Theodosius <Bithynius>; Clavius, Christoph, Theodosii Tripolitae Sphaericorum libri tres

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          <p>
            <s xml:id="echoid-s10145" xml:space="preserve">
              <pb o="320" file="332" n="332" rhead=""/>
            minus erit, & </s>
            <s xml:id="echoid-s10146" xml:space="preserve">proinde & </s>
            <s xml:id="echoid-s10147" xml:space="preserve">recta: </s>
            <s xml:id="echoid-s10148" xml:space="preserve">BD, minor, quam recta DC. </s>
            <s xml:id="echoid-s10149" xml:space="preserve">Abſciſſa erge
              <lb/>
            recta DE, ipſi BD, æquali, erit EC, differentia inter ſegmenta BD,
              <lb/>
            DC. </s>
            <s xml:id="echoid-s10150" xml:space="preserve">Dico quadratum lateris AC, ſuperare quadratum lateris AB, rectan-
              <lb/>
            gulo ſub BC, EC, comprehenſo. </s>
            <s xml:id="echoid-s10151" xml:space="preserve">Quia enim recta BE, ſecta eſt bifariam in
              <lb/>
            D, eiq́; </s>
            <s xml:id="echoid-s10152" xml:space="preserve">addita in continuum recta EC, erit rectangulum ſub BC, EC,
              <lb/>
              <figure xlink:label="fig-332-01" xlink:href="fig-332-01a" number="177">
                <image file="332-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/YC97H42F/figures/332-01"/>
              </figure>
            contentum vna cum quadrato rectæ DE, qua-
              <lb/>
            drato rectæ DC, æquale. </s>
            <s xml:id="echoid-s10153" xml:space="preserve">Addito ergo quadrato
              <lb/>
              <note position="left" xlink:label="note-332-01" xlink:href="note-332-01a" xml:space="preserve">@. ſecundi.</note>
            communi rectæ AD, erit rectangulum ſub BC,
              <lb/>
            EC, vnà cum quadratis rectarum DE, AD, hoc
              <lb/>
            eſt, rectarum BD, AD, hoc eſt, cum quadrato
              <lb/>
            rectæ AB, æquale quadratis rectarum DC, AD,
              <lb/>
            hoc eſt, quadrato rectæ AC. </s>
            <s xml:id="echoid-s10154" xml:space="preserve">Maius ergo eſt qua-
              <lb/>
            dratum lateris AC, quam quadratum lateris
              <lb/>
            AB, rectangulo ſub BC, EC, comprehenſo.
              <lb/>
            </s>
            <s xml:id="echoid-s10155" xml:space="preserve">quod eſt propoſitum.</s>
            <s xml:id="echoid-s10156" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10157" xml:space="preserve">CADAT deinde perpendicularis AD, ex-
              <lb/>
            tra triangulum in baſim CB, productam, vt in
              <lb/>
            figura poſteriori. </s>
            <s xml:id="echoid-s10158" xml:space="preserve">Abſciſſa recta DE, ipſi DB,
              <lb/>
            æquali, erit recta EC, compoſita ex baſe BC, & </s>
            <s xml:id="echoid-s10159" xml:space="preserve">
              <lb/>
            EB, quæ dupla eſt lineæ DB, inter perpendicu-
              <lb/>
            larem, & </s>
            <s xml:id="echoid-s10160" xml:space="preserve">angulum B. </s>
            <s xml:id="echoid-s10161" xml:space="preserve">Dico rurſus, quadratum
              <lb/>
            lateris AC, ſuperare quadratum lateris AB, rectangulo ſub BC, EC, com-
              <lb/>
              <note position="left" xlink:label="note-332-02" xlink:href="note-332-02a" xml:space="preserve">@. fecundi.</note>
            prehenſo. </s>
            <s xml:id="echoid-s10162" xml:space="preserve">Eritenim rurſus rectangulum ſub BC, EC, vnà cum quadrato re-
              <lb/>
            ctæ DB, quadrato rectæ DC, æquale. </s>
            <s xml:id="echoid-s10163" xml:space="preserve">Addito ergo quadrato communi rectę
              <lb/>
            AD, erit rectangulum ſub BC, EC, vnà cum quadratis rectarum DB, AD,
              <lb/>
            hoc eſt, cum quadrato rectę AB, æquale quadratis rectarum DC, AD, hoc
              <lb/>
            eſt, quadrato rectæ AC. </s>
            <s xml:id="echoid-s10164" xml:space="preserve">Excedit igitur quadratum lateris AC, quadratum
              <lb/>
            lateris AB, rectangulo contento ſub BC, EC.</s>
            <s xml:id="echoid-s10165" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10166" xml:space="preserve">ALITER. </s>
            <s xml:id="echoid-s10167" xml:space="preserve">Quoniã quadratis ex AD, DC, quadratum ex AC; </s>
            <s xml:id="echoid-s10168" xml:space="preserve">& </s>
            <s xml:id="echoid-s10169" xml:space="preserve">qua-
              <lb/>
              <note position="left" xlink:label="note-332-03" xlink:href="note-332-03a" xml:space="preserve">47 primi.</note>
            dratis ex AD, DB, quadratum ex AB, æquale eſt: </s>
            <s xml:id="echoid-s10170" xml:space="preserve">idem erit exceſſus qua-
              <lb/>
            drati ex AC, ſupra quadratum ex AB, qui quadratorum ex AD, DC, ſu-
              <lb/>
            pra quadrata ex AD, DB: </s>
            <s xml:id="echoid-s10171" xml:space="preserve">Et, ablato communi quadrato ex AD, idem, qui
              <lb/>
            quadratiex DC, ſupra quadratum ex DB, per pronunciatum 17. </s>
            <s xml:id="echoid-s10172" xml:space="preserve">lib 1. </s>
            <s xml:id="echoid-s10173" xml:space="preserve">Eucl.
