Clavius, Christoph, Geometria practica

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          <pb o="347" file="375" n="375" rhead="LIBER OCTAVVS."/>
          <p>
            <s xml:id="echoid-s16234" xml:space="preserve">
              <emph style="sc">Qvod</emph>
            ſi diameter latere Rhombi minor fuerit, ſit datus exceſſus A, lateris
              <lb/>
            inaliquo Rhombo ſupra diametrum, vna cum angulo L. </s>
            <s xml:id="echoid-s16235" xml:space="preserve">Conſtruatur Rhom-
              <lb/>
            bus quantuſcunque BDCE, habens angulum D, æqualem dato angulo L, vt in
              <lb/>
            tertio Rhombo. </s>
            <s xml:id="echoid-s16236" xml:space="preserve">Et quia vt latus ſuperet diametrum, ducenda eſt diameter per
              <lb/>
            angulos obtuſos, (quod diameter per acutos angulos ducta ſemper maior
              <note symbol="a" position="right" xlink:label="note-375-01" xlink:href="note-375-01a" xml:space="preserve">19. primi.</note>
            Rhombilatere) ducatur diameter BC, quamlatus BD, excedatrecta DF, quę ſi
              <lb/>
            æqualis fuerit exceſſui dato A, factum erit, quod jubetur: </s>
            <s xml:id="echoid-s16237" xml:space="preserve">Siver ò inæqualis:
              <lb/>
            </s>
            <s xml:id="echoid-s16238" xml:space="preserve">fiat vt DF, ad exceſſum A, ita BD, latus ad B G, compleaturque Rhombus G I,
              <lb/>
            circa eandem diametrum, quem dico eſſe quæſitum. </s>
            <s xml:id="echoid-s16239" xml:space="preserve">Abſciſſa namq; </s>
            <s xml:id="echoid-s16240" xml:space="preserve">recta GK,
              <lb/>
            æquali exceſſui A: </s>
            <s xml:id="echoid-s16241" xml:space="preserve">fiet demonſtratio, vt in quadrato, vt perſpicuum eſt, ſi loco
              <lb/>
            diametrorum BD, BG, in quadrato, ſumantur hic latera BD, BG.</s>
            <s xml:id="echoid-s16242" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s16243" xml:space="preserve">
              <emph style="sc">Tvnc</emph>
            autem latus Rhombimaius erit diametro (vt hoc etiam obiter mo-
              <lb/>
            neamus) cum ſemiſsis anguli obtuſi maior fuerit angulo acuto eiuſdẽ Rhom-
              <lb/>
            bi. </s>
            <s xml:id="echoid-s16244" xml:space="preserve">Nam ſi in tertio Rhombo angulus CBD, quiſemiſsis eſt anguli obtuſi B, vt
              <lb/>
            in ſchol. </s>
            <s xml:id="echoid-s16245" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s16246" xml:space="preserve">34. </s>
            <s xml:id="echoid-s16247" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s16248" xml:space="preserve">1. </s>
            <s xml:id="echoid-s16249" xml:space="preserve">Euclid. </s>
            <s xml:id="echoid-s16250" xml:space="preserve">oſtendimus, maiorſit angulo acuto D; </s>
            <s xml:id="echoid-s16251" xml:space="preserve">
              <note symbol="b" position="right" xlink:label="note-375-02" xlink:href="note-375-02a" xml:space="preserve">19. primi.</note>
            latus BD, hoc eſt, CD, maius diametro BC, in triangulo BCD. </s>
            <s xml:id="echoid-s16252" xml:space="preserve">Quando autem
              <lb/>
            ſemiſsis anguli obtuſi fuerit minor angulo acuto, vt in Rhombo ſecundo; </s>
            <s xml:id="echoid-s16253" xml:space="preserve">
              <note symbol="c" position="right" xlink:label="note-375-03" xlink:href="note-375-03a" xml:space="preserve">19. primi.</note>
            diameter latere maior in triangulo B C D.</s>
            <s xml:id="echoid-s16254" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s16255" xml:space="preserve">
              <emph style="sc">Tertio</emph>
            ſit datus exceſſus A, diametri rectanguli alicuius ſupra alterum
              <lb/>
            laterum inæqualium, vna cum angulo L, quem diameter cum eo latere conſti-
              <lb/>
            tuit, velvna cum proportione M, ad N, quam illud latus ad alterum habet. </s>
            <s xml:id="echoid-s16256" xml:space="preserve">Si
              <lb/>
            ergo angulus L, eſt ſemirecto minor, vel certè proportio M, ad N, maiors in-
              <lb/>
            æqualitatis, vt in priori rectangulo, erit A, exceſſus diametri ſupra maius latus:
              <lb/>
            </s>
            <s xml:id="echoid-s16257" xml:space="preserve">Si verò angulus L, eſt maior ſemirecto, vel proportio M, ad N, minoris inæqua-
              <lb/>
              <figure xlink:label="fig-375-01" xlink:href="fig-375-01a" number="264">
                <image file="375-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/375-01"/>
              </figure>
            litatis, erit A, exceſſus diametri ſupra minus latus. </s>
            <s xml:id="echoid-s16258" xml:space="preserve">Conſtituatur ergo angulus
              <lb/>
            CBD, angulo L, æqualis, fiatque rectangulum BCDE, circa aſſumptam diame-
              <lb/>
            trum BD. </s>
            <s xml:id="echoid-s16259" xml:space="preserve">Vel fiat B C, quanta cunque ad CD, perpendicularem, vt M, ad N:
              <lb/>
            </s>
            <s xml:id="echoid-s16260" xml:space="preserve">completo que rectangulo CE, ducatur diameter B D, excedens latus B G, recta
              <lb/>
            D F, quæ ſi fuerit æqualis dato exceſſui A, conſtructum erit rectangulum C E,
              <lb/>
            quod quæritur: </s>
            <s xml:id="echoid-s16261" xml:space="preserve">Si verò inæqualis, fiat vt D F, ad exceſſum datum A, ita B D,
              <lb/>
            ad B G, compleaturque rectangulum H I, quod erit quæſitum. </s>
            <s xml:id="echoid-s16262" xml:space="preserve">Ab-
              <lb/>
            ſciſſa enim recta G K, æquali exceſſui A, demonſtrabitur propoſitum, vt
              <lb/>
            in quadrato.</s>
            <s xml:id="echoid-s16263" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s16264" xml:space="preserve">
              <emph style="sc">Qvarto</emph>
            & </s>
            <s xml:id="echoid-s16265" xml:space="preserve">vltimo ſit in aliquo Rhomboide datus exceſſus A, diametri
              <lb/>
            ſupra vtrumuis inæqualium laterum, vna cum angulo Rhomboidis O, & </s>
            <s xml:id="echoid-s16266" xml:space="preserve">inſu-
              <lb/>
            per cum angulo L, quem diameter cum latere, cuius exceſſus ſumptus eſt, </s>
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