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-s42993" xml:space="preserve">
              <pb o="653" file="0669" n="669" rhead="LIBER OCTAVVS."/>
            multumq́ue perueſtigaſſem, occurrit tandem mihi demonſtratio, quam libuit Appendicis loco
              <lb/>
              <note position="right" xlink:label="note-0669-01" xlink:href="note-0669-01a" xml:space="preserve">Inuen io decli-
                <lb/>
              nationum om-
                <lb/>
              nium arcuum
                <lb/>
              diurnorum f
                <unsure/>
              a-
                <lb/>
              cilima una cum
                <lb/>
              demonſtratio
                <unsure/>
              -
                <lb/>
              ne.</note>
            hic ſubiungere. </s>
            <s xml:id="echoid-s42994" xml:space="preserve">Quæ vt planius intelligatur, repetenda erit tota conſtructio. </s>
            <s xml:id="echoid-s42995" xml:space="preserve">Ex A, centro ad
              <lb/>
            interuallum cuiuſlibet rectæ A B, circulus deſcribatur B C G D, in quo ſumantur duo arcus B C,
              <lb/>
            B D, complemento altitudinis poli æquales, ita vt ſi A B, ponatur communis ſectio Æquato-
              <lb/>
            ris, & </s>
            <s xml:id="echoid-s42996" xml:space="preserve">Meridiani, quem refert circulus B C G D, arcus B C, B D, ſint declinationes du@rum
              <lb/>
            parallelorum, quorum al-
              <lb/>
              <figure xlink:label="fig-0669-01" xlink:href="fig-0669-01a" number="430">
                <image file="0669-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0669-01"/>
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            ter, nempequi per C, du-
              <lb/>
            citur, maximus eſt eorum,
              <lb/>
            qui ſemper apparent, @ha-
              <lb/>
            betq́ue arcum diurnum ho
              <lb/>
              <note position="left" xlink:label="note-0669-02" xlink:href="note-0669-02a" xml:space="preserve">10</note>
            rarum 24. </s>
            <s xml:id="echoid-s42997" xml:space="preserve">cum totus ſupra
              <lb/>
            Horizontem extet, alter ve-
              <lb/>
            ro per D, ductus, maximus
              <lb/>
            eorum, qui ſemper occul-
              <lb/>
            tantur, habetq́; </s>
            <s xml:id="echoid-s42998" xml:space="preserve">arcum diur
              <lb/>
            num horarum o, cum to-
              <lb/>
            tus ſub Horizonte lateat.
              <lb/>
            </s>
            <s xml:id="echoid-s42999" xml:space="preserve">Ducta a utem recta C D, ſe-
              <lb/>
            cante rectã A B, in E, erunt
              <lb/>
              <note position="left" xlink:label="note-0669-03" xlink:href="note-0669-03a" xml:space="preserve">20</note>
            rectæ E C, E D, æquales, & </s>
            <s xml:id="echoid-s43000" xml:space="preserve">
              <lb/>
            anguli ad E, recti. </s>
            <s xml:id="echoid-s43001" xml:space="preserve">quod de-
              <lb/>
            monſtrabitur, vt propoſ. </s>
            <s xml:id="echoid-s43002" xml:space="preserve">1.
