Clavius, Christoph, Geometria practica

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            <s xml:id="echoid-s11225" xml:space="preserve">
              <pb o="241" file="271" n="271" rhead="LIBER SEXTVS."/>
            Quoniam enim triangulum B C F, ad triangulum D E F, duplicatam
              <note symbol="a" position="right" xlink:label="note-271-01" xlink:href="note-271-01a" xml:space="preserve">19. ſexti.</note>
            portionem habet lateris B F, ad latus D F, hoc eſt, rectæ L M, ad rectam O:
              <lb/>
            </s>
            <s xml:id="echoid-s11226" xml:space="preserve">Habet autem & </s>
            <s xml:id="echoid-s11227" xml:space="preserve">L M, ad M N, duplicatam proportionem eius, quam habet
              <lb/>
            L M, ad O, quod L M, O, M N, ſint continuè proportionales. </s>
            <s xml:id="echoid-s11228" xml:space="preserve">Igitur erit vt
              <lb/>
            triangulum B C F, ad triangulum D E F, ita L M, ad M N; </s>
            <s xml:id="echoid-s11229" xml:space="preserve">Et per conuerſio-
              <lb/>
            nem rationis, vt triangulum B C F, ad Trapezium B E, ita L M, ad L N. </s>
            <s xml:id="echoid-s11230" xml:space="preserve">
              <lb/>
            Cum ergo ſit, vt LM, ad LN, ita quadratum K, ad quadratum G, quod
              <note symbol="b" position="right" xlink:label="note-271-02" xlink:href="note-271-02a" xml:space="preserve">coroll. 2@.
                <lb/>
              ſexti.</note>
            H I, L N, continuè ſint proportionales, erit quo que vt triangulum B C F, ad
              <lb/>
            trapezium B E, ita quadratum K, ad quadratum G, hoc eſt, ita triangulum
              <lb/>
            BCF, quod ipſi K, æquale eſt, ad rectilineum A, ipſi G, æquale. </s>
            <s xml:id="echoid-s11231" xml:space="preserve">Quo circa cum
              <lb/>
            triangulum B C F, ad trapezium B E, & </s>
            <s xml:id="echoid-s11232" xml:space="preserve">ad rectilineum A, eandem habeat pro-
              <lb/>
            portionem; </s>
            <s xml:id="echoid-s11233" xml:space="preserve"> æqualia erunt trapezium BE, & </s>
            <s xml:id="echoid-s11234" xml:space="preserve">rectilineum A, quod eſt
              <note symbol="c" position="right" xlink:label="note-271-03" xlink:href="note-271-03a" xml:space="preserve">9. quinti.</note>
            ſitum.</s>
            <s xml:id="echoid-s11235" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11236" xml:space="preserve">4. </s>
            <s xml:id="echoid-s11237" xml:space="preserve">
              <emph style="sc">Sit</emph>
            deinde ſuper B C, verſus R, S, vbianguli R B C, SCB, duobus re-
              <lb/>
            ctis ſunt maiores, non autem verſus punctum concurſus F, conſtruendum trape-
              <lb/>
            zium rectilineo A, cuiuſcunque magnitudinis ſit, æquale, habens latus oppo-
              <lb/>
            ſitum rectæ B C, parallelum. </s>
            <s xml:id="echoid-s11238" xml:space="preserve"> Fiat rurſus triangulo B C F, æquale
              <note symbol="d" position="right" xlink:label="note-271-04" xlink:href="note-271-04a" xml:space="preserve">14. ſecundi.</note>
            tum K, cuius latus L M; </s>
            <s xml:id="echoid-s11239" xml:space="preserve">& </s>
            <s xml:id="echoid-s11240" xml:space="preserve">rectilineo A, aliud quadratum G, æquale, cuius
              <lb/>
            latus HI, per ea, quæ ad propoſitionem 14. </s>
            <s xml:id="echoid-s11241" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s11242" xml:space="preserve">2. </s>
            <s xml:id="echoid-s11243" xml:space="preserve">Euclìd. </s>
            <s xml:id="echoid-s11244" xml:space="preserve">vel potius per ea, quæ
              <lb/>
            Num. </s>
            <s xml:id="echoid-s11245" xml:space="preserve">4. </s>
            <s xml:id="echoid-s11246" xml:space="preserve">cap. </s>
            <s xml:id="echoid-s11247" xml:space="preserve">4. </s>
            <s xml:id="echoid-s11248" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s11249" xml:space="preserve">4. </s>
            <s xml:id="echoid-s11250" xml:space="preserve">huius docuimus. </s>
            <s xml:id="echoid-s11251" xml:space="preserve">Dein de lateribus L M, HI, inueniatur
              <lb/>
            tertia proportionalis MP, quæ ipſi LM, in continuum & </s>
            <s xml:id="echoid-s11252" xml:space="preserve">directum ſit poſi-
              <lb/>
            ta: </s>
            <s xml:id="echoid-s11253" xml:space="preserve">at que inter totam L P, & </s>
            <s xml:id="echoid-s11254" xml:space="preserve">L M, reperta ſit media proportionalis Q: </s>
            <s xml:id="echoid-s11255" xml:space="preserve">ac
              <lb/>
            poſtremo, vt Q, ad L P, ita fiat FB, ad F R: </s>
            <s xml:id="echoid-s11256" xml:space="preserve">ipſique BC, parallela agatur R S.
