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-div524" type="section" level="1" n="144">
          <p style="it">
            <s xml:id="echoid-s10091" xml:space="preserve">
              <pb o="157" file="0177" n="177" rhead="LIBER SECVNDVS."/>
            toris aſſignanda; </s>
            <s xml:id="echoid-s10092" xml:space="preserve">atque adeo horologia horizontalia ex eius Protypo deſcripta falſa eſſe, vbi poli altitu
              <lb/>
            do maior eſt, aut minor, quàm grad. </s>
            <s xml:id="echoid-s10093" xml:space="preserve">45. </s>
            <s xml:id="echoid-s10094" xml:space="preserve">Idem dicendum eſt de V erticalibus horologijs. </s>
            <s xml:id="echoid-s10095" xml:space="preserve">Quamuis enim in
              <lb/>
            illis Orontius recte aſſumat lineam Verticalem F H, & </s>
            <s xml:id="echoid-s10096" xml:space="preserve">axem mundi H K, errat tamen in linea F K,
              <lb/>
            quam pro linea Aequatoris accipit, propterea quòd ea ad axem H K, perpendicularis non eſt, vt
              <lb/>
            demonſtrauimus.</s>
            <s xml:id="echoid-s10097" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s10098" xml:space="preserve">TVRPIVS adhuc lapſus eſt Orontius in propoſ. </s>
            <s xml:id="echoid-s10099" xml:space="preserve">7. </s>
            <s xml:id="echoid-s10100" xml:space="preserve">eiuſdem lib. </s>
            <s xml:id="echoid-s10101" xml:space="preserve">1. </s>
            <s xml:id="echoid-s10102" xml:space="preserve">horologiorum, vbi totum axem
              <lb/>
              <note position="right" xlink:label="note-0177-01" xlink:href="note-0177-01a" xml:space="preserve">Maior errot
                <lb/>
              Orontii.</note>
            A F, inter centrum A, & </s>
            <s xml:id="echoid-s10103" xml:space="preserve">lineam Verticalis circuli F H, interiectũ pro linea Aequatoris accepit, quod
              <lb/>
            nullibi verum eſſe poteſt, cum recta A L, quæ valde inæqualis eſt rectæ A F, ſit linea Aequatoris,
              <lb/>
            vt diximus.</s>
            <s xml:id="echoid-s10104" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div556" type="section" level="1" n="145">
          <head xml:id="echoid-head148" xml:space="preserve">PROBLEMA 2. PROPOSITIO 2.</head>
          <note position="left" xml:space="preserve">10</note>
          <p>
            <s xml:id="echoid-s10105" xml:space="preserve">PARALLELOS, ſiue arcus ſignorum Zodiaci, hoc eſt, commu
              <lb/>
            nes ſectiones plani horologii, & </s>
            <s xml:id="echoid-s10106" xml:space="preserve">conorum, quorum baſes ſunt paral-
              <lb/>
            leli ſignorum Zodiaci, vertex autem centrum mundi, in prædicto horo
              <lb/>
            logio horizontali deſcribere.</s>
            <s xml:id="echoid-s10107" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10108" xml:space="preserve">REPETATVR portio Analemmatis præcedentis propoſ. </s>
            <s xml:id="echoid-s10109" xml:space="preserve">perficiaturq; </s>
            <s xml:id="echoid-s10110" xml:space="preserve">Meridianus A B C,
              <lb/>
              <note position="right" xlink:label="note-0177-03" xlink:href="note-0177-03a" xml:space="preserve">Deſcriptio at-
                <lb/>
              cuum ſignorũ
                <lb/>
              Zodiaci in prę-
                <lb/>
              dicto horologio
                <lb/>
              horizontali, ex
                <lb/>
              Analemmate.</note>
            in quo ex Analemmate propoſ. </s>
            <s xml:id="echoid-s10111" xml:space="preserve">1. </s>
            <s xml:id="echoid-s10112" xml:space="preserve">præcedentis lib. </s>
            <s xml:id="echoid-s10113" xml:space="preserve">conſtructo diametri parallelorum ducantur,
              <lb/>
              <note position="left" xlink:label="note-0177-04" xlink:href="note-0177-04a" xml:space="preserve">20</note>
            vna cum diametris oppoſita ſigna connectentibus,
              <lb/>
              <figure xlink:label="fig-0177-01" xlink:href="fig-0177-01a" number="130">
                <image file="0177-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0177-01"/>
              </figure>
            vt ſiant trianguia per axem in conis, quorum baſes
              <lb/>
            funt ipſi paralleli, vertex autem communis centrum
              <lb/>
