space="preserve">quadratum ex E M, duobus
              <lb/>
              <note position="left" xlink:label="note-0548-07" xlink:href="note-0548-07a" xml:space="preserve">47. primi.</note>
            quadratis ex E N, N M, & </s>
            <s xml:id="echoid-s34281" xml:space="preserve">quadratum ex E P, duobus quadratis ex E O, O P; </s>
            <s xml:id="echoid-s34282" xml:space="preserve">erunt duo quadrata
              <lb/>
            ex E L, L K, æqualia tam duobus quadratis ex E N, N M, quàm duobus ex E O, O P. </s>
            <s xml:id="echoid-s34283" xml:space="preserve">Cum igitur
              <lb/>
            & </s>
            <s xml:id="echoid-s34284" xml:space="preserve">quadratum ex E N, & </s>
            <s xml:id="echoid-s34285" xml:space="preserve">ex E O, minus ſit quadrato ex E L, quòd tam linea E N, quàm E O, minor
              <lb/>
              <note position="left" xlink:label="note-0548-08" xlink:href="note-0548-08a" xml:space="preserve">19. primi.</note>
            ſit in triangulis rectangulis E L N, E L O, recta E L; </s>
            <s xml:id="echoid-s34286" xml:space="preserve">erit tam reliquum quadratum rectæ N M,
              <lb/>
            quàm rectæ O P, maius quadrato reliquo rectę L K; </s>
            <s xml:id="echoid-s34287" xml:space="preserve">atque ob id vtrauis recta N M, O P, maior erit
              <lb/>
              <note position="left" xlink:label="note-0548-09" xlink:href="note-0548-09a" xml:space="preserve">50</note>
            quàm recta L K) abſcindantur ipſi K L, duæ æquales N Q, O R; </s>
            <s xml:id="echoid-s34288" xml:space="preserve">atque per puncta Q, R, ex cen
              <lb/>
            tro E, duæ rectæ educantur E Q S, E R T, ſecantes circunferentiam Meridiani in S, & </s>
            <s xml:id="echoid-s34289" xml:space="preserve">T. </s>
            <s xml:id="echoid-s34290" xml:space="preserve">Quibus
              <lb/>
            rite peractis, inuentæ erunt omnes dictæ ſex circun ferentiæ ad tempus propo ſitum, cum nimirum
              <lb/>
            Sol in puncto Aequatoris K, exiſtit. </s>
            <s xml:id="echoid-s34291" xml:space="preserve">Nam, vt in ſequenti cap. </s>
            <s xml:id="echoid-s34292" xml:space="preserve">demonſtrabimus, H K, erit circunfe-
              <lb/>
            rentia hectemoria; </s>
            <s xml:id="echoid-s34293" xml:space="preserve">B M, horaria; </s>
            <s xml:id="echoid-s34294" xml:space="preserve">A P, deſcenſiua; </s>
            <s xml:id="echoid-s34295" xml:space="preserve">B F, meridiana; </s>
            <s xml:id="echoid-s34296" xml:space="preserve">A T, Verticalis; </s>
            <s xml:id="echoid-s34297" xml:space="preserve">& </s>
            <s xml:id="echoid-s34298" xml:space="preserve">A S, hori-
              <lb/>
            zontalis. </s>
            <s xml:id="echoid-s34299" xml:space="preserve">Aliorum porro linea mentorum huius figuræ, cuiuſmodi ſunt lineæ F Y, S V, T X, F Z,
              <lb/>
            K N, K O, vſus apparebit in cap. </s>
            <s xml:id="echoid-s34300" xml:space="preserve">7. </s>
            <s xml:id="echoid-s34301" xml:space="preserve">huius lib.</s>
            <s xml:id="echoid-s34302" xml:space="preserve"/>
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          <head xml:id="echoid-head499" style="it" xml:space="preserve">SCHOLIVM.</head>
          <p style="it">
            <s xml:id="echoid-s34303" xml:space="preserve">EX dictis patet ratio, qua, Sole exiſtente in Aequatore, ſeorſum inueſtigari poſſit quæcunque </s>
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