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-div185" type="section" level="1" n="55">
          <p>
            <s xml:id="echoid-s3275" xml:space="preserve">
              <pb o="50" file="0070" n="70" rhead="GNOMONICES"/>
            rallelum in punctis oppoſitis: </s>
            <s xml:id="echoid-s3276" xml:space="preserve">erit eorum, & </s>
            <s xml:id="echoid-s3277" xml:space="preserve">maximi parallelorum ea-
              <lb/>
              <note position="left" xlink:label="note-0070-01" xlink:href="note-0070-01a" xml:space="preserve">Maximus pa-
                <lb/>
              rallelorum, &
                <lb/>
              duo circuli ma
                <lb/>
              ximi tangentes
                <lb/>
              quemcunque
                <lb/>
              patallelum in
                <lb/>
              duobus punctis
                <lb/>
              oppoſitis habẽt
                <lb/>
              vnã eand@mq́;
                <lb/>
              ſectionem com
                <lb/>
              munem.</note>
            dem communis ſectio.</s>
            <s xml:id="echoid-s3278" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3279" xml:space="preserve">IN Sphæra A B C D, tangant duo circuli maximi A C, B D, parallelum B C, in punctis op-
              <lb/>
            poſitis B, C, quorum communis ſectio ſit recta E F. </s>
            <s xml:id="echoid-s3280" xml:space="preserve">Dico maximum parallelorum G H, ſecare
              <lb/>
            vtrumque per rectam E F, hoc eſt, tranſire per puncta E, F, ita vt recta E F, ſit communis ſectio
              <lb/>
            trium circulorum maximorum A C, B D, G H. </s>
            <s xml:id="echoid-s3281" xml:space="preserve">Per polum enim I, parallelorum B C, G H, & </s>
            <s xml:id="echoid-s3282" xml:space="preserve">
              <lb/>
            per contactum B, deſcribatur circulus maximus A B C D, qui cum per propoſ. </s>
            <s xml:id="echoid-s3283" xml:space="preserve">15. </s>
            <s xml:id="echoid-s3284" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s3285" xml:space="preserve">1. </s>
            <s xml:id="echoid-s3286" xml:space="preserve">Theo-
              <lb/>
              <figure xlink:label="fig-0070-01" xlink:href="fig-0070-01a" number="52">
                <image file="0070-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0070-01"/>
              </figure>
            doſii, ſecet parallelum B C, bifariam, tranſibit
              <lb/>
            quoque per contactum oppoſitum C. </s>
            <s xml:id="echoid-s3287" xml:space="preserve">Quia er-
              <lb/>
              <note position="left" xlink:label="note-0070-02" xlink:href="note-0070-02a" xml:space="preserve">10</note>
            go circulus maximus A B C D, deſcriptus per
              <lb/>
            polum paralleli B C, & </s>
            <s xml:id="echoid-s3288" xml:space="preserve">per contactus B, C,
              <lb/>
            tranſit quoque per polos circulorum A C, B D,
              <lb/>
            per propoſ. </s>
            <s xml:id="echoid-s3289" xml:space="preserve">5. </s>
            <s xml:id="echoid-s3290" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s3291" xml:space="preserve">2. </s>
            <s xml:id="echoid-s3292" xml:space="preserve">Theodoſii, ſecabit neceſ-
              <lb/>
            ſario, per propoſ. </s>
            <s xml:id="echoid-s3293" xml:space="preserve">9. </s>
            <s xml:id="echoid-s3294" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s3295" xml:space="preserve">2. </s>
            <s xml:id="echoid-s3296" xml:space="preserve">eiuſdem, eorum ſeg-
              <lb/>
            menta A E F, B E F, C E F, D E F, bifariam in
              <lb/>
            punctis A, B, C, D. </s>
            <s xml:id="echoid-s3297" xml:space="preserve">Cum ergo hæc ſegmenta ſe-
              <lb/>
            micirculi ſint, (quod maximi circuli cum ſint,
              <lb/>
            ſe mutuo bifariam ſecent in punctis E, F, per
              <lb/>
            propoſ. </s>
            <s xml:id="echoid-s3298" xml:space="preserve">11. </s>
            <s xml:id="echoid-s3299" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s3300" xml:space="preserve">1. </s>
            <s xml:id="echoid-s3301" xml:space="preserve">Theodoſii) quadrantes erunt
              <lb/>