            D. </s>
            <s xml:id="echoid-s10114" xml:space="preserve">Erit igitur ex demonſtratis in propoſ. </s>
            <s xml:id="echoid-s10115" xml:space="preserve">4. </s>
            <s xml:id="echoid-s10116" xml:space="preserve">5. </s>
            <s xml:id="echoid-s10117" xml:space="preserve">6. </s>
            <s xml:id="echoid-s10118" xml:space="preserve">& </s>
            <s xml:id="echoid-s10119" xml:space="preserve">
              <lb/>
            7. </s>
            <s xml:id="echoid-s10120" xml:space="preserve">ſuperioris lib. </s>
            <s xml:id="echoid-s10121" xml:space="preserve">KR, diameter conicæ ſectionis, quá
              <lb/>
            Sol in principio ♋, exiſtens deſcribit; </s>
            <s xml:id="echoid-s10122" xml:space="preserve">L R, diameter
              <lb/>
              <note position="right" xlink:label="note-0177-05" xlink:href="note-0177-05a" xml:space="preserve">Diametri coni-
                <lb/>
              carũ ſectionũ,
                <lb/>
              Sole in princi-
                <lb/>
              pijs ſignorum
                <lb/>
              exiſtente.</note>
            ſectionis, quam Sol in primo puncto ♊, & </s>
            <s xml:id="echoid-s10123" xml:space="preserve">♌, de-
              <lb/>
            ſcribit; </s>
            <s xml:id="echoid-s10124" xml:space="preserve">M R, diameter ſectionis, quam Sol in initio
              <lb/>
            ♉, & </s>
            <s xml:id="echoid-s10125" xml:space="preserve">♍, deſcribit: </s>
            <s xml:id="echoid-s10126" xml:space="preserve">At verò NO, PO, QO, diame-
              <lb/>
            tri erunt ſectionum conicarum, quas Sol in oppo-
              <lb/>
              <note position="left" xlink:label="note-0177-06" xlink:href="note-0177-06a" xml:space="preserve">30</note>
            ſitis parallelis, nempe in parallelis ♑; </s>
            <s xml:id="echoid-s10127" xml:space="preserve">♐ & </s>
            <s xml:id="echoid-s10128" xml:space="preserve">♒; </s>
            <s xml:id="echoid-s10129" xml:space="preserve">♏, & </s>
            <s xml:id="echoid-s10130" xml:space="preserve">
              <lb/>
            ♓, exiſtens deſcribit.</s>
            <s xml:id="echoid-s10131" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10132" xml:space="preserve">PORRO hæ diametri conicarum ſectionum
              <lb/>
              <note position="right" xlink:label="note-0177-07" xlink:href="note-0177-07a" xml:space="preserve">Qua ration@
                <lb/>
              diametri coni-
                <lb/>
              carum ſectionũ
                <lb/>
              in quocunque
                <lb/>
              Analẽmate in-
                <lb/>
              ueniantur.</note>
            inuenientur eodem pacto in quocunque alio Ana-
              <lb/>
            lemmate, quod vel maius ſit, vel minus hoc noſtro
              <lb/>
            propoſito, etiam ſi horologium ſine portione Ana-
              <lb/>
            lemmatis conſtructum ſit, vt in præcedenti ſcholio docuimus; </s>
            <s xml:id="echoid-s10133" xml:space="preserve">dummodo in alio illo Analem-
              <lb/>
            mate ex diametro Verticalis infra centrum abſcindatur recta gnomoni aſſumpto æqualis, produ-
              <lb/>
            cta ipſa diametro Verticalis, ſi id longitudo gnomonis requirat; </s>
            <s xml:id="echoid-s10134" xml:space="preserve">& </s>
            <s xml:id="echoid-s10135" xml:space="preserve">per extremum punctum re-
              <lb/>
            cta ducatur parallela diametro Horizontis, per quam planum horologij horizontalis duci conci-
              <lb/>
              <note position="left" xlink:label="note-0177-08" xlink:href="note-0177-08a" xml:space="preserve">40</note>
            pitur. </s>
            <s xml:id="echoid-s10136" xml:space="preserve">Hæc enim recta in maiori, vel minori Analemmate à diametris ſignorum oppoſitorum ſe-
              <lb/>
            cabitur in partes æquales partibus rectæ R O, in noſtro hoc Analemmate: </s>
            <s xml:id="echoid-s10137" xml:space="preserve">Quod ita oſtendi po-
              <lb/>
            teſt. </s>
            <s xml:id="echoid-s10138" xml:space="preserve">Quoniam tam illa recta, quàm hæc R O, æqualiter à centro ſui Analemmatis diſtar, & </s>
            <s xml:id="echoid-s10139" xml:space="preserve">angu-
              <lb/>