              <lb/>
            </s>
            <s xml:id="echoid-s43003" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s43004" xml:space="preserve">1. </s>
            <s xml:id="echoid-s43005" xml:space="preserve">in Analemmate de-
              <lb/>
            monſtratum eſt, rectam
              <lb/>
            M N, in O, bifariam, & </s>
            <s xml:id="echoid-s43006" xml:space="preserve">ad
              <lb/>
            angulos rectos ſecari. </s>
            <s xml:id="echoid-s43007" xml:space="preserve">De-
              <lb/>
            ſcripto deinde ex E, circa
              <lb/>
            C D, circulo, eoq́ue diui-
              <lb/>
            ſo in partes 48. </s>
            <s xml:id="echoid-s43008" xml:space="preserve">æquales,
              <lb/>
              <note position="left" xlink:label="note-0669-04" xlink:href="note-0669-04a" xml:space="preserve">30</note>
            cõnectantur quælibet duo puncta à puncto C, vel D, æque remota lineis rectis occultis, quæ
              <lb/>
            omnes ipſi A B, parallelæ erunt, ex ſcholio propoſ. </s>
            <s xml:id="echoid-s43009" xml:space="preserve">27. </s>
            <s xml:id="echoid-s43010" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s43011" xml:space="preserve">3. </s>
            <s xml:id="echoid-s43012" xml:space="preserve">Eucl. </s>
            <s xml:id="echoid-s43013" xml:space="preserve">& </s>
            <s xml:id="echoid-s43014" xml:space="preserve">per puncta, quibus illæ
              <lb/>
            rectam C D, ſecant, ex A, rectæ educantur vſquead circumferentiam C B D. </s>
            <s xml:id="echoid-s43015" xml:space="preserve">Hæ enim abſcin-
              <lb/>
            dent arcus declinationum omnium arcuum diurnorum, ipſæq́ue lineæ radij arcuum diurnorũ
              <lb/>
            erunt, initio ſumpto à radi
              <unsure/>
            o A D, horæ 0. </s>
            <s xml:id="echoid-s43016" xml:space="preserve">& </s>
            <s xml:id="echoid-s43017" xml:space="preserve">progrediendo per radium A B, horarum 12, vſque
              <lb/>
            ad radium A C, horarum 24. </s>
            <s xml:id="echoid-s43018" xml:space="preserve">ita vt proxima linea ipſi A D, ſit radius arcus diurni horæ 1. </s>
            <s xml:id="echoid-s43019" xml:space="preserve">ſequẽs
              <lb/>
            horarum 2. </s>
            <s xml:id="echoid-s43020" xml:space="preserve">& </s>
            <s xml:id="echoid-s43021" xml:space="preserve">ſic deinceps; </s>
            <s xml:id="echoid-s43022" xml:space="preserve">adeo vt quælibet recta ex A, per aliquod punctorum ſemidiametri
              <lb/>
            D E, ducta radium illius arcus diurni referat, qui tot horis à 12. </s>
            <s xml:id="echoid-s43023" xml:space="preserve">horis deficit, quot partibus ex
              <lb/>
            12. </s>
            <s xml:id="echoid-s43024" xml:space="preserve">illis, in quas quadrans D F, diuiſus eſt, punctum illud quadrantis D F, per quod linea ipſi
              <lb/>
            A B, acta parallela punctum illius radij in ſemidiametro D E, offert, à puncto F, diſtat. </s>
            <s xml:id="echoid-s43025" xml:space="preserve">Hoc eſt,
              <lb/>
            vt quemadmodum S T, ipſi A B, æquidiſtans ducitur per punctum S, quatuor duodecimis par-
              <lb/>
              <note position="left" xlink:label="note-0669-05" xlink:href="note-0669-05a" xml:space="preserve">40</note>
            tibus quadrantis D F, à puncto F, remotum, ita recta A T V, ſit radius arcus diurni horarum 8.