              <note position="left" xlink:label="note-0070-03" xlink:href="note-0070-03a" xml:space="preserve">20</note>
            ſegmenta A E, A F, B E, B F, C E, C F, D E,
              <lb/>
            D F, vtpote ſemicirculorum dimidia. </s>
            <s xml:id="echoid-s3302" xml:space="preserve">Rurſus
              <lb/>
            quia circulus maximus A B C D, cum per po-
              <lb/>
            los circulorum G H, B D, incedat, ſecat ſegmen
              <lb/>
            ta circulorum G H, B D, quæ quidem per pro-
              <lb/>
            poſ. </s>
            <s xml:id="echoid-s3303" xml:space="preserve">11. </s>
            <s xml:id="echoid-s3304" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s3305" xml:space="preserve">1. </s>
            <s xml:id="echoid-s3306" xml:space="preserve">Theodoſii, ſemicirculi ſunt, bifa-
              <lb/>
            riam, ex propoſ. </s>
            <s xml:id="echoid-s3307" xml:space="preserve">9. </s>
            <s xml:id="echoid-s3308" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s3309" xml:space="preserve">2. </s>
            <s xml:id="echoid-s3310" xml:space="preserve">Theodoſii, in punctis G, B; </s>
            <s xml:id="echoid-s3311" xml:space="preserve">erunt arcus circuli B D, inter punctum B, & </s>
            <s xml:id="echoid-s3312" xml:space="preserve">
              <lb/>
            circulum G H, poſiti, quadrantes: </s>
            <s xml:id="echoid-s3313" xml:space="preserve">ac propterea cum B E, B F, oſtenſi ſint quadrantes, tranſibit
              <lb/>
            neceſſario circulus G H, per puncta E, F, atque adeò vtrumque circulum A C, B D, per rectam
              <lb/>
            E F, ſecabit. </s>
            <s xml:id="echoid-s3314" xml:space="preserve">Quare recta E F, communis ſectio eſt trium circulorum maximorum A C, B D, G H;
              <lb/>
            </s>
            <s xml:id="echoid-s3315" xml:space="preserve">
              <note position="left" xlink:label="note-0070-04" xlink:href="note-0070-04a" xml:space="preserve">30</note>
            Ac proinde, ſi in ſphęra duo circuli maximi tangant vnum, &</s>
            <s xml:id="echoid-s3316" xml:space="preserve">c. </s>
            <s xml:id="echoid-s3317" xml:space="preserve">Quod demonſtrandum erat,</s>
          </p>
        </div>
        <div xml:id="echoid-div188" type="section" level="1" n="56">
          <head xml:id="echoid-head59" xml:space="preserve">COROLLARIVM.</head>
          <p>
            <s xml:id="echoid-s3318" xml:space="preserve">QVONIAM oſtenſum eſt, arcus B E, B F, inter contactum B, & </s>
            <s xml:id="echoid-s3319" xml:space="preserve">maximum parallelorum G H,
              <lb/>
              <note position="left" xlink:label="note-0070-05" xlink:href="note-0070-05a" xml:space="preserve">Quatuor arcus
                <lb/>
              Eclipticæ inter
                <lb/>
              puncta ſolſtitio
                <lb/>
              rum, & æquino
                <lb/>
              ctiorum; Item
                <lb/>
              Horizontis in-
                <lb/>
              ter Aequatorẽ,
                <lb/>
              ac Meridianũ;
                <lb/>
              omnium deni-
                <lb/>
              que circulorum
                <lb/>
              horarum ab or.
                <lb/>
              vel occ. inter
                <lb/>
              Aequatorem, &
                <lb/>
              puncta, in qui-
                <lb/>
              bus maximum
                <lb/>
              parallelorũ ſem
                <lb/>
              per apparentiũ,
                <lb/>
              & maximũ ſem
                <lb/>
              per latentium,
                <lb/>
              tangunt, inter-
                <lb/>
              poſiti ſunt qua-
                <lb/>
              drantes.</note>
            poſitos, eſſe quadrantes, efficitur, arcus cuiuslibet circuli maximi tangentis aliquem parallelorum poſi-
              <lb/>
            tos inter contactum, & </s>
            <s xml:id="echoid-s3320" xml:space="preserve">maximum parallelorum eſſe quadrantes. </s>
            <s xml:id="echoid-s3321" xml:space="preserve">Eadem enim in omnibus eſt demon-
              <lb/>
            ſtratio, cum ſemper circuli maximi per polos parallelorum, & </s>
            <s xml:id="echoid-s3322" xml:space="preserve">contactus deſcripti, tranſeant, per propoſ.