            li, quos diametri oppoſitorum ſignorum cum diametro Æquatoris faciunt, in quolibet Analem-
              <lb/>
            mate ſunt eiuſdem magnitudinis, cum ſemper eiſdem declinationibus eorundem ſignorum inſi-
              <lb/>
              <note position="right" xlink:label="note-0177-09" xlink:href="note-0177-09a" xml:space="preserve">27. tertij.</note>
            ſtant ad centra; </s>
            <s xml:id="echoid-s10140" xml:space="preserve">efficitur vt & </s>
            <s xml:id="echoid-s10141" xml:space="preserve">anguli, quos eædem diametri cum diametro Verticalis circuli fa-
              <lb/>
            ciunt, (qui quidem vel componuntur ex illis, & </s>
            <s xml:id="echoid-s10142" xml:space="preserve">ex angulo altitudinis poli contento ſub diametro
              <lb/>
            Æquatoris, & </s>
            <s xml:id="echoid-s10143" xml:space="preserve">diametro Verticalis, vel relinquuntur poſt detractionem illorum ex eodem angulo
              <lb/>
            altitudinis poli) æquales inter ſe ſint, cum & </s>
            <s xml:id="echoid-s10144" xml:space="preserve">anguli contenti ſub diamctro Verticalis, & </s>
            <s xml:id="echoid-s10145" xml:space="preserve">diametro
              <lb/>
            Æquatoris æquales ſint. </s>
            <s xml:id="echoid-s10146" xml:space="preserve">Quare cum anguli, quos rectæ per extremitatem gnomonis (nempe per
              <lb/>
              <note position="left" xlink:label="note-0177-10" xlink:href="note-0177-10a" xml:space="preserve">50</note>
            punctum G, in noſtro Analemmate, & </s>
            <s xml:id="echoid-s10147" xml:space="preserve">per punctũ huic reſpondens in alio Analemmate.) </s>
            <s xml:id="echoid-s10148" xml:space="preserve">ductæ
              <lb/>
            diametro Horizontis æquidiſtantes cum diametro Verticalis faciunt, recti ſint, (qualis in noſtro
              <lb/>
            Analemmate eſtangulus G.) </s>
            <s xml:id="echoid-s10149" xml:space="preserve">& </s>
            <s xml:id="echoid-s10150" xml:space="preserve">anguli, quos in vtroq; </s>
            <s xml:id="echoid-s10151" xml:space="preserve">Analemmate radius cuiuſuis ſigni cum ea-
              <lb/>
            dem diametro Verticalis cóſtituit, æquales quoque, vt diximus; </s>
            <s xml:id="echoid-s10152" xml:space="preserve">(Sunt enim cũ illis, quos æquales
              <lb/>
            oſtendimus, ad verticem.) </s>
            <s xml:id="echoid-s10153" xml:space="preserve">reperientur ſemper bina triangula in vtroq; </s>
            <s xml:id="echoid-s10154" xml:space="preserve">Analemmate, nempe vnũ
              <lb/>
            in vno, & </s>
            <s xml:id="echoid-s10155" xml:space="preserve">in altero alterum, habentia binos angulos æquales, vtrumq; </s>
            <s xml:id="echoid-s10156" xml:space="preserve">vtriq;</s>
            <s xml:id="echoid-s10157" xml:space="preserve">. Cum igitur & </s>
            <s xml:id="echoid-s10158" xml:space="preserve">latus
              <lb/>
            habeant æquale, quod dictis angulis adiacet, nempe magnitudinem ſtyli; </s>
            <s xml:id="echoid-s10159" xml:space="preserve">habebunt quoq; </s>
            <s xml:id="echoid-s10160" xml:space="preserve">reliqua
              <lb/>
            latera æqualia, nimirum illa, quæ inter extremitatem ſtyli, & </s>
            <s xml:id="echoid-s10161" xml:space="preserve">radium cuiuſq; </s>
            <s xml:id="echoid-s10162" xml:space="preserve">ſigni in vtroq; </s>
            <s xml:id="echoid-s10163" xml:space="preserve">Ana-
              <lb/>
              <note position="right" xlink:label="note-0177-11" xlink:href="note-0177-11a" xml:space="preserve">26. primi.</note>
            lemmate interijciuntur, &</s>
            <s xml:id="echoid-s10164" xml:space="preserve">c. </s>
            <s xml:id="echoid-s10165" xml:space="preserve">Quod etiam inde patere poteſt; </s>
            <s xml:id="echoid-s10166" xml:space="preserve">quòd ſi Analemma illud maius ſuper-
              <lb/>
            poni intelligatur huic noſtro, ita vt centra, & </s>
            <s xml:id="echoid-s10167" xml:space="preserve">diametri Horizontis, Verticalis, atq; </s>
            <s xml:id="echoid-s10168" xml:space="preserve">Æquatoris in-
              <lb/>
            ter ſe congruant, recta per extremitatem ſtyli in illo ducta congruat rectæ R O, in noſtro </s>
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