              <lb/>
            </s>
            <s xml:id="echoid-s10174" xml:space="preserve">Sed quadratum ex DC, ſuperat quadratum ex DB, rectangulo ſub BC, CE,
              <lb/>
            comprehenſo; </s>
            <s xml:id="echoid-s10175" xml:space="preserve">propterea quòd quadratum ex DC, æquale eſt quadrato ex
              <lb/>
              <note position="left" xlink:label="note-332-04" xlink:href="note-332-04a" xml:space="preserve">@. ſecundi.</note>
            D B, vel ex DE, in prima ſigura, vnà cum rectangulo ſub BC, CE, contento.
              <lb/>
            </s>
            <s xml:id="echoid-s10176" xml:space="preserve">Igitur & </s>
            <s xml:id="echoid-s10177" xml:space="preserve">quadratum ex AC, ſuperat quadratum ex AB, rectangulo com-
              <lb/>
            prehenſo ſũb BC, CE. </s>
            <s xml:id="echoid-s10178" xml:space="preserve">Quocirca, Si ab angulo trianguli cuiuſuis duobus
              <lb/>
            lateribus inæqualibus com prehenſo linea perpendicularis ad baſim ducatur,
              <lb/>
            &</s>
            <s xml:id="echoid-s10179" xml:space="preserve">c. </s>
            <s xml:id="echoid-s10180" xml:space="preserve">Quod oſtendendum erat.</s>
            <s xml:id="echoid-s10181" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div850" type="section" level="1" n="464">
          <head xml:id="echoid-head496" xml:space="preserve">COROLLARIVM.</head>
          <note position="left" xml:space="preserve">Perpẽdicu
            <lb/>
          laris in lſo
            <lb/>
          ſcele ſecat
            <lb/>
          baſim bifa
            <lb/>
          riam.</note>
          <p>
            <s xml:id="echoid-s10182" xml:space="preserve">EX demonſtratis conſtat, In Iſoſcele perpendicularem ſecare baſim bifariam. </s>
            <s xml:id="echoid-s10183" xml:space="preserve">Nam ſi in
              <lb/>
            priore triangulo latera AB, AC, ponantur æqualia, erunt eorum@uadrata quoque æqualia.
              <lb/>
            </s>
            <s xml:id="echoid-s10184" xml:space="preserve">Quare cum quadratum ex AB, æquale ſit quadratis ex AD, BD; </s>
            <s xml:id="echoid-s10185" xml:space="preserve">& </s>
            <s xml:id="echoid-s10186" xml:space="preserve">quadratum ex AC,
              <lb/>
              <note position="left" xlink:label="note-332-06" xlink:href="note-332-06a" xml:space="preserve">47. primi.</note>
            quadratis ex AD, CD: </s>
            <s xml:id="echoid-s10187" xml:space="preserve">erunt quoque quadrata ex AD, BD, quadratis ex AD, CD, æqua-
              <lb/>
            lia: </s>
            <s xml:id="echoid-s10188" xml:space="preserve">Ablatoque communi quadrato rectæ AD, reliqua erunt quadrata ex BD, CD; </s>
            <s xml:id="echoid-s10189" xml:space="preserve">æqua-
              <lb/>
            lia, & </s>
            <s xml:id="echoid-s10190" xml:space="preserve">proinde rectæ BD, CD, æquales.</s>
            <s xml:id="echoid-s10191" xml:space="preserve"/>
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