              <lb/>
            </s>
            <s xml:id="echoid-s43026" xml:space="preserve">qui nimirum quatuor horis à 12. </s>
            <s xml:id="echoid-s43027" xml:space="preserve">horis deficit, & </s>
            <s xml:id="echoid-s43028" xml:space="preserve">ſic de cæteris. </s>
            <s xml:id="echoid-s43029" xml:space="preserve">Item vt quælibet recta ex A, per
              <lb/>
            aliquod punctorum ſemidiametri C E, ducta radium illius arcus diurni referat, qui tot horis ſu-
              <lb/>
            perat horas 12. </s>
            <s xml:id="echoid-s43030" xml:space="preserve">quot partibus ex illis 12. </s>
            <s xml:id="echoid-s43031" xml:space="preserve">in quas quadrans C F, diuiſus eſt, punctum illud quadran
              <lb/>
            tis C F, per quod linea ipſi A B, acta parallela punctum illius radij in ſemidiametro C E, offert, à
              <lb/>
            puncto F, diſtat. </s>
            <s xml:id="echoid-s43032" xml:space="preserve">Hoc eſt, vt quemadmodum H I, ipſi A B, æquidiſtans ducitur per punctum H,
              <lb/>
            quatuor duodecimis partibus quadrantis C F, à puncto F, remotum, ita recta A I K, radius ſit
              <lb/>
            arcus diurni horarum 16. </s>
            <s xml:id="echoid-s43033" xml:space="preserve">quatuor horis ſuperans horas 12. </s>
            <s xml:id="echoid-s43034" xml:space="preserve">atque ita de reliquis. </s>
            <s xml:id="echoid-s43035" xml:space="preserve">Quod in hunc
              <lb/>
            modum demonſtrabimus.</s>
            <s xml:id="echoid-s43036" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s43037" xml:space="preserve">DVCTA diametro Horizontis D e, ſecet axis a P, radium Aequatoris B A, productum ad
              <lb/>
              <note position="left" xlink:label="note-0669-06" xlink:href="note-0669-06a" xml:space="preserve">50</note>
            angulos rectos in centro A, ſitq́ue polus arcticus n, & </s>
            <s xml:id="echoid-s43038" xml:space="preserve">antarcticus p. </s>
            <s xml:id="echoid-s43039" xml:space="preserve">Ductis quoque K L, V X, dia
              <lb/>
            metris parallelorum, quorum prior oſtendendus eſt habere arcum diurnum horarum 16. </s>
            <s xml:id="echoid-s43040" xml:space="preserve">poſte-
              <lb/>
            rior vero horarum 8. </s>
            <s xml:id="echoid-s43041" xml:space="preserve">deſcribantur circa K L, V X, ex O, Z, ſemicirculi parallelorum K P L, V a X,
              <lb/>
            & </s>
            <s xml:id="echoid-s43042" xml:space="preserve">ex M, Y, punctis, vbi parallelorum diametri ab Horizontis diametro ſecantur, erigantur ad
              <lb/>
            diametros perpendiculares M N, Y b, quæ communes ſectiones erunt parallelorum, & </s>
            <s xml:id="echoid-s43043" xml:space="preserve">Horizon-
              <lb/>
            tis, vt in ſuperioribus demonſtratum eſt: </s>
            <s xml:id="echoid-s43044" xml:space="preserve">atque adeo K N, arcus erit ſemidiurnus paralleli K P L,
              <lb/>
            & </s>
            <s xml:id="echoid-s43045" xml:space="preserve">V b, atcus ſemidiurnus paralleli V a X. </s>
            <s xml:id="echoid-s43046" xml:space="preserve">Quoniam igitur eſt, vt D A, ad A Q, ita D E, ad E I:
              <lb/>
            </s>
            <s xml:id="echoid-s43047" xml:space="preserve">
              <note position="right" xlink:label="note-0669-07" xlink:href="note-0669-07a" xml:space="preserve">2. ſexti.</note>
              <note position="right" xlink:label="note-0669-08" xlink:href="note-0669-08a" xml:space="preserve">11. quinti.</note>
            Item vt D A, ad A Q, ita I R, ad R Q; </s>
            <s xml:id="echoid-s43048" xml:space="preserve">erit quoque vt D E, ad E I, ita I R, ad R Q: </s>
            <s xml:id="echoid-s43049" xml:space="preserve">Vt autem I R,
              <lb/>
            ad R Q, ita eſt, ex ijs, quæ in ſcholio propoſ. </s>
            <s xml:id="echoid-s43050" xml:space="preserve">4. </s>
            <s xml:id="echoid-s43051" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s43052" xml:space="preserve">6. </s>
            <s xml:id="echoid-s43053" xml:space="preserve">Eucl. </s>
            <s xml:id="echoid-s43054" xml:space="preserve">demonſtrauimus, K O, ad O M; </s>
            <s xml:id="echoid-s43055" xml:space="preserve">quòd
              <lb/>
            in triangulo A K M, in quo recta A O, ducta eſt, recta I Q, baſi K M, ęquidiſtet, Igitur erit quo-
              <lb/>
            que, vt D E, ſinus totus circuli C F D, ad E I, ſinum rectum arcus F H, ita K O, ſinus totus </s>
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