              <lb/>
            </s>
            <s xml:id="echoid-s3323" xml:space="preserve">5. </s>
            <s xml:id="echoid-s3324" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s3325" xml:space="preserve">2. </s>
            <s xml:id="echoid-s3326" xml:space="preserve">Theodoſii, per polos etiam circulorum tangentium; </s>
            <s xml:id="echoid-s3327" xml:space="preserve">atque adeò ſingulorum ſegmenta inter con-
              <lb/>
            tactus, & </s>
            <s xml:id="echoid-s3328" xml:space="preserve">maximum parallelorum poſita, quæ quidem per propoſ. </s>
            <s xml:id="echoid-s3329" xml:space="preserve">11. </s>
            <s xml:id="echoid-s3330" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s3331" xml:space="preserve">1. </s>
            <s xml:id="echoid-s3332" xml:space="preserve">Theodoſii, ſemicirculi ſunt,
              <lb/>
            bifariam ſecent, per propoſ. </s>
            <s xml:id="echoid-s3333" xml:space="preserve">9. </s>
            <s xml:id="echoid-s3334" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s3335" xml:space="preserve">2. </s>
            <s xml:id="echoid-s3336" xml:space="preserve">Theodoſii, hoc eſt, in quadrantes diuidant. </s>
            <s xml:id="echoid-s3337" xml:space="preserve">Huiuſmodi ſunt quatuor
              <lb/>
              <note position="left" xlink:label="note-0070-06" xlink:href="note-0070-06a" xml:space="preserve">40</note>
            arcus Zodiaci inter Aequatorem, & </s>
            <s xml:id="echoid-s3338" xml:space="preserve">puncta ſolſtitiorum, in quibus Zodiacus tropicos Aequatori paralle-
              <lb/>
            los tangit, intercepti. </s>
            <s xml:id="echoid-s3339" xml:space="preserve">Item quatuor arcus Horizontis inter Aequatorem & </s>
            <s xml:id="echoid-s3340" xml:space="preserve">puncta, in quibus Horizon tan
              <lb/>
            git maximum parallelorum ſem per apparentium, & </s>
            <s xml:id="echoid-s3341" xml:space="preserve">maximum ſemper deliteſcentium, ſecaturq; </s>
            <s xml:id="echoid-s3342" xml:space="preserve">à Meri-
              <lb/>
            diano, poſiti. </s>
            <s xml:id="echoid-s3343" xml:space="preserve">Omnes denique arcus circulorum horas ab ortu, vel occaſu indicantium inter Aequatorem,
              <lb/>
            & </s>
            <s xml:id="echoid-s3344" xml:space="preserve">puncta, in quibus maximum parallelorum ſemper apparentium, & </s>
            <s xml:id="echoid-s3345" xml:space="preserve">maximum ſemper latentium, tan-
              <lb/>
            gunt, interpoſiti. </s>
            <s xml:id="echoid-s3346" xml:space="preserve">Nam omnes hi arcus quadrantes ſunt, vt demonſtratum eſt.</s>
            <s xml:id="echoid-s3347" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div190" type="section" level="1" n="57">
          <head xml:id="echoid-head60" xml:space="preserve">THEOREMA 15. PROPOSITIO 17.</head>
          <p>
            <s xml:id="echoid-s3348" xml:space="preserve">SI in Sphæra duo circuli maximi tangant vnum, eundemq́; </s>
            <s xml:id="echoid-s3349" xml:space="preserve">paralle-
              <lb/>
              <note position="left" xlink:label="note-0070-07" xlink:href="note-0070-07a" xml:space="preserve">Tres circuli ma
                <lb/>
              ximi, quorum
                <lb/>
              vnus quidem ſe
                <lb/>
              cer quemcun-
                <lb/>
              que parallelum
                <lb/>
              per polos, alii
                <lb/>
              vero eundem
                <lb/>
              tangant in pun
                <lb/>
              ctis æqualiter
                <lb/>
              hinc inde remo
                <lb/>
              tis ab vtrouis
                <lb/>
              punctorum, in
                <lb/>
              quibus ab alte-
                <lb/>
              ro circulo ma-
                <lb/>
              ximo ſecatur,
                <lb/>
              habent unam
                <lb/>
              eandemq́; ſe-
                <lb/>
              ctionem com
                <lb/>
              munem.</note>
              <note position="left" xlink:label="note-0070-08" xlink:href="note-0070-08a" xml:space="preserve">50</note>
            lum; </s>
            <s xml:id="echoid-s3350" xml:space="preserve">ſecet autem alius circulus maximus eundem parallelum per polos
              <lb/>
            parallelorum, æqualiterque diſtet à punctis contactuum: </s>
            <s xml:id="echoid-s3351" xml:space="preserve">erit circulo-
              <lb/>
            rum tangentium, & </s>
            <s xml:id="echoid-s3352" xml:space="preserve">ſecantis eadem ſectio communis.</s>
            <s xml:id="echoid-s3353" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3354" xml:space="preserve">IN Sphæra A B C D, tangant primum duo circuli maximi A C, B D, parallelum B C, in pun-
              <lb/>
            ctis oppoſitis B, C, ita vt BIC, B k C, ſemicirculi ſint, ſitq́ue eorum communis ſectio recta E F:
              <lb/>
            </s>
            <s xml:id="echoid-s3355" xml:space="preserve">Secet autem eundem parallelum B C, alius circulus maximus G H, per paralleli polos G, H, in-
              <lb/>
            cedens in punctis I, K, ęqualiter diſtantibus à punctis B, C, ita vt arcus I B, I C, & </s>
            <s xml:id="echoid-s3356" xml:space="preserve">K B, k C, qua-
              <lb/>
            drantes ſint. </s>
            <s xml:id="echoid-s3357" xml:space="preserve">Dico circulum G H, ſecare vtrumque circulum maximum A C, B D, per rectam
              <lb/>
            E F, hoc eſt, tranſire per puncta E, F, ita vt recta E F, communis ſectio ſit trium maximorum </s>
          </p>
        </div>
      </text>
    </echo>
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