Clavius, Christoph, Geometria practica

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        <div xml:id="echoid-div1037" type="section" level="1" n="373">
          <pb o="360" file="388" n="388" rhead="GEOMETR. PRACT."/>
        </div>
        <div xml:id="echoid-div1040" type="section" level="1" n="374">
          <head xml:id="echoid-head401" xml:space="preserve">SCHOLIVM.</head>
          <p>
            <s xml:id="echoid-s16818" xml:space="preserve">
              <emph style="sc">Hoc</emph>
            Theorema valdè vtile eſt ad deſcriptionem paralleli cuiuſuis circuli
              <lb/>
            maximi per datum punctum in Aſtrolabio, vt ex propoſ. </s>
            <s xml:id="echoid-s16819" xml:space="preserve">18. </s>
            <s xml:id="echoid-s16820" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s16821" xml:space="preserve">2. </s>
            <s xml:id="echoid-s16822" xml:space="preserve">Aſtrolabij per-
              <lb/>
            ſpicuum eſt: </s>
            <s xml:id="echoid-s16823" xml:space="preserve">cum multa ibi demonſtrari poſsint per hoc Theorema, ſine ijs,
              <lb/>
            quæ ex Aſtrolabij deſcriptione pendent.</s>
            <s xml:id="echoid-s16824" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1041" type="section" level="1" n="375">
          <head xml:id="echoid-head402" xml:space="preserve">THEOR. 11. PROPOS. 29.</head>
          <p>
            <s xml:id="echoid-s16825" xml:space="preserve">DESCRIPTIONEM Pentagoni æquilateri, & </s>
            <s xml:id="echoid-s16826" xml:space="preserve">æquianguli ſupra
              <lb/>
            datam rectam ab Alberto Durero traditam, & </s>
            <s xml:id="echoid-s16827" xml:space="preserve">quam omnes fere Ar-
              <lb/>
            chitecti, atq; </s>
            <s xml:id="echoid-s16828" xml:space="preserve">artifices approbant, falſam eſſe, demonſtrare.</s>
            <s xml:id="echoid-s16829" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s16830" xml:space="preserve">
              <emph style="sc">Praxis</emph>
            hæc eſt. </s>
            <s xml:id="echoid-s16831" xml:space="preserve">Sit data recta A B. </s>
            <s xml:id="echoid-s16832" xml:space="preserve">Ex centris A, B, & </s>
            <s xml:id="echoid-s16833" xml:space="preserve">interuallo eodem
              <lb/>
            AB, deſcribantur duo circuli ſe ſe interſecantes in C, D. </s>
            <s xml:id="echoid-s16834" xml:space="preserve">Ducta autem CD, quã-
              <lb/>
            tacunque, deſcribatur eodem interuallo AB, ex C, per A, B, circulus rectam CD,
              <lb/>
            in E, & </s>
            <s xml:id="echoid-s16835" xml:space="preserve">priores circulos ſecans in F, G. </s>
            <s xml:id="echoid-s16836" xml:space="preserve">Item ducantur ex F, G, per E, rectæ ſe-
              <lb/>
            cantes priores circulos in H, I. </s>
            <s xml:id="echoid-s16837" xml:space="preserve">Denique eodem interuallo ex HI, duo arcus de-
              <lb/>
            ſcripti ſe ſe interſecent in K@ iunganturque rectæ AI, IK, KH, HB. </s>
            <s xml:id="echoid-s16838" xml:space="preserve">Putat ergo Du-
              <lb/>
            rerus, pentagonum ABHKI, eſſe æquilaterum, & </s>
            <s xml:id="echoid-s16839" xml:space="preserve">æquiangulum. </s>
            <s xml:id="echoid-s16840" xml:space="preserve">quod falſum
              <lb/>
            eſt. </s>
            <s xml:id="echoid-s16841" xml:space="preserve">Nam æquilaterum quidem eſt, ex deſcriptione, non autem æquiangulum.
              <lb/>
            </s>
            <s xml:id="echoid-s16842" xml:space="preserve">quod vt manifeſtum fiat, demonſtranda ſunt prius nonnulla.</s>
            <s xml:id="echoid-s16843" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s16844" xml:space="preserve">1. </s>
            <s xml:id="echoid-s16845" xml:space="preserve">
              <emph style="sc">Arcvs</emph>
            tres FA, AB, BG, ſextæ partes circuliſunt, quod rectæ eos ſubtẽ-
              <lb/>
            dentes ſemidiametri ſint circuli FABG, ex conſtructione. </s>
            <s xml:id="echoid-s16846" xml:space="preserve">Igitur FABG, ſemi-
              <lb/>
              <figure xlink:label="fig-388-01" xlink:href="fig-388-01a" number="280">
                <image file="388-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/388-01"/>
              </figure>
              <note symbol="a" position="left" xlink:label="note-388-01" xlink:href="note-388-01a" xml:space="preserve">31. tertij.</note>
            circulus eſt, cuius diameter FG; </s>
            <s xml:id="echoid-s16847" xml:space="preserve"> ideoque
              <note symbol="b" position="left" xlink:label="note-388-02" xlink:href="note-388-02a" xml:space="preserve">ſchol. 27.