              <lb/>
            </s>
            <s xml:id="echoid-s11257" xml:space="preserve">Dico trapezium B S, rectilineo A, eſſe æquale. </s>
            <s xml:id="echoid-s11258" xml:space="preserve"> Quoniam enim
              <note symbol="e" position="right" xlink:label="note-271-05" xlink:href="note-271-05a" xml:space="preserve">19. ſexti.</note>
            BCF, ad triangulum R S F, proportionem habet duplicatam lateris F B, ad
              <lb/>
            latus F R, hoc eſt, proportionis Q, ad L P; </s>
            <s xml:id="echoid-s11259" xml:space="preserve">Eſt autem & </s>
            <s xml:id="echoid-s11260" xml:space="preserve">proportio L M, ad
              <lb/>
            L P, duplicata proportionis L M, ad Q, vel Q, ad L P, quod tres rectæ L M,
              <lb/>
            Q, L P, ſint continuè proportionales. </s>
            <s xml:id="echoid-s11261" xml:space="preserve">Igitur erit vt triangulum B C F, ad
              <lb/>
            triangulum R S F, ita L M, ad L P; </s>
            <s xml:id="echoid-s11262" xml:space="preserve">ideo que etiam per diuiſionem rationis con-
              <lb/>
            trariam in ſcholio propoſ. </s>
            <s xml:id="echoid-s11263" xml:space="preserve">17. </s>
            <s xml:id="echoid-s11264" xml:space="preserve">libr. </s>
            <s xml:id="echoid-s11265" xml:space="preserve">5. </s>
            <s xml:id="echoid-s11266" xml:space="preserve">Euclid. </s>
            <s xml:id="echoid-s11267" xml:space="preserve">à nobis demonſtratam, vt trian-
              <lb/>
            gulum BCF, ad trapezium BS, ita L M, ad M P. </s>
            <s xml:id="echoid-s11268" xml:space="preserve"> Vtautem L M, ad M P,
              <note symbol="f" position="right" xlink:label="note-271-06" xlink:href="note-271-06a" xml:space="preserve">coroll. 2@.
                <lb/>
              ſexti.</note>
            eſt quadratum K, ad quadratum G, quod tres L M, H I, M P, ſint continuè
              <lb/>
            proportionales. </s>
            <s xml:id="echoid-s11269" xml:space="preserve">Igitur erit quoque, vt triangulum B C F, ad trapezium B S,
              <lb/>
            ita quadratum K, ad quadratum G. </s>
            <s xml:id="echoid-s11270" xml:space="preserve">Cum ergo triangulo B C F, conſtructum
              <lb/>
            ſit æquale quadratum K: </s>
            <s xml:id="echoid-s11271" xml:space="preserve"> erit quoque trapezium B S, quadrato G,
              <note symbol="g" position="right" xlink:label="note-271-07" xlink:href="note-271-07a" xml:space="preserve">14. quinti.</note>
            hoc eſt, rectilineo A, cui quadratum G, conſtructum eſt æquale. </s>
            <s xml:id="echoid-s11272" xml:space="preserve">quod eſt pro-
              <lb/>
            poſitum.</s>
            <s xml:id="echoid-s11273" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s11274" xml:space="preserve">
              <emph style="sc">Qvod</emph>
            ſi quando duæ rectæ B F, C F, in tam remoto puncto concurrant,
              <lb/>
            vt vix haberi poſsit, (quod quidem tunc accidet, cum ipſæ rectæ ferè pa-
              <lb/>
            rallelæ ſunt) abſoluemus problema, etiamſi punctum concurſus F, non habea-
              <lb/>
            mus, huncin modum. </s>
            <s xml:id="echoid-s11275" xml:space="preserve">Sumpto vtcunque puncto T, in altera earum, nimirum
              <lb/>
            in C F, agatur T V, alteri BF, parallela; </s>
            <s xml:id="echoid-s11276" xml:space="preserve">& </s>
            <s xml:id="echoid-s11277" xml:space="preserve">duabus B C, C V, inueniatur tertia
              <lb/>
            proportionalis X. </s>
            <s xml:id="echoid-s11278" xml:space="preserve">Conſtructo deinde ex ſcholio propoſ. </s>
            <s xml:id="echoid-s11279" xml:space="preserve">14. </s>
            <s xml:id="echoid-s11280" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s11281" xml:space="preserve">2. </s>
            <s xml:id="echoid-s11282" xml:space="preserve">Euclid. </s>
            <s xml:id="echoid-s11283" xml:space="preserve">vel
              <lb/>
            potius, vt Num. </s>
            <s xml:id="echoid-s11284" xml:space="preserve">4. </s>
            <s xml:id="echoid-s11285" xml:space="preserve">cap. </s>
            <s xml:id="echoid-s11286" xml:space="preserve">4. </s>
            <s xml:id="echoid-s11287" xml:space="preserve">libr. </s>
            <s xml:id="echoid-s11288" xml:space="preserve">4. </s>
            <s xml:id="echoid-s11289" xml:space="preserve">huius docuimus, quadrato G, æquali rectili-
              <lb/>
            neo A, inueniatur tribus BC, X, H I, quarta proportionalis IY, agatur que Y Z,
              <lb/>
            lateribus qua drati parallela. </s>
            <s xml:id="echoid-s11290" xml:space="preserve"> Et quoniam eſt, vt triangulum B C F, (ſi
              <note symbol="h" position="right" xlink:label="note-271-08" xlink:href="note-271-08a" xml:space="preserve">coroll. 19.
                <lb/>
              ſexti.</note>
            ficeretur) ad triangulum V C T, ita recta B C, ad rectam X, hoc eſt, ita H </s>
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