Clavius, Christoph, Geometria practica

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          <p>
            <s xml:id="echoid-s3907" xml:space="preserve">
              <pb o="101" file="131" n="131" rhead="LIBER TERTIVS."/>
            ſarum. </s>
            <s xml:id="echoid-s3908" xml:space="preserve"> Et quia eſt, vt AD, ad DE, ita AF, ad FG: </s>
            <s xml:id="echoid-s3909" xml:space="preserve"> eritrectangulo ſub A D,
              <note symbol="a" position="right" xlink:label="note-131-01" xlink:href="note-131-01a" xml:space="preserve">4. ſexti.</note>
            æquale rectangulum ſub D E, AF. </s>
            <s xml:id="echoid-s3910" xml:space="preserve">Eadem ratione erit rectangulo ſub a d, F G.
              <lb/>
            </s>
            <s xml:id="echoid-s3911" xml:space="preserve">
              <note symbol="b" position="right" xlink:label="note-131-02" xlink:href="note-131-02a" xml:space="preserve">16. ſexti.</note>
            rectangulum ſub dH, aF, æquale: </s>
            <s xml:id="echoid-s3912" xml:space="preserve">propterea quod etiam eſt vta d, ad dH,
              <note symbol="c" position="right" xlink:label="note-131-03" xlink:href="note-131-03a" xml:space="preserve">4. ſexti.</note>
            aF, ad F G. </s>
            <s xml:id="echoid-s3913" xml:space="preserve">Cum ergo rectangulum ſub AD, FG, æquale ſit rectangulo ſub a d,
              <lb/>
            F G, quod rectæ A D, a d, æquales ſint: </s>
            <s xml:id="echoid-s3914" xml:space="preserve">erit quo que rectangulum ſub dH, aF,
              <lb/>
            rectangulo ſub DE, AF, hoc eſt, ſub dI, AF, æquale; </s>
            <s xml:id="echoid-s3915" xml:space="preserve"> ideo que erit, vt dH,
              <note symbol="d" position="right" xlink:label="note-131-04" xlink:href="note-131-04a" xml:space="preserve">16. ſexti.</note>
            ad d I, ſecundam, ita AF, tertia ad AF, quartam: </s>
            <s xml:id="echoid-s3916" xml:space="preserve">Et permutando, vt tota dH, ad
              <lb/>
            totam AF, ita ablata dI, ad ablatam aF. </s>
            <s xml:id="echoid-s3917" xml:space="preserve"> Igitur erit quoque reliqua H I, ad
              <note symbol="e" position="right" xlink:label="note-131-05" xlink:href="note-131-05a" xml:space="preserve">19. quinti.</note>
            quam Aa, vt tota d H, ad totam A F. </s>
            <s xml:id="echoid-s3918" xml:space="preserve">Quocirca ſit fiat,</s>
          </p>
          <note style="it" position="right" xml:space="preserve">
            <lb/>
          Vt H I, differentia \\ vmbrarum verſa- \\ rum # ad Aa, differentiam \\ ſtationum: # Ita dH, vmbra verſa \\ propinquioris ſtatio- \\ nis, ſiue maior, # ad A F, \\ diſtantiã
            <lb/>
          </note>
          <p>
            <s xml:id="echoid-s3919" xml:space="preserve">producetur A F, diſtantia nota in partibus differentiæ ſtationum Aa, notæ.</s>
            <s xml:id="echoid-s3920" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3921" xml:space="preserve">2. </s>
            <s xml:id="echoid-s3922" xml:space="preserve">
              <emph style="sc">Eadem</emph>
            prorſus ratio eſt in quadrato pendulo. </s>
            <s xml:id="echoid-s3923" xml:space="preserve">Nam filum perpendiculi
              <lb/>
            abſcindit quo que triangula ADE, ad H, triangulis AFG, aFG, æquiangula: </s>
            <s xml:id="echoid-s3924" xml:space="preserve">pro-
              <lb/>
              <note symbol="f" position="right" xlink:label="note-131-07" xlink:href="note-131-07a" xml:space="preserve">29. primi.</note>
            pterea, quod tam anguli D, F, rectiſunt, & </s>
            <s xml:id="echoid-s3925" xml:space="preserve">angulus F, hoc eſt, alternus B A E, angulo AGF, externus interno æqualis; </s>
            <s xml:id="echoid-s3926" xml:space="preserve">quam anguli d, F, recti, & </s>
            <s xml:id="echoid-s3927" xml:space="preserve">angulus H, id
              <lb/>
            eſt, alternus ba H, angulo a G F, externus interno æqualis. </s>
            <s xml:id="echoid-s3928" xml:space="preserve">Reliqua demonſtra-
              <lb/>
            buntur, vt prius. </s>
            <s xml:id="echoid-s3929" xml:space="preserve">ſunt enim vmbræ verſæ in pendulo quadrato vmbris in ſtabili
              <lb/>
            æquales. </s>
            <s xml:id="echoid-s3930" xml:space="preserve">Nam cum duo anguli D, E, in triangulo ADE, quadrati penduli æqua-
              <lb/>
            les ſint duobus angulis D, E, in triangulo ADE, quadrati ſtabilis, quod ea trian-
              <lb/>