                <lb/>
              tertij.</note>
            FEG, in ſemicirculo rectus: </s>
            <s xml:id="echoid-s16848" xml:space="preserve"> Et diameter F G, re- ctæ AB, parallela, ob arcus A F, B G, æquales. </s>
            <s xml:id="echoid-s16849" xml:space="preserve">Et
              <lb/>
            quoniã, vt conſtat ex demonſtratione praxis ſcho-
              <lb/>
            lij propoſ. </s>
            <s xml:id="echoid-s16850" xml:space="preserve">@0. </s>
            <s xml:id="echoid-s16851" xml:space="preserve">& </s>
            <s xml:id="echoid-s16852" xml:space="preserve">11. </s>
            <s xml:id="echoid-s16853" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s16854" xml:space="preserve">1. </s>
            <s xml:id="echoid-s16855" xml:space="preserve">Euclid. </s>
            <s xml:id="echoid-s16856" xml:space="preserve">recta C D, ſecat re-
              <lb/>
              <note symbol="c" position="left" xlink:label="note-388-03" xlink:href="note-388-03a" xml:space="preserve">29. primi.</note>
            ctam AB, bifariam in M, & </s>
            <s xml:id="echoid-s16857" xml:space="preserve">ad angulos rectos; </s>
            <s xml:id="echoid-s16858" xml:space="preserve"> ſe- cabit eadem parallela quoque F G, ad angulosre-
              <lb/>
              <note symbol="d" position="left" xlink:label="note-388-04" xlink:href="note-388-04a" xml:space="preserve">ſchol. 27.
                <lb/>
              tertij.</note>
            ctos in C. </s>
            <s xml:id="echoid-s16859" xml:space="preserve"> Eadem quoq; </s>
            <s xml:id="echoid-s16860" xml:space="preserve">CD, ſecabit arcum A B, bifariamin E, ac propterea toti arcus EF, EG, ęqua
              <lb/>
              <note symbol="e" position="left" xlink:label="note-388-05" xlink:href="note-388-05a" xml:space="preserve">6. quanti.</note>
            les erunt, videlicet quadrantes; </s>
            <s xml:id="echoid-s16861" xml:space="preserve"> ideoq; </s>
            <s xml:id="echoid-s16862" xml:space="preserve">rectæ EF, EG, latera ſunt quadrati in circulo F A B G, deſcri-
              <lb/>
              <note symbol="f" position="left" xlink:label="note-388-06" xlink:href="note-388-06a" xml:space="preserve">ſchol. 34.
                <lb/>
              primi.</note>
            pti, eiuſque diameter FG. </s>
            <s xml:id="echoid-s16863" xml:space="preserve"> Igitur anguli F, G, ſemi- recti erunt: </s>
            <s xml:id="echoid-s16864" xml:space="preserve">ac proinde cum anguliad C, recti ſint,
              <lb/>
              <note symbol="g" position="left" xlink:label="note-388-07" xlink:href="note-388-07a" xml:space="preserve">32. primi.</note>
            erunt quo que O E M, NEM, ſemirecti; </s>
            <s xml:id="echoid-s16865" xml:space="preserve">ideoq; </s>
            <s xml:id="echoid-s16866" xml:space="preserve">&</s>
            <s xml:id="echoid-s16867" xml:space="preserve"> EOM, ENM, ſemirecti. </s>
            <s xml:id="echoid-s16868" xml:space="preserve"> Ac proinde tam latera E M, N O, quam E M, M N,
              <note symbol="h" position="left" xlink:label="note-388-08" xlink:href="note-388-08a" xml:space="preserve">6. primi.</note>
            qualia: </s>
            <s xml:id="echoid-s16869" xml:space="preserve">atqueidcirco & </s>
            <s xml:id="echoid-s16870" xml:space="preserve">OM, NM, inter ſe æqualia erunt; </s>
            <s xml:id="echoid-s16871" xml:space="preserve">nec non & </s>
            <s xml:id="echoid-s16872" xml:space="preserve">totæ OB,
              <lb/>
            NA, æquales erunt. </s>
            <s xml:id="echoid-s16873" xml:space="preserve"> Immo & </s>
            <s xml:id="echoid-s16874" xml:space="preserve">EO, EN, erunt æquales, quod latera EM,
              <note symbol="i" position="left" xlink:label="note-388-09" xlink:href="note-388-09a" xml:space="preserve">4. primi.</note>
            laterib. </s>
            <s xml:id="echoid-s16875" xml:space="preserve">EM, MN, æqualia ſint, cõprehendãtq; </s>
            <s xml:id="echoid-s16876" xml:space="preserve">angulos æquales, vt pote rectos.</s>
            <s xml:id="echoid-s16877" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s16878" xml:space="preserve">2. </s>
            <s xml:id="echoid-s16879" xml:space="preserve">
              <emph style="sc">Deinde</emph>
            quialatera AN, AI, lateribus BO, BH, æqualia ſunt; </s>
            <s xml:id="echoid-s16880" xml:space="preserve">ſuntq; </s>
            <s xml:id="echoid-s16881" xml:space="preserve">an-
              <lb/>
            guli N, O, ſemirecti æquales, & </s>
            <s xml:id="echoid-s16882" xml:space="preserve">vterque reliquorum angulorum I, H, minorre-
              <lb/>
              <note symbol="k" position="left" xlink:label="note-388-10" xlink:href="note-388-10a" xml:space="preserve">19. primi.</note>
            cto; </s>
            <s xml:id="echoid-s16883" xml:space="preserve"> quod vterque minor ſit ſemirecto ad O, & </s>
            <s xml:id="echoid-s16884" xml:space="preserve">N; </s>
            <s xml:id="echoid-s16885" xml:space="preserve">propterea quod tam latus AN, minus eſt latere AI, ꝗ̃ latus B O, latere BH: </s>
            <s xml:id="echoid-s16886" xml:space="preserve">eruntper ea, quæ ad finem lib.</s>
            <s xml:id="echoid-s16887" xml:space="preserve"/>
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