Clavius, Christoph, In Sphaeram Ioannis de Sacro Bosco commentarius

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        <div xml:id="echoid-div217" type="section" level="1" n="73">
          <p>
            <s xml:id="echoid-s4167" xml:space="preserve">
              <pb o="83" file="119" n="120" rhead="Ioan. de Sacro Boſco."/>
            turq́ue rectangulum B E F C, quod erit duplum trianguli A B C; </s>
            <s xml:id="echoid-s4168" xml:space="preserve">Item duplũ
              <lb/>
              <note position="right" xlink:label="note-119-01" xlink:href="note-119-01a" xml:space="preserve">41. primi.</note>
            rectanguli A D B E. </s>
            <s xml:id="echoid-s4169" xml:space="preserve">Quare rectangulum A D B E, quod nimirum continetur
              <lb/>
              <note position="right" xlink:label="note-119-02" xlink:href="note-119-02a" xml:space="preserve">36. primi.</note>
            ſub perpendiculari A D, & </s>
            <s xml:id="echoid-s4170" xml:space="preserve">dimidio baſis B D, æquale eſt triangulo A B C. </s>
            <s xml:id="echoid-s4171" xml:space="preserve">Di
              <lb/>
            uidat ſecundo perpendicularis A D, baſim B C, non bifariam, uel etiam ca-
              <lb/>
            dat in baſim C B, protractam, ut in 2. </s>
            <s xml:id="echoid-s4172" xml:space="preserve">& </s>
            <s xml:id="echoid-s4173" xml:space="preserve">3. </s>
            <s xml:id="echoid-s4174" xml:space="preserve">figura; </s>
            <s xml:id="echoid-s4175" xml:space="preserve">Et per A, ducatur rurſus
              <lb/>
            A F, in utramque partem æquidiſtans rectæ B C, compleaturq́ue rectangulũ
              <lb/>
            A D C F. </s>
            <s xml:id="echoid-s4176" xml:space="preserve">Diuiſa deinde B C, bifariam in G, ducantur rectæ B E, G H, ipſi
              <lb/>
            A D, æquidiſtantes, eritq́ue G H, æqualis perpendiculari A D. </s>
            <s xml:id="echoid-s4177" xml:space="preserve">Quoniam igi-
              <lb/>
              <note position="right" xlink:label="note-119-03" xlink:href="note-119-03a" xml:space="preserve">34. primi.</note>
            tur rectangulum B C E F, duplum eſt trianguli A B C; </s>
            <s xml:id="echoid-s4178" xml:space="preserve">Item duplum rectangu
              <lb/>
              <note position="right" xlink:label="note-119-04" xlink:href="note-119-04a" xml:space="preserve">41. primi.</note>
            li B E H G; </s>
            <s xml:id="echoid-s4179" xml:space="preserve">erit rectangulum B E H G, quod continetur ſub perpendiculari
              <lb/>
              <note position="right" xlink:label="note-119-05" xlink:href="note-119-05a" xml:space="preserve">36. primi.</note>
            G H, uel A D, & </s>
            <s xml:id="echoid-s4180" xml:space="preserve">dimidio baſis B G, æquale triangulo A B C. </s>
            <s xml:id="echoid-s4181" xml:space="preserve">Area igitur cu-
              <lb/>
            iuslibet trianguli æqualis eſt, &</s>
            <s xml:id="echoid-s4182" xml:space="preserve">c. </s>
            <s xml:id="echoid-s4183" xml:space="preserve">quod erat oſtendendum.</s>
            <s xml:id="echoid-s4184" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div220" type="section" level="1" n="74">
          <head xml:id="echoid-head78" style="it" xml:space="preserve">THEOR. 2. PROPOS. 2.</head>
          <p style="it">
            <s xml:id="echoid-s4185" xml:space="preserve">
              <emph style="sc">Area</emph>
            cuiuslibet figuræ regularis æqualis eſt rectangulo contento ſub
              <lb/>
              <note position="right" xlink:label="note-119-06" xlink:href="note-119-06a" xml:space="preserve">Regularis
                <unsure/>
                <lb/>
              figura quæ
                <lb/>
              cunque cui
                <lb/>
              rectangulo
                <lb/>
              ęqualis ſit.</note>
            perpendiculari à centro figurę ad unum latus ducta, & </s>
            <s xml:id="echoid-s4186" xml:space="preserve">ſub dimidiato ambi-
              <unsure/>
              <lb/>
            tu eiuſdem figuræ.</s>
            <s xml:id="echoid-s4187" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4188" xml:space="preserve">
              <emph style="sc">Sit</emph>
            figura regularis quæcunque A B C D E F, & </s>
            <s xml:id="echoid-s4189" xml:space="preserve">centrum eius punctum
              <lb/>
            G, à quo ducatur G H, perpendicularis ad unum latus, nempe ad A B: </s>
            <s xml:id="echoid-s4190" xml:space="preserve">Sit
              <lb/>
              <figure xlink:label="fig-119-01" xlink:href="fig-119-01a" number="20">
                <image file="119-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/119-01"/>
              </figure>
            quoque rectãgulum I K-
              <lb/>
            L M, contentum ſub I K,
              <lb/>
            quæ æqualis ſit perpendi-
              <lb/>
            culari G H, & </s>
            <s xml:id="echoid-s4191" xml:space="preserve">ſub K L, re-
              <lb/>
            cta, quæ æqualis ponatur
              <lb/>
            dimidiæ parti ambitu fi-
              <lb/>
            guræ A B C D E F. </s>
            <s xml:id="echoid-s4192" xml:space="preserve">Dico
              <lb/>
            huic rectangulo æqualem
              <lb/>
            eſſe figuram regularẽ A
              <lb/>
            B C D E F. </s>
            <s xml:id="echoid-s4193" xml:space="preserve">Ducãtur em̃
              <lb/>
            ex G, ad ſingulos angulos
              <lb/>
            lineæ rectæ, ut tota figura
              <lb/>
            in triangula reſoluatur,
              <lb/>
            quæ omnia æqualia inter
              <lb/>
            ſe erunt, ut in corollario
              <lb/>
            propoſ. </s>
            <s xml:id="echoid-s4194" xml:space="preserve">8. </s>
            <s xml:id="echoid-s4195" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s4196" xml:space="preserve">1. </s>
            <s xml:id="echoid-s4197" xml:space="preserve">Eucl. </s>
            <s xml:id="echoid-s4198" xml:space="preserve">de-
              <lb/>
            monſtratum eſt à nobis;
              <lb/>
            </s>
            <s xml:id="echoid-s4199" xml:space="preserve">propterea quòd omnia la-
              <lb/>
            tera triangulorum à pun-
              <lb/>
            cto G, exeuntia ſint inter
              <lb/>
            ſæ æqualia, habeantq́; </s>
            <s xml:id="echoid-s4200" xml:space="preserve">ba-
              <lb/>
            ſes æquales, nempe latera
              <lb/>
            figuræ regularis. </s>
            <s xml:id="echoid-s4201" xml:space="preserve">Hinc e-
              <lb/>
            nim efficitur, omnes angu
              <lb/>
            los ad G, æq uales eſſe, ac proinde, ex dicto corollario, triangula ipſa inter ſe
              <lb/>
              <note position="right" xlink:label="note-119-07" xlink:href="note-119-07a" xml:space="preserve">8. primi.</note>
            quoque eſſe æqualia. </s>
            <s xml:id="echoid-s4202" xml:space="preserve">Quoniam igitur rectangulum cõtentum ſub G H, </s>
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