              <note symbol="g" position="right" xlink:label="note-131-08" xlink:href="note-131-08a" xml:space="preserve">26. primi.</note>
            gula ſint, vt oſtendimus, æquiangula: </s>
            <s xml:id="echoid-s3931" xml:space="preserve">ſint autem & </s>
            <s xml:id="echoid-s3932" xml:space="preserve">latera AD, AD æqualia; </s>
            <s xml:id="echoid-s3933" xml:space="preserve"> e- runt & </s>
            <s xml:id="echoid-s3934" xml:space="preserve">rectæ D E, D E, hoc eſt, vmbræ verſæ, æquales. </s>
            <s xml:id="echoid-s3935" xml:space="preserve">Eademque ratione verſæ
              <lb/>
            vmbræ d H, d H, æquales erunt, &</s>
            <s xml:id="echoid-s3936" xml:space="preserve">c.</s>
            <s xml:id="echoid-s3937" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3938" xml:space="preserve">3. </s>
            <s xml:id="echoid-s3939" xml:space="preserve">
              <emph style="sc">Si</emph>
            in vtraq; </s>
            <s xml:id="echoid-s3940" xml:space="preserve">ſtatione vmbra recta abſcindatur à linea fiduciæ, vel à filo per-
              <lb/>
            pendiculi, vtin E, & </s>
            <s xml:id="echoid-s3941" xml:space="preserve">H, quod quidem ſemper continget, quando diſtantia A F,
              <lb/>
            minor eſt altitudine FG, quod tunc angulus A, maior fiat angulo G, ac
              <note symbol="h" position="right" xlink:label="note-131-09" xlink:href="note-131-09a" xml:space="preserve">18. primi.</note>
            de ſemirecto maior, quem cum AD, conſtitueret radius per C, emiſſus. </s>
            <s xml:id="echoid-s3942" xml:space="preserve">Eritque
              <lb/>
            vmbra recta BE, in remotiore ſtatione ma-
              <lb/>
              <figure xlink:label="fig-131-01" xlink:href="fig-131-01a" number="59">
                <image file="131-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/131-01"/>
              </figure>
            ior, quã vmbra recta b H, in ſtatione pro-
              <lb/>
            pinquiore, quòd angulus FaG, maior
              <note symbol="i" position="right" xlink:label="note-131-10" xlink:href="note-131-10a" xml:space="preserve">16. primi.</note>
            angulo F A G; </s>
            <s xml:id="echoid-s3943" xml:space="preserve">ac proinde baH, minor an-
              <lb/>
            gulo BAE. </s>
            <s xml:id="echoid-s3944" xml:space="preserve">Auferatur BI, ipſi bH, æqualis,
              <lb/>
            vt I E, differentia ſit vmbrarum rectarum.
              <lb/>
            </s>
            <s xml:id="echoid-s3945" xml:space="preserve">Et quia triangula ABE, AFG, æquiangula
              <lb/>
            ſunt, propter angulos rectos B, F, & </s>
            <s xml:id="echoid-s3946" xml:space="preserve">
              <note symbol="k" position="right" xlink:label="note-131-11" xlink:href="note-131-11a" xml:space="preserve">29. primi.</note>
            ternos æquales B A E, A G F: </s>
            <s xml:id="echoid-s3947" xml:space="preserve"> erit vt A
              <note symbol="l" position="right" xlink:label="note-131-12" xlink:href="note-131-12a" xml:space="preserve">4. ſexti.</note>
            ad B E, ita F G, ad A F, & </s>
            <s xml:id="echoid-s3948" xml:space="preserve">permutando, vt
              <lb/>
            AB, ad F G, ita BE, ad A F. </s>
            <s xml:id="echoid-s3949" xml:space="preserve">Eademratione,
              <lb/>
            quia triãgula a b H, a F G, æquiãgula ſunt,
              <lb/>
              <note symbol="m" position="right" xlink:label="note-131-13" xlink:href="note-131-13a" xml:space="preserve">29. primi.</note>
            propter rectos angulos b, F, & </s>
            <s xml:id="echoid-s3950" xml:space="preserve">alternos æquales b a H, a G F, erit vt ab, ad b H,
              <note symbol="n" position="right" xlink:label="note-131-14" xlink:href="note-131-14a" xml:space="preserve">4. ſexti.</note>
            ita F G, ad a F: </s>
            <s xml:id="echoid-s3951" xml:space="preserve">Et permutando vt a b, ad
              <lb/>
            FG, ita b H, ad A F. </s>
            <s xml:id="echoid-s3952" xml:space="preserve">Cum ergo ſit, vt AB, ad
              <lb/>
            F G, ita a b, ad FG, propter rectas æquales
              <lb/>
            AB, a b. </s>
            <s xml:id="echoid-s3953" xml:space="preserve"> erit quo que vt BE, tota ad A
              <note symbol="o" position="right" xlink:label="note-131-15" xlink:href="note-131-15a" xml:space="preserve">11. quinti.</note>
            </